id	sid	tid	token	lemma	pos
fumecheng-7385	1	1	facta	facta	PROPN
fumecheng-7385	1	2	universitatis	universitatis	PROPN
fumecheng-7385	1	3	series	series	NOUN
fumecheng-7385	1	4	:	:	PUNCT
fumecheng-7385	1	5	mechanical	mechanical	ADJ
fumecheng-7385	1	6	engineering	engineering	NOUN
fumecheng-7385	1	7	vol	vol	NOUN
fumecheng-7385	1	8	.	.	PROPN
fumecheng-7385	2	1	19	19	NUM
fumecheng-7385	2	2	,	,	PUNCT
fumecheng-7385	2	3	no	no	DET
fumecheng-7385	2	4	4	4	NUM
fumecheng-7385	2	5	,	,	PUNCT
fumecheng-7385	2	6	2021	2021	NUM
fumecheng-7385	2	7	,	,	PUNCT
fumecheng-7385	2	8	pp	pp	ADV
fumecheng-7385	2	9	.	.	PUNCT
fumecheng-7385	3	1	735	735	NUM
fumecheng-7385	3	2	750	750	NUM
fumecheng-7385	3	3	https://doi.org/10.22190/fume210125033h	https://doi.org/10.22190/fume210125033h	NOUN
fumecheng-7385	3	4	©	©	PROPN
fumecheng-7385	3	5	2021	2021	NUM
fumecheng-7385	3	6	by	by	ADP
fumecheng-7385	3	7	university	university	PROPN
fumecheng-7385	3	8	of	of	ADP
fumecheng-7385	3	9	niš	niš	PROPN
fumecheng-7385	3	10	,	,	PUNCT
fumecheng-7385	3	11	serbia	serbia	PROPN
fumecheng-7385	3	12	|	|	ADV
fumecheng-7385	3	13	creative	creative	ADJ
fumecheng-7385	3	14	commons	common	NOUN
fumecheng-7385	3	15	license	license	NOUN
fumecheng-7385	3	16	:	:	PUNCT
fumecheng-7385	3	17	cc	cc	VERB
fumecheng-7385	3	18	by	by	ADP
fumecheng-7385	3	19	-	-	PUNCT
fumecheng-7385	3	20	nc	nc	VERB
fumecheng-7385	3	21	-	-	PUNCT
fumecheng-7385	3	22	nd	nd	ADV
fumecheng-7385	3	23	original	original	ADJ
fumecheng-7385	3	24	scientific	scientific	NOUN
fumecheng-7385	3	25	paper	paper	VERB
fumecheng-7385	3	26	the	the	DET
fumecheng-7385	3	27	enhanced	enhanced	ADJ
fumecheng-7385	3	28	homotopy	homotopy	NOUN
fumecheng-7385	3	29	perturbation	perturbation	NOUN
fumecheng-7385	3	30	method	method	NOUN
fumecheng-7385	3	31	for	for	ADP
fumecheng-7385	3	32	axial	axial	ADJ
fumecheng-7385	3	33	vibration	vibration	NOUN
fumecheng-7385	3	34	of	of	ADP
fumecheng-7385	3	35	strings	string	NOUN
fumecheng-7385	3	36	ji	ji	PROPN
fumecheng-7385	3	37	-	-	PROPN
fumecheng-7385	3	38	huan	huan	PROPN
fumecheng-7385	3	39	he1,2,3	he1,2,3	PROPN
fumecheng-7385	3	40	,	,	PUNCT
fumecheng-7385	4	1	yusry	yusry	PROPN
fumecheng-7385	4	2	o.	o.	PROPN
fumecheng-7385	4	3	el	el	PROPN
fumecheng-7385	4	4	-	-	NOUN
fumecheng-7385	4	5	dib4	dib4	NOUN
fumecheng-7385	4	6	1school	1school	NUM
fumecheng-7385	4	7	of	of	ADP
fumecheng-7385	4	8	science	science	NOUN
fumecheng-7385	4	9	,	,	PUNCT
fumecheng-7385	4	10	xi'an	xi'an	PROPN
fumecheng-7385	4	11	university	university	PROPN
fumecheng-7385	4	12	of	of	ADP
fumecheng-7385	4	13	architecture	architecture	NOUN
fumecheng-7385	4	14	and	and	CCONJ
fumecheng-7385	4	15	technology	technology	NOUN
fumecheng-7385	4	16	,	,	PUNCT
fumecheng-7385	4	17	xi’an	xi’an	PROPN
fumecheng-7385	4	18	,	,	PUNCT
fumecheng-7385	4	19	china	china	PROPN
fumecheng-7385	4	20	2school	2school	NUM
fumecheng-7385	4	21	of	of	ADP
fumecheng-7385	4	22	mathematics	mathematic	NOUN
fumecheng-7385	4	23	and	and	CCONJ
fumecheng-7385	4	24	information	information	NOUN
fumecheng-7385	4	25	science	science	NOUN
fumecheng-7385	4	26	,	,	PUNCT
fumecheng-7385	4	27	henan	henan	PROPN
fumecheng-7385	4	28	polytechnic	polytechnic	PROPN
fumecheng-7385	4	29	university	university	PROPN
fumecheng-7385	4	30	,	,	PUNCT
fumecheng-7385	4	31	jiaozuo	jiaozuo	PROPN
fumecheng-7385	4	32	,	,	PUNCT
fumecheng-7385	4	33	china	china	PROPN
fumecheng-7385	4	34	3national	3national	NUM
fumecheng-7385	4	35	engineering	engineering	NOUN
fumecheng-7385	4	36	laboratory	laboratory	NOUN
fumecheng-7385	4	37	for	for	ADP
fumecheng-7385	4	38	modern	modern	ADJ
fumecheng-7385	4	39	silk	silk	NOUN
fumecheng-7385	4	40	,	,	PUNCT
fumecheng-7385	4	41	college	college	NOUN
fumecheng-7385	4	42	of	of	ADP
fumecheng-7385	4	43	textile	textile	NOUN
fumecheng-7385	4	44	and	and	CCONJ
fumecheng-7385	4	45	clothing	clothing	NOUN
fumecheng-7385	4	46	engineering	engineering	NOUN
fumecheng-7385	4	47	,	,	PUNCT
fumecheng-7385	4	48	soochow	soochow	PROPN
fumecheng-7385	4	49	university	university	PROPN
fumecheng-7385	4	50	,	,	PUNCT
fumecheng-7385	4	51	suzhou	suzhou	PROPN
fumecheng-7385	4	52	,	,	PUNCT
fumecheng-7385	4	53	china	china	PROPN
fumecheng-7385	4	54	4department	4department	NUM
fumecheng-7385	4	55	of	of	ADP
fumecheng-7385	4	56	mathematics	mathematic	NOUN
fumecheng-7385	4	57	,	,	PUNCT
fumecheng-7385	4	58	faculty	faculty	NOUN
fumecheng-7385	4	59	of	of	ADP
fumecheng-7385	4	60	education	education	NOUN
fumecheng-7385	4	61	,	,	PUNCT
fumecheng-7385	4	62	ain	ain	PROPN
fumecheng-7385	4	63	shams	shams	PROPN
fumecheng-7385	4	64	university	university	PROPN
fumecheng-7385	4	65	,	,	PUNCT
fumecheng-7385	4	66	roxy	roxy	PROPN
fumecheng-7385	4	67	,	,	PUNCT
fumecheng-7385	4	68	cairo	cairo	PROPN
fumecheng-7385	4	69	,	,	PUNCT
fumecheng-7385	4	70	egypt	egypt	PROPN
fumecheng-7385	4	71	abstract	abstract	PROPN
fumecheng-7385	4	72	.	.	PUNCT
fumecheng-7385	5	1	a	a	DET
fumecheng-7385	5	2	governing	govern	VERB
fumecheng-7385	5	3	equation	equation	NOUN
fumecheng-7385	5	4	is	be	AUX
fumecheng-7385	5	5	established	establish	VERB
fumecheng-7385	5	6	for	for	ADP
fumecheng-7385	5	7	string	string	NOUN
fumecheng-7385	5	8	axial	axial	ADJ
fumecheng-7385	5	9	vibrations	vibration	NOUN
fumecheng-7385	5	10	with	with	ADP
fumecheng-7385	5	11	temporal	temporal	ADJ
fumecheng-7385	5	12	and	and	CCONJ
fumecheng-7385	5	13	spatial	spatial	ADJ
fumecheng-7385	5	14	damping	damp	VERB
fumecheng-7385	5	15	forces	force	NOUN
fumecheng-7385	5	16	by	by	ADP
fumecheng-7385	5	17	the	the	DET
fumecheng-7385	5	18	hamilton	hamilton	PROPN
fumecheng-7385	5	19	principle	principle	PROPN
fumecheng-7385	5	20	.	.	PUNCT
fumecheng-7385	6	1	it	it	PRON
fumecheng-7385	6	2	is	be	AUX
fumecheng-7385	6	3	an	an	DET
fumecheng-7385	6	4	extension	extension	NOUN
fumecheng-7385	6	5	of	of	ADP
fumecheng-7385	6	6	the	the	DET
fumecheng-7385	6	7	well	well	ADV
fumecheng-7385	6	8	-	-	PUNCT
fumecheng-7385	6	9	known	know	VERB
fumecheng-7385	6	10	klein	klein	PROPN
fumecheng-7385	6	11	-	-	PUNCT
fumecheng-7385	6	12	gordon	gordon	PROPN
fumecheng-7385	6	13	equation	equation	NOUN
fumecheng-7385	6	14	.	.	PUNCT
fumecheng-7385	7	1	the	the	DET
fumecheng-7385	7	2	classical	classical	ADJ
fumecheng-7385	7	3	homotopy	homotopy	NOUN
fumecheng-7385	7	4	perturbation	perturbation	NOUN
fumecheng-7385	7	5	method	method	NOUN
fumecheng-7385	7	6	(	(	PUNCT
fumecheng-7385	7	7	hpm	hpm	NOUN
fumecheng-7385	7	8	)	)	PUNCT
fumecheng-7385	7	9	fails	fail	VERB
fumecheng-7385	7	10	to	to	PART
fumecheng-7385	7	11	analyze	analyze	VERB
fumecheng-7385	7	12	this	this	DET
fumecheng-7385	7	13	equation	equation	NOUN
fumecheng-7385	7	14	,	,	PUNCT
fumecheng-7385	7	15	and	and	CCONJ
fumecheng-7385	7	16	a	a	DET
fumecheng-7385	7	17	modification	modification	NOUN
fumecheng-7385	7	18	with	with	ADP
fumecheng-7385	7	19	an	an	DET
fumecheng-7385	7	20	exponential	exponential	ADJ
fumecheng-7385	7	21	decay	decay	NOUN
fumecheng-7385	7	22	parameter	parameter	NOUN
fumecheng-7385	7	23	is	be	AUX
fumecheng-7385	7	24	suggested	suggest	VERB
fumecheng-7385	7	25	.	.	PUNCT
fumecheng-7385	8	1	the	the	DET
fumecheng-7385	8	2	analysis	analysis	NOUN
fumecheng-7385	8	3	shows	show	VERB
fumecheng-7385	8	4	that	that	SCONJ
fumecheng-7385	8	5	the	the	DET
fumecheng-7385	8	6	amplitude	amplitude	NOUN
fumecheng-7385	8	7	behaves	behave	VERB
fumecheng-7385	8	8	as	as	ADP
fumecheng-7385	8	9	an	an	DET
fumecheng-7385	8	10	exponential	exponential	ADJ
fumecheng-7385	8	11	decay	decay	NOUN
fumecheng-7385	8	12	by	by	ADP
fumecheng-7385	8	13	the	the	DET
fumecheng-7385	8	14	damping	damp	VERB
fumecheng-7385	8	15	parameter	parameter	NOUN
fumecheng-7385	8	16	.	.	PUNCT
fumecheng-7385	9	1	furthermore	furthermore	ADV
fumecheng-7385	9	2	,	,	PUNCT
fumecheng-7385	9	3	the	the	DET
fumecheng-7385	9	4	frequency	frequency	NOUN
fumecheng-7385	9	5	equation	equation	NOUN
fumecheng-7385	9	6	is	be	AUX
fumecheng-7385	9	7	established	establish	VERB
fumecheng-7385	9	8	and	and	CCONJ
fumecheng-7385	9	9	the	the	DET
fumecheng-7385	9	10	stability	stability	NOUN
fumecheng-7385	9	11	condition	condition	NOUN
fumecheng-7385	9	12	is	be	AUX
fumecheng-7385	9	13	performed	perform	VERB
fumecheng-7385	9	14	.	.	PUNCT
fumecheng-7385	10	1	the	the	DET
fumecheng-7385	10	2	modified	modify	VERB
fumecheng-7385	10	3	homotopy	homotopy	NOUN
fumecheng-7385	10	4	perturbation	perturbation	NOUN
fumecheng-7385	10	5	method	method	NOUN
fumecheng-7385	10	6	yields	yield	VERB
fumecheng-7385	10	7	a	a	DET
fumecheng-7385	10	8	more	more	ADV
fumecheng-7385	10	9	effective	effective	ADJ
fumecheng-7385	10	10	result	result	NOUN
fumecheng-7385	10	11	for	for	ADP
fumecheng-7385	10	12	the	the	DET
fumecheng-7385	10	13	nonlinear	nonlinear	ADJ
fumecheng-7385	10	14	oscillators	oscillator	NOUN
fumecheng-7385	10	15	and	and	CCONJ
fumecheng-7385	10	16	helps	help	VERB
fumecheng-7385	10	17	to	to	PART
fumecheng-7385	10	18	overcome	overcome	VERB
fumecheng-7385	10	19	the	the	DET
fumecheng-7385	10	20	shortcoming	shortcoming	NOUN
fumecheng-7385	10	21	of	of	ADP
fumecheng-7385	10	22	the	the	DET
fumecheng-7385	10	23	classical	classical	ADJ
fumecheng-7385	10	24	approach	approach	NOUN
fumecheng-7385	10	25	.	.	PUNCT
fumecheng-7385	11	1	the	the	DET
fumecheng-7385	11	2	comparison	comparison	NOUN
fumecheng-7385	11	3	between	between	ADP
fumecheng-7385	11	4	the	the	DET
fumecheng-7385	11	5	analytical	analytical	ADJ
fumecheng-7385	11	6	solution	solution	NOUN
fumecheng-7385	11	7	and	and	CCONJ
fumecheng-7385	11	8	the	the	DET
fumecheng-7385	11	9	numerical	numerical	ADJ
fumecheng-7385	11	10	solution	solution	NOUN
fumecheng-7385	11	11	shows	show	VERB
fumecheng-7385	11	12	an	an	DET
fumecheng-7385	11	13	excellent	excellent	ADJ
fumecheng-7385	11	14	agreement	agreement	NOUN
fumecheng-7385	11	15	.	.	PUNCT
fumecheng-7385	12	1	key	key	ADJ
fumecheng-7385	12	2	words	word	NOUN
fumecheng-7385	12	3	:	:	PUNCT
fumecheng-7385	12	4	homotopy	homotopy	VERB
fumecheng-7385	12	5	perturbations	perturbation	NOUN
fumecheng-7385	12	6	method	method	NOUN
fumecheng-7385	12	7	,	,	PUNCT
fumecheng-7385	12	8	exponential	exponential	ADJ
fumecheng-7385	12	9	decay	decay	NOUN
fumecheng-7385	12	10	parameter	parameter	NOUN
fumecheng-7385	12	11	,	,	PUNCT
fumecheng-7385	12	12	damping	damp	VERB
fumecheng-7385	12	13	duffing	duffing	NOUN
fumecheng-7385	12	14	equation	equation	NOUN
fumecheng-7385	12	15	,	,	PUNCT
fumecheng-7385	12	16	damping	damp	VERB
fumecheng-7385	12	17	nonlinear	nonlinear	ADJ
fumecheng-7385	12	18	klein	klein	PROPN
fumecheng-7385	12	19	-	-	PUNCT
fumecheng-7385	12	20	gordon	gordon	PROPN
fumecheng-7385	12	21	equation	equation	NOUN
fumecheng-7385	12	22	1	1	NUM
fumecheng-7385	12	23	.	.	PUNCT
fumecheng-7385	13	1	introduction	introduction	NOUN
fumecheng-7385	13	2	string	string	NOUN
fumecheng-7385	13	3	axial	axial	ADJ
fumecheng-7385	13	4	vibrations	vibration	NOUN
fumecheng-7385	13	5	arise	arise	VERB
fumecheng-7385	13	6	in	in	ADP
fumecheng-7385	13	7	various	various	ADJ
fumecheng-7385	13	8	fields	field	NOUN
fumecheng-7385	13	9	,	,	PUNCT
fumecheng-7385	13	10	e.g.	e.g.	ADV
fumecheng-7385	13	11	,	,	PUNCT
fumecheng-7385	13	12	suspension	suspension	NOUN
fumecheng-7385	13	13	bridge	bridge	NOUN
fumecheng-7385	13	14	,	,	PUNCT
fumecheng-7385	13	15	drill	drill	NOUN
fumecheng-7385	13	16	string	string	NOUN
fumecheng-7385	13	17	,	,	PUNCT
fumecheng-7385	13	18	and	and	CCONJ
fumecheng-7385	13	19	ring	ring	NOUN
fumecheng-7385	13	20	spinning	spinning	NOUN
fumecheng-7385	13	21	;	;	PUNCT
fumecheng-7385	13	22	the	the	DET
fumecheng-7385	13	23	vibration	vibration	NOUN
fumecheng-7385	13	24	property	property	NOUN
fumecheng-7385	13	25	will	will	AUX
fumecheng-7385	13	26	significantly	significantly	ADV
fumecheng-7385	13	27	affect	affect	VERB
fumecheng-7385	13	28	the	the	DET
fumecheng-7385	13	29	safety	safety	NOUN
fumecheng-7385	13	30	and	and	CCONJ
fumecheng-7385	13	31	the	the	DET
fumecheng-7385	13	32	life	life	NOUN
fumecheng-7385	13	33	span	span	NOUN
fumecheng-7385	13	34	,	,	PUNCT
fumecheng-7385	13	35	and	and	CCONJ
fumecheng-7385	13	36	it	it	PRON
fumecheng-7385	13	37	can	can	AUX
fumecheng-7385	13	38	be	be	AUX
fumecheng-7385	13	39	described	describe	VERB
fumecheng-7385	13	40	by	by	ADP
fumecheng-7385	13	41	nonlinear	nonlinear	ADJ
fumecheng-7385	13	42	differential	differential	ADJ
fumecheng-7385	13	43	equations	equation	NOUN
fumecheng-7385	13	44	with	with	ADP
fumecheng-7385	13	45	possible	possible	ADJ
fumecheng-7385	13	46	two	two	NUM
fumecheng-7385	13	47	-	-	PUNCT
fumecheng-7385	13	48	fractal	fractal	ADJ
fumecheng-7385	13	49	derivatives	derivative	NOUN
fumecheng-7385	13	50	,	,	PUNCT
fumecheng-7385	13	51	which	which	PRON
fumecheng-7385	13	52	are	be	AUX
fumecheng-7385	13	53	difficult	difficult	ADJ
fumecheng-7385	13	54	to	to	PART
fumecheng-7385	13	55	solve	solve	VERB
fumecheng-7385	13	56	exactly	exactly	ADV
fumecheng-7385	13	57	.	.	PUNCT
fumecheng-7385	14	1	the	the	DET
fumecheng-7385	14	2	scientists	scientist	NOUN
fumecheng-7385	14	3	have	have	AUX
fumecheng-7385	14	4	made	make	VERB
fumecheng-7385	14	5	great	great	ADJ
fumecheng-7385	14	6	efforts	effort	NOUN
fumecheng-7385	14	7	to	to	PART
fumecheng-7385	14	8	provide	provide	VERB
fumecheng-7385	14	9	information	information	NOUN
fumecheng-7385	14	10	about	about	ADP
fumecheng-7385	14	11	the	the	DET
fumecheng-7385	14	12	approximate	approximate	ADJ
fumecheng-7385	14	13	solutions	solution	NOUN
fumecheng-7385	14	14	of	of	ADP
fumecheng-7385	14	15	these	these	DET
fumecheng-7385	14	16	equations	equation	NOUN
fumecheng-7385	15	1	[	[	X
fumecheng-7385	15	2	1	1	NUM
fumecheng-7385	15	3	-	-	SYM
fumecheng-7385	15	4	6	6	NUM
fumecheng-7385	15	5	]	]	PUNCT
fumecheng-7385	15	6	.	.	PUNCT
fumecheng-7385	16	1	of	of	ADP
fumecheng-7385	16	2	the	the	DET
fumecheng-7385	16	3	nonlinear	nonlinear	ADJ
fumecheng-7385	16	4	vibration	vibration	NOUN
fumecheng-7385	16	5	systems	system	NOUN
fumecheng-7385	16	6	that	that	PRON
fumecheng-7385	16	7	have	have	AUX
fumecheng-7385	16	8	been	be	AUX
fumecheng-7385	16	9	fascinating	fascinating	ADJ
fumecheng-7385	16	10	to	to	ADP
fumecheng-7385	16	11	engineers	engineer	NOUN
fumecheng-7385	16	12	and	and	CCONJ
fumecheng-7385	16	13	scientists	scientist	NOUN
fumecheng-7385	16	14	,	,	PUNCT
fumecheng-7385	16	15	by	by	ADP
fumecheng-7385	16	16	far	far	ADV
fumecheng-7385	16	17	received	receive	VERB
fumecheng-7385	16	18	january	january	PROPN
fumecheng-7385	16	19	25	25	NUM
fumecheng-7385	16	20	,	,	PUNCT
fumecheng-7385	16	21	2021	2021	NUM
fumecheng-7385	16	22	/	/	SYM
fumecheng-7385	16	23	accepted	accept	VERB
fumecheng-7385	16	24	march	march	PROPN
fumecheng-7385	16	25	11	11	NUM
fumecheng-7385	16	26	,	,	PUNCT
fumecheng-7385	16	27	2021	2021	NUM
fumecheng-7385	16	28	corresponding	correspond	VERB
fumecheng-7385	16	29	author	author	NOUN
fumecheng-7385	16	30	:	:	PUNCT
fumecheng-7385	16	31	yusry	yusry	PROPN
fumecheng-7385	16	32	o.	o.	PROPN
fumecheng-7385	16	33	el	el	PROPN
fumecheng-7385	16	34	-	-	PROPN
fumecheng-7385	16	35	dib	dib	PROPN
fumecheng-7385	16	36	department	department	NOUN
fumecheng-7385	16	37	of	of	ADP
fumecheng-7385	16	38	mathematics	mathematic	NOUN
fumecheng-7385	16	39	,	,	PUNCT
fumecheng-7385	16	40	faculty	faculty	NOUN
fumecheng-7385	16	41	of	of	ADP
fumecheng-7385	16	42	education	education	NOUN
fumecheng-7385	16	43	,	,	PUNCT
fumecheng-7385	16	44	ain	ain	PROPN
fumecheng-7385	16	45	shams	shams	PROPN
fumecheng-7385	16	46	university	university	PROPN
fumecheng-7385	16	47	,	,	PUNCT
fumecheng-7385	16	48	roxy	roxy	PROPN
fumecheng-7385	16	49	,	,	PUNCT
fumecheng-7385	16	50	cairo	cairo	PROPN
fumecheng-7385	16	51	,	,	PUNCT
fumecheng-7385	16	52	egypt	egypt	PROPN
fumecheng-7385	16	53	e	e	PROPN
fumecheng-7385	16	54	-	-	NOUN
fumecheng-7385	16	55	mail	mail	NOUN
fumecheng-7385	16	56	:	:	PUNCT
fumecheng-7385	16	57	yusryeldib52@hotmail.com	yusryeldib52@hotmail.com	X
fumecheng-7385	17	1	736	736	NUM
fumecheng-7385	17	2	j.-h	j.-h	NOUN
fumecheng-7385	17	3	.	.	PUNCT
fumecheng-7385	18	1	he	he	PRON
fumecheng-7385	18	2	,	,	PUNCT
fumecheng-7385	18	3	y.	y.	PROPN
fumecheng-7385	18	4	o.	o.	PROPN
fumecheng-7385	18	5	el	el	PROPN
fumecheng-7385	18	6	-	-	PROPN
fumecheng-7385	18	7	dib	dib	VERB
fumecheng-7385	18	8	the	the	DET
fumecheng-7385	18	9	most	most	ADV
fumecheng-7385	18	10	perplexing	perplexing	ADJ
fumecheng-7385	18	11	is	be	AUX
fumecheng-7385	18	12	the	the	DET
fumecheng-7385	18	13	frequency	frequency	NOUN
fumecheng-7385	18	14	-	-	PUNCT
fumecheng-7385	18	15	amplitude	amplitude	NOUN
fumecheng-7385	18	16	relationship	relationship	NOUN
fumecheng-7385	18	17	.	.	PUNCT
fumecheng-7385	19	1	a	a	DET
fumecheng-7385	19	2	simple	simple	ADJ
fumecheng-7385	19	3	but	but	CCONJ
fumecheng-7385	19	4	accurate	accurate	ADJ
fumecheng-7385	19	5	approach	approach	NOUN
fumecheng-7385	19	6	to	to	ADP
fumecheng-7385	19	7	the	the	DET
fumecheng-7385	19	8	relationship	relationship	NOUN
fumecheng-7385	19	9	is	be	AUX
fumecheng-7385	19	10	much	much	ADV
fumecheng-7385	19	11	needed	need	VERB
fumecheng-7385	19	12	in	in	ADP
fumecheng-7385	19	13	practical	practical	ADJ
fumecheng-7385	19	14	applications	application	NOUN
fumecheng-7385	19	15	[	[	X
fumecheng-7385	19	16	7	7	NUM
fumecheng-7385	19	17	-	-	SYM
fumecheng-7385	19	18	9	9	NUM
fumecheng-7385	19	19	]	]	PUNCT
fumecheng-7385	19	20	.	.	PUNCT
fumecheng-7385	20	1	it	it	PRON
fumecheng-7385	20	2	was	be	AUX
fumecheng-7385	20	3	revealed	reveal	VERB
fumecheng-7385	20	4	that	that	SCONJ
fumecheng-7385	20	5	nanofiber	nanofiber	PROPN
fumecheng-7385	20	6	’s	’s	PART
fumecheng-7385	20	7	surface	surface	NOUN
fumecheng-7385	20	8	morphology	morphology	NOUN
fumecheng-7385	20	9	can	can	AUX
fumecheng-7385	20	10	be	be	AUX
fumecheng-7385	20	11	controlled	control	VERB
fumecheng-7385	20	12	by	by	ADP
fumecheng-7385	20	13	the	the	DET
fumecheng-7385	20	14	vibration	vibration	NOUN
fumecheng-7385	20	15	’s	’s	PART
fumecheng-7385	20	16	frequency	frequency	NOUN
fumecheng-7385	20	17	-	-	PUNCT
fumecheng-7385	20	18	amplitude	amplitude	NOUN
fumecheng-7385	20	19	relationship	relationship	NOUN
fumecheng-7385	20	20	[	[	X
fumecheng-7385	20	21	10	10	NUM
fumecheng-7385	20	22	]	]	PUNCT
fumecheng-7385	20	23	,	,	PUNCT
fumecheng-7385	20	24	and	and	CCONJ
fumecheng-7385	20	25	a	a	DET
fumecheng-7385	20	26	successful	successful	ADJ
fumecheng-7385	20	27	finding	finding	NOUN
fumecheng-7385	20	28	of	of	ADP
fumecheng-7385	20	29	the	the	DET
fumecheng-7385	20	30	fangzhu	fangzhu	NOUN
fumecheng-7385	20	31	’s	’s	PART
fumecheng-7385	20	32	vibration	vibration	NOUN
fumecheng-7385	20	33	property	property	NOUN
fumecheng-7385	20	34	has	have	AUX
fumecheng-7385	20	35	revealed	reveal	VERB
fumecheng-7385	20	36	the	the	DET
fumecheng-7385	20	37	hidden	hidden	ADJ
fumecheng-7385	20	38	nanotechnology	nanotechnology	NOUN
fumecheng-7385	20	39	in	in	ADP
fumecheng-7385	20	40	ancient	ancient	ADJ
fumecheng-7385	20	41	china	china	PROPN
fumecheng-7385	21	1	[	[	X
fumecheng-7385	21	2	11	11	NUM
fumecheng-7385	21	3	-	-	SYM
fumecheng-7385	21	4	13	13	NUM
fumecheng-7385	21	5	]	]	PUNCT
fumecheng-7385	21	6	.	.	PUNCT
fumecheng-7385	22	1	the	the	DET
fumecheng-7385	22	2	variational	variational	ADJ
fumecheng-7385	22	3	principle	principle	NOUN
fumecheng-7385	22	4	for	for	ADP
fumecheng-7385	22	5	nonlinear	nonlinear	ADJ
fumecheng-7385	22	6	differential	differential	ADJ
fumecheng-7385	22	7	equations	equation	NOUN
fumecheng-7385	22	8	is	be	AUX
fumecheng-7385	22	9	another	another	DET
fumecheng-7385	22	10	effective	effective	ADJ
fumecheng-7385	22	11	analytical	analytical	ADJ
fumecheng-7385	22	12	method	method	NOUN
fumecheng-7385	22	13	[	[	X
fumecheng-7385	22	14	14,15	14,15	NUM
fumecheng-7385	22	15	]	]	PUNCT
fumecheng-7385	22	16	.	.	PUNCT
fumecheng-7385	23	1	the	the	DET
fumecheng-7385	23	2	string	string	NOUN
fumecheng-7385	23	3	axial	axial	ADJ
fumecheng-7385	23	4	vibration	vibration	NOUN
fumecheng-7385	23	5	can	can	AUX
fumecheng-7385	23	6	be	be	AUX
fumecheng-7385	23	7	modeled	model	VERB
fumecheng-7385	23	8	by	by	ADP
fumecheng-7385	23	9	the	the	DET
fumecheng-7385	23	10	klein	klein	PROPN
fumecheng-7385	23	11	-	-	PUNCT
fumecheng-7385	23	12	gordon	gordon	PROPN
fumecheng-7385	23	13	equation	equation	NOUN
fumecheng-7385	23	14	(	(	PUNCT
fumecheng-7385	23	15	kg	kg	PROPN
fumecheng-7385	23	16	)	)	PUNCT
fumecheng-7385	23	17	,	,	PUNCT
fumecheng-7385	23	18	which	which	PRON
fumecheng-7385	23	19	is	be	AUX
fumecheng-7385	23	20	a	a	DET
fumecheng-7385	23	21	significant	significant	ADJ
fumecheng-7385	23	22	group	group	NOUN
fumecheng-7385	23	23	of	of	ADP
fumecheng-7385	23	24	partial	partial	ADJ
fumecheng-7385	23	25	differential	differential	NOUN
fumecheng-7385	23	26	equations	equation	NOUN
fumecheng-7385	23	27	;	;	PUNCT
fumecheng-7385	23	28	it	it	PRON
fumecheng-7385	23	29	is	be	AUX
fumecheng-7385	23	30	also	also	ADV
fumecheng-7385	23	31	found	find	VERB
fumecheng-7385	23	32	in	in	ADP
fumecheng-7385	23	33	relativistic	relativistic	ADJ
fumecheng-7385	23	34	quantum	quantum	ADJ
fumecheng-7385	23	35	mechanics	mechanic	NOUN
fumecheng-7385	23	36	and	and	CCONJ
fumecheng-7385	23	37	field	field	NOUN
fumecheng-7385	23	38	theory	theory	NOUN
fumecheng-7385	23	39	.	.	PUNCT
fumecheng-7385	24	1	el	el	PROPN
fumecheng-7385	24	2	-	-	PROPN
fumecheng-7385	24	3	dib	dib	PROPN
fumecheng-7385	24	4	[	[	X
fumecheng-7385	24	5	16	16	NUM
fumecheng-7385	24	6	]	]	PUNCT
fumecheng-7385	24	7	introduced	introduce	VERB
fumecheng-7385	24	8	the	the	DET
fumecheng-7385	24	9	multiple	multiple	ADJ
fumecheng-7385	24	10	-	-	PUNCT
fumecheng-7385	24	11	scale	scale	NOUN
fumecheng-7385	24	12	homotopy	homotopy	NOUN
fumecheng-7385	24	13	perturbation	perturbation	NOUN
fumecheng-7385	24	14	method	method	NOUN
fumecheng-7385	24	15	(	(	PUNCT
fumecheng-7385	24	16	he	he	PRON
fumecheng-7385	24	17	’s	’	VERB
fumecheng-7385	24	18	multiple	multiple	ADJ
fumecheng-7385	24	19	-	-	PUNCT
fumecheng-7385	24	20	scale	scale	NOUN
fumecheng-7385	24	21	method	method	NOUN
fumecheng-7385	24	22	)	)	PUNCT
fumecheng-7385	24	23	as	as	ADP
fumecheng-7385	24	24	an	an	DET
fumecheng-7385	24	25	outer	outer	ADJ
fumecheng-7385	24	26	perturbation	perturbation	NOUN
fumecheng-7385	24	27	of	of	ADP
fumecheng-7385	24	28	the	the	DET
fumecheng-7385	24	29	nonlinear	nonlinear	ADJ
fumecheng-7385	24	30	kg	kg	PROPN
fumecheng-7385	24	31	equation	equation	NOUN
fumecheng-7385	24	32	.	.	PUNCT
fumecheng-7385	25	1	a	a	DET
fumecheng-7385	25	2	highly	highly	ADV
fumecheng-7385	25	3	accurate	accurate	ADJ
fumecheng-7385	25	4	periodic	periodic	ADJ
fumecheng-7385	25	5	unsteady	unsteady	ADJ
fumecheng-7385	25	6	solution	solution	NOUN
fumecheng-7385	25	7	was	be	AUX
fumecheng-7385	25	8	derived	derive	VERB
fumecheng-7385	25	9	from	from	ADP
fumecheng-7385	25	10	three	three	NUM
fumecheng-7385	25	11	order	order	NOUN
fumecheng-7385	25	12	perturbations	perturbation	NOUN
fumecheng-7385	25	13	.	.	PUNCT
fumecheng-7385	26	1	furthermore	furthermore	ADV
fumecheng-7385	26	2	,	,	PUNCT
fumecheng-7385	26	3	a	a	DET
fumecheng-7385	26	4	complete	complete	ADJ
fumecheng-7385	26	5	approximate	approximate	ADJ
fumecheng-7385	26	6	solution	solution	NOUN
fumecheng-7385	26	7	consisting	consist	VERB
fumecheng-7385	26	8	of	of	ADP
fumecheng-7385	26	9	a	a	DET
fumecheng-7385	26	10	temporal	temporal	ADJ
fumecheng-7385	26	11	solution	solution	NOUN
fumecheng-7385	26	12	,	,	PUNCT
fumecheng-7385	26	13	which	which	PRON
fumecheng-7385	26	14	functions	function	NOUN
fumecheng-7385	26	15	as	as	ADP
fumecheng-7385	26	16	an	an	DET
fumecheng-7385	26	17	outer	outer	ADJ
fumecheng-7385	26	18	expansion	expansion	NOUN
fumecheng-7385	26	19	along	along	ADP
fumecheng-7385	26	20	with	with	ADP
fumecheng-7385	26	21	the	the	DET
fumecheng-7385	26	22	spatial	spatial	ADJ
fumecheng-7385	26	23	solution	solution	NOUN
fumecheng-7385	26	24	serving	serve	VERB
fumecheng-7385	26	25	as	as	ADP
fumecheng-7385	26	26	an	an	DET
fumecheng-7385	26	27	inner	inner	ADJ
fumecheng-7385	26	28	expansion	expansion	NOUN
fumecheng-7385	26	29	of	of	ADP
fumecheng-7385	26	30	the	the	DET
fumecheng-7385	26	31	nonlinear	nonlinear	ADJ
fumecheng-7385	26	32	kg	kg	PROPN
fumecheng-7385	26	33	equation	equation	NOUN
fumecheng-7385	26	34	,	,	PUNCT
fumecheng-7385	26	35	was	be	AUX
fumecheng-7385	26	36	achieved	achieve	VERB
fumecheng-7385	26	37	.	.	PUNCT
fumecheng-7385	27	1	el	el	PROPN
fumecheng-7385	27	2	-	-	PROPN
fumecheng-7385	27	3	dib	dib	PROPN
fumecheng-7385	27	4	et	et	NOUN
fumecheng-7385	27	5	al	al	PROPN
fumecheng-7385	27	6	.	.	PUNCT
fumecheng-7385	28	1	[	[	X
fumecheng-7385	28	2	17,18	17,18	X
fumecheng-7385	28	3	]	]	PUNCT
fumecheng-7385	28	4	recently	recently	ADV
fumecheng-7385	28	5	proposed	propose	VERB
fumecheng-7385	28	6	a	a	DET
fumecheng-7385	28	7	new	new	ADJ
fumecheng-7385	28	8	approach	approach	NOUN
fumecheng-7385	28	9	to	to	ADP
fumecheng-7385	28	10	the	the	DET
fumecheng-7385	28	11	study	study	NOUN
fumecheng-7385	28	12	of	of	ADP
fumecheng-7385	28	13	the	the	DET
fumecheng-7385	28	14	nonlinear	nonlinear	ADJ
fumecheng-7385	28	15	instability	instability	NOUN
fumecheng-7385	28	16	analysis	analysis	NOUN
fumecheng-7385	28	17	.	.	PUNCT
fumecheng-7385	29	1	their	their	PRON
fumecheng-7385	29	2	analysis	analysis	NOUN
fumecheng-7385	29	3	has	have	AUX
fumecheng-7385	29	4	revealed	reveal	VERB
fumecheng-7385	29	5	a	a	DET
fumecheng-7385	29	6	nonlinear	nonlinear	ADJ
fumecheng-7385	29	7	pde	pde	NOUN
fumecheng-7385	29	8	that	that	PRON
fumecheng-7385	29	9	controls	control	VERB
fumecheng-7385	29	10	the	the	DET
fumecheng-7385	29	11	surface	surface	NOUN
fumecheng-7385	29	12	deflection	deflection	NOUN
fumecheng-7385	29	13	of	of	ADP
fumecheng-7385	29	14	the	the	DET
fumecheng-7385	29	15	interface	interface	NOUN
fumecheng-7385	29	16	.	.	PUNCT
fumecheng-7385	30	1	they	they	PRON
fumecheng-7385	30	2	have	have	AUX
fumecheng-7385	30	3	transferred	transfer	VERB
fumecheng-7385	30	4	the	the	DET
fumecheng-7385	30	5	characteristic	characteristic	ADJ
fumecheng-7385	30	6	equation	equation	NOUN
fumecheng-7385	30	7	to	to	ADP
fumecheng-7385	30	8	a	a	DET
fumecheng-7385	30	9	kg	kg	NOUN
fumecheng-7385	30	10	equation	equation	NOUN
fumecheng-7385	30	11	.	.	PUNCT
fumecheng-7385	31	1	through	through	ADP
fumecheng-7385	31	2	a	a	DET
fumecheng-7385	31	3	traveling	travel	VERB
fumecheng-7385	31	4	–	–	PUNCT
fumecheng-7385	31	5	wave	wave	NOUN
fumecheng-7385	31	6	solution	solution	NOUN
fumecheng-7385	31	7	,	,	PUNCT
fumecheng-7385	31	8	they	they	PRON
fumecheng-7385	31	9	have	have	AUX
fumecheng-7385	31	10	examined	examine	VERB
fumecheng-7385	31	11	the	the	DET
fumecheng-7385	31	12	stability	stability	NOUN
fumecheng-7385	31	13	profile	profile	NOUN
fumecheng-7385	31	14	.	.	PUNCT
fumecheng-7385	32	1	it	it	PRON
fumecheng-7385	32	2	is	be	AUX
fumecheng-7385	32	3	important	important	ADJ
fumecheng-7385	32	4	to	to	PART
fumecheng-7385	32	5	note	note	VERB
fumecheng-7385	32	6	that	that	SCONJ
fumecheng-7385	32	7	the	the	DET
fumecheng-7385	32	8	temporal	temporal	ADJ
fumecheng-7385	32	9	damped	damped	NOUN
fumecheng-7385	32	10	kg	kg	NOUN
fumecheng-7385	32	11	equation	equation	NOUN
fumecheng-7385	32	12	is	be	AUX
fumecheng-7385	32	13	not	not	PART
fumecheng-7385	32	14	naturally	naturally	ADV
fumecheng-7385	32	15	dissipative	dissipative	ADJ
fumecheng-7385	32	16	.	.	PUNCT
fumecheng-7385	33	1	so	so	ADV
fumecheng-7385	33	2	,	,	PUNCT
fumecheng-7385	33	3	the	the	DET
fumecheng-7385	33	4	introduction	introduction	NOUN
fumecheng-7385	33	5	of	of	ADP
fumecheng-7385	33	6	the	the	DET
fumecheng-7385	33	7	dissipative	dissipative	ADJ
fumecheng-7385	33	8	mechanisms	mechanism	NOUN
fumecheng-7385	33	9	is	be	AUX
fumecheng-7385	33	10	necessary	necessary	ADJ
fumecheng-7385	33	11	to	to	PART
fumecheng-7385	33	12	force	force	VERB
fumecheng-7385	33	13	the	the	DET
fumecheng-7385	33	14	energy	energy	NOUN
fumecheng-7385	33	15	to	to	PART
fumecheng-7385	33	16	decay	decay	VERB
fumecheng-7385	33	17	to	to	ADP
fumecheng-7385	33	18	zero	zero	NUM
fumecheng-7385	33	19	when	when	SCONJ
fumecheng-7385	33	20	time	time	NOUN
fumecheng-7385	33	21	goes	go	VERB
fumecheng-7385	33	22	to	to	ADP
fumecheng-7385	33	23	infinity	infinity	NOUN
fumecheng-7385	33	24	.	.	PUNCT
fumecheng-7385	34	1	indeed	indeed	ADV
fumecheng-7385	34	2	,	,	PUNCT
fumecheng-7385	34	3	the	the	DET
fumecheng-7385	34	4	appearance	appearance	NOUN
fumecheng-7385	34	5	of	of	ADP
fumecheng-7385	34	6	the	the	DET
fumecheng-7385	34	7	damping	damp	VERB
fumecheng-7385	34	8	terms	term	NOUN
fumecheng-7385	34	9	given	give	VERB
fumecheng-7385	34	10	in	in	ADP
fumecheng-7385	34	11	the	the	DET
fumecheng-7385	34	12	damped	damped	NOUN
fumecheng-7385	34	13	kg	kg	NOUN
fumecheng-7385	34	14	equation	equation	NOUN
fumecheng-7385	34	15	is	be	AUX
fumecheng-7385	34	16	not	not	PART
fumecheng-7385	34	17	required	require	VERB
fumecheng-7385	34	18	by	by	ADP
fumecheng-7385	34	19	itself	itself	PRON
fumecheng-7385	34	20	to	to	PART
fumecheng-7385	34	21	gauge	gauge	VERB
fumecheng-7385	34	22	the	the	DET
fumecheng-7385	34	23	energy	energy	NOUN
fumecheng-7385	34	24	e(t	e(t	NOUN
fumecheng-7385	34	25	)	)	PUNCT
fumecheng-7385	34	26	associated	associate	VERB
fumecheng-7385	34	27	with	with	ADP
fumecheng-7385	34	28	the	the	DET
fumecheng-7385	34	29	problem	problem	NOUN
fumecheng-7385	34	30	,	,	PUNCT
fumecheng-7385	34	31	but	but	CCONJ
fumecheng-7385	34	32	it	it	PRON
fumecheng-7385	34	33	is	be	AUX
fumecheng-7385	34	34	a	a	DET
fumecheng-7385	34	35	non	non	ADJ
fumecheng-7385	34	36	-	-	ADJ
fumecheng-7385	34	37	increasing	increasing	ADJ
fumecheng-7385	34	38	function	function	NOUN
fumecheng-7385	34	39	of	of	ADP
fumecheng-7385	34	40	the	the	DET
fumecheng-7385	34	41	parameter	parameter	NOUN
fumecheng-7385	34	42	t.	t.	PROPN
fumecheng-7385	34	43	uniform	uniform	PROPN
fumecheng-7385	34	44	decay	decay	NOUN
fumecheng-7385	34	45	rate	rate	NOUN
fumecheng-7385	34	46	estimates	estimate	NOUN
fumecheng-7385	34	47	to	to	ADP
fumecheng-7385	34	48	the	the	DET
fumecheng-7385	34	49	problem	problem	NOUN
fumecheng-7385	34	50	have	have	AUX
fumecheng-7385	34	51	been	be	AUX
fumecheng-7385	34	52	considered	consider	VERB
fumecheng-7385	34	53	by	by	ADP
fumecheng-7385	34	54	cavalcanti	cavalcanti	PROPN
fumecheng-7385	34	55	et	et	PROPN
fumecheng-7385	34	56	al	al	PROPN
fumecheng-7385	34	57	.	.	PUNCT
fumecheng-7385	35	1	[	[	X
fumecheng-7385	35	2	19	19	NUM
fumecheng-7385	35	3	-	-	SYM
fumecheng-7385	35	4	21	21	NUM
fumecheng-7385	35	5	]	]	PUNCT
fumecheng-7385	35	6	.	.	PUNCT
fumecheng-7385	36	1	the	the	DET
fumecheng-7385	36	2	maximum	maximum	ADJ
fumecheng-7385	36	3	principles	principle	NOUN
fumecheng-7385	36	4	of	of	ADP
fumecheng-7385	36	5	the	the	DET
fumecheng-7385	36	6	optimal	optimal	ADJ
fumecheng-7385	36	7	control	control	NOUN
fumecheng-7385	36	8	problems	problem	NOUN
fumecheng-7385	36	9	,	,	PUNCT
fumecheng-7385	36	10	governed	govern	VERB
fumecheng-7385	36	11	by	by	ADP
fumecheng-7385	36	12	a	a	DET
fumecheng-7385	36	13	damped	damped	NOUN
fumecheng-7385	36	14	kg	kg	X
fumecheng-7385	36	15	equation	equation	NOUN
fumecheng-7385	36	16	with	with	ADP
fumecheng-7385	36	17	state	state	NOUN
fumecheng-7385	36	18	constraints	constraint	NOUN
fumecheng-7385	36	19	,	,	PUNCT
fumecheng-7385	36	20	were	be	AUX
fumecheng-7385	36	21	examined	examine	VERB
fumecheng-7385	36	22	by	by	ADP
fumecheng-7385	36	23	parka	parka	PROPN
fumecheng-7385	36	24	and	and	CCONJ
fumecheng-7385	36	25	jeong	jeong	PROPN
fumecheng-7385	37	1	[	[	X
fumecheng-7385	37	2	22	22	NUM
fumecheng-7385	37	3	]	]	PUNCT
fumecheng-7385	37	4	.	.	PUNCT
fumecheng-7385	38	1	lin	lin	PROPN
fumecheng-7385	38	2	and	and	CCONJ
fumecheng-7385	38	3	cui	cui	PROPN
fumecheng-7385	38	4	[	[	X
fumecheng-7385	38	5	23	23	NUM
fumecheng-7385	38	6	]	]	PUNCT
fumecheng-7385	38	7	investigated	investigate	VERB
fumecheng-7385	38	8	a	a	DET
fumecheng-7385	38	9	damped	damped	ADJ
fumecheng-7385	38	10	nonlinear	nonlinear	NOUN
fumecheng-7385	38	11	kg	kg	PROPN
fumecheng-7385	38	12	equation	equation	NOUN
fumecheng-7385	38	13	,	,	PUNCT
fumecheng-7385	38	14	taking	take	VERB
fumecheng-7385	38	15	into	into	ADP
fumecheng-7385	38	16	consideration	consideration	NOUN
fumecheng-7385	38	17	a	a	DET
fumecheng-7385	38	18	kernel	kernel	NOUN
fumecheng-7385	38	19	space	space	NOUN
fumecheng-7385	38	20	.	.	PUNCT
fumecheng-7385	39	1	they	they	PRON
fumecheng-7385	39	2	assumed	assume	VERB
fumecheng-7385	39	3	a	a	DET
fumecheng-7385	39	4	new	new	ADJ
fumecheng-7385	39	5	technique	technique	NOUN
fumecheng-7385	39	6	in	in	ADP
fumecheng-7385	39	7	solving	solve	VERB
fumecheng-7385	39	8	this	this	DET
fumecheng-7385	39	9	equation	equation	NOUN
fumecheng-7385	39	10	to	to	PART
fumecheng-7385	39	11	emphasize	emphasize	VERB
fumecheng-7385	39	12	the	the	DET
fumecheng-7385	39	13	feasibility	feasibility	NOUN
fumecheng-7385	39	14	and	and	CCONJ
fumecheng-7385	39	15	the	the	DET
fumecheng-7385	39	16	rigor	rigor	NOUN
fumecheng-7385	39	17	of	of	ADP
fumecheng-7385	39	18	the	the	DET
fumecheng-7385	39	19	method	method	NOUN
fumecheng-7385	39	20	.	.	PUNCT
fumecheng-7385	40	1	the	the	DET
fumecheng-7385	40	2	local	local	ADJ
fumecheng-7385	40	3	solution	solution	NOUN
fumecheng-7385	40	4	of	of	ADP
fumecheng-7385	40	5	the	the	DET
fumecheng-7385	40	6	initial	initial	ADJ
fumecheng-7385	40	7	-	-	PUNCT
fumecheng-7385	40	8	boundary	boundary	NOUN
fumecheng-7385	40	9	value	value	NOUN
fumecheng-7385	40	10	problem	problem	NOUN
fumecheng-7385	40	11	for	for	ADP
fumecheng-7385	40	12	a	a	DET
fumecheng-7385	40	13	class	class	NOUN
fumecheng-7385	40	14	of	of	ADP
fumecheng-7385	40	15	fourth	fourth	ADJ
fumecheng-7385	40	16	-	-	PUNCT
fumecheng-7385	40	17	order	order	NOUN
fumecheng-7385	40	18	wave	wave	NOUN
fumecheng-7385	40	19	equations	equation	NOUN
fumecheng-7385	40	20	with	with	ADP
fumecheng-7385	40	21	a	a	DET
fumecheng-7385	40	22	high	high	ADJ
fumecheng-7385	40	23	damping	damp	VERB
fumecheng-7385	40	24	term	term	NOUN
fumecheng-7385	40	25	was	be	AUX
fumecheng-7385	40	26	obtained	obtain	VERB
fumecheng-7385	40	27	by	by	ADP
fumecheng-7385	40	28	using	use	VERB
fumecheng-7385	40	29	fixed	fix	VERB
fumecheng-7385	40	30	point	point	NOUN
fumecheng-7385	40	31	theory	theory	NOUN
fumecheng-7385	40	32	[	[	X
fumecheng-7385	40	33	24	24	NUM
fumecheng-7385	40	34	]	]	PUNCT
fumecheng-7385	40	35	.	.	PUNCT
fumecheng-7385	41	1	he	he	PRON
fumecheng-7385	41	2	and	and	CCONJ
fumecheng-7385	41	3	el	el	PROPN
fumecheng-7385	41	4	-	-	PROPN
fumecheng-7385	41	5	dib	dib	PROPN
fumecheng-7385	41	6	[	[	X
fumecheng-7385	41	7	25	25	NUM
fumecheng-7385	41	8	]	]	PUNCT
fumecheng-7385	41	9	used	use	VERB
fumecheng-7385	41	10	the	the	DET
fumecheng-7385	41	11	reducing	reduce	VERB
fumecheng-7385	41	12	rank	rank	NOUN
fumecheng-7385	41	13	method	method	NOUN
fumecheng-7385	41	14	to	to	PART
fumecheng-7385	41	15	solve	solve	VERB
fumecheng-7385	41	16	a	a	DET
fumecheng-7385	41	17	third	third	ADJ
fumecheng-7385	41	18	-	-	PUNCT
fumecheng-7385	41	19	order	order	NOUN
fumecheng-7385	41	20	damped	damp	VERB
fumecheng-7385	41	21	nonlinear	nonlinear	ADJ
fumecheng-7385	41	22	equation	equation	NOUN
fumecheng-7385	41	23	produced	produce	VERB
fumecheng-7385	41	24	from	from	ADP
fumecheng-7385	41	25	the	the	DET
fumecheng-7385	41	26	strong	strong	ADJ
fumecheng-7385	41	27	damped	damped	NOUN
fumecheng-7385	41	28	nonlinear	nonlinear	PROPN
fumecheng-7385	41	29	kg	kg	PROPN
fumecheng-7385	41	30	equation	equation	NOUN
fumecheng-7385	41	31	one	one	NUM
fumecheng-7385	41	32	of	of	ADP
fumecheng-7385	41	33	the	the	DET
fumecheng-7385	41	34	most	most	ADV
fumecheng-7385	41	35	traditional	traditional	ADJ
fumecheng-7385	41	36	techniques	technique	NOUN
fumecheng-7385	41	37	to	to	PART
fumecheng-7385	41	38	find	find	VERB
fumecheng-7385	41	39	an	an	DET
fumecheng-7385	41	40	approximate	approximate	ADJ
fumecheng-7385	41	41	solution	solution	NOUN
fumecheng-7385	41	42	is	be	AUX
fumecheng-7385	41	43	the	the	DET
fumecheng-7385	41	44	homotopy	homotopy	NOUN
fumecheng-7385	41	45	perturbation	perturbation	NOUN
fumecheng-7385	41	46	method	method	NOUN
fumecheng-7385	41	47	(	(	PUNCT
fumecheng-7385	41	48	hpm	hpm	NOUN
fumecheng-7385	41	49	)	)	PUNCT
fumecheng-7385	41	50	.	.	PUNCT
fumecheng-7385	42	1	the	the	DET
fumecheng-7385	42	2	major	major	ADJ
fumecheng-7385	42	3	property	property	NOUN
fumecheng-7385	42	4	of	of	ADP
fumecheng-7385	42	5	the	the	DET
fumecheng-7385	42	6	hpm	hpm	NOUN
fumecheng-7385	42	7	is	be	AUX
fumecheng-7385	42	8	its	its	PRON
fumecheng-7385	42	9	ability	ability	NOUN
fumecheng-7385	42	10	and	and	CCONJ
fumecheng-7385	42	11	flexibility	flexibility	NOUN
fumecheng-7385	42	12	to	to	PART
fumecheng-7385	42	13	examine	examine	VERB
fumecheng-7385	42	14	a	a	DET
fumecheng-7385	42	15	wide	wide	ADJ
fumecheng-7385	42	16	class	class	NOUN
fumecheng-7385	42	17	of	of	ADP
fumecheng-7385	42	18	nonlinear	nonlinear	ADJ
fumecheng-7385	42	19	differential	differential	ADJ
fumecheng-7385	42	20	equations	equation	NOUN
fumecheng-7385	42	21	conveniently	conveniently	ADV
fumecheng-7385	42	22	and	and	CCONJ
fumecheng-7385	42	23	accurately	accurately	ADV
fumecheng-7385	42	24	[	[	X
fumecheng-7385	42	25	26	26	NUM
fumecheng-7385	42	26	]	]	PUNCT
fumecheng-7385	42	27	.	.	PUNCT
fumecheng-7385	43	1	it	it	PRON
fumecheng-7385	43	2	has	have	AUX
fumecheng-7385	43	3	been	be	AUX
fumecheng-7385	43	4	developed	develop	VERB
fumecheng-7385	43	5	and	and	CCONJ
fumecheng-7385	43	6	improved	improve	VERB
fumecheng-7385	43	7	by	by	ADP
fumecheng-7385	43	8	scientists	scientist	NOUN
fumecheng-7385	43	9	and	and	CCONJ
fumecheng-7385	43	10	engineers	engineer	NOUN
fumecheng-7385	43	11	.	.	PUNCT
fumecheng-7385	44	1	the	the	DET
fumecheng-7385	44	2	hpm	hpm	NOUN
fumecheng-7385	44	3	with	with	ADP
fumecheng-7385	44	4	two	two	NUM
fumecheng-7385	44	5	expanding	expand	VERB
fumecheng-7385	44	6	parameters	parameter	NOUN
fumecheng-7385	44	7	was	be	AUX
fumecheng-7385	44	8	suggested	suggest	VERB
fumecheng-7385	44	9	by	by	ADP
fumecheng-7385	44	10	el	el	PROPN
fumecheng-7385	44	11	-	-	PROPN
fumecheng-7385	44	12	dib	dib	PROPN
fumecheng-7385	44	13	[	[	X
fumecheng-7385	44	14	27	27	NUM
fumecheng-7385	44	15	]	]	PUNCT
fumecheng-7385	44	16	.	.	PUNCT
fumecheng-7385	45	1	a	a	DET
fumecheng-7385	45	2	combination	combination	NOUN
fumecheng-7385	45	3	of	of	ADP
fumecheng-7385	45	4	the	the	DET
fumecheng-7385	45	5	hpm	hpm	NOUN
fumecheng-7385	45	6	and	and	CCONJ
fumecheng-7385	45	7	the	the	DET
fumecheng-7385	45	8	laplace	laplace	NOUN
fumecheng-7385	45	9	transforms	transform	VERB
fumecheng-7385	45	10	were	be	AUX
fumecheng-7385	45	11	used	use	VERB
fumecheng-7385	45	12	by	by	ADP
fumecheng-7385	45	13	el	el	PROPN
fumecheng-7385	45	14	-	-	PROPN
fumecheng-7385	45	15	dib	dib	PROPN
fumecheng-7385	45	16	and	and	CCONJ
fumecheng-7385	45	17	moatimid	moatimid	NOUN
fumecheng-7385	46	1	[	[	X
fumecheng-7385	46	2	25	25	NUM
fumecheng-7385	46	3	]	]	PUNCT
fumecheng-7385	46	4	.	.	PUNCT
fumecheng-7385	47	1	el	el	PROPN
fumecheng-7385	47	2	-	-	PROPN
fumecheng-7385	47	3	dib	dib	PROPN
fumecheng-7385	47	4	[	[	X
fumecheng-7385	47	5	29	29	NUM
fumecheng-7385	47	6	]	]	PUNCT
fumecheng-7385	47	7	suggested	suggest	VERB
fumecheng-7385	47	8	a	a	DET
fumecheng-7385	47	9	modified	modified	ADJ
fumecheng-7385	47	10	version	version	NOUN
fumecheng-7385	47	11	of	of	ADP
fumecheng-7385	47	12	the	the	DET
fumecheng-7385	47	13	hpm	hpm	NOUN
fumecheng-7385	47	14	by	by	ADP
fumecheng-7385	47	15	the	the	DET
fumecheng-7385	47	16	multiple	multiple	ADJ
fumecheng-7385	47	17	scales	scale	NOUN
fumecheng-7385	47	18	technique	technique	NOUN
fumecheng-7385	47	19	.	.	PUNCT
fumecheng-7385	48	1	this	this	DET
fumecheng-7385	48	2	new	new	ADJ
fumecheng-7385	48	3	modification	modification	NOUN
fumecheng-7385	48	4	works	work	VERB
fumecheng-7385	48	5	well	well	ADV
fumecheng-7385	48	6	,	,	PUNCT
fumecheng-7385	48	7	particularly	particularly	ADV
fumecheng-7385	48	8	for	for	ADP
fumecheng-7385	48	9	nonlinear	nonlinear	ADJ
fumecheng-7385	48	10	oscillators	oscillator	NOUN
fumecheng-7385	48	11	.	.	PUNCT
fumecheng-7385	49	1	ren	ren	NOUN
fumecheng-7385	49	2	et	et	PROPN
fumecheng-7385	49	3	al	al	PROPN
fumecheng-7385	49	4	.	.	PUNCT
fumecheng-7385	50	1	[	[	X
fumecheng-7385	50	2	30	30	NUM
fumecheng-7385	50	3	]	]	PUNCT
fumecheng-7385	50	4	developed	develop	VERB
fumecheng-7385	50	5	the	the	DET
fumecheng-7385	50	6	multiple	multiple	ADJ
fumecheng-7385	50	7	scale	scale	NOUN
fumecheng-7385	50	8	by	by	ADP
fumecheng-7385	50	9	combining	combine	VERB
fumecheng-7385	50	10	it	it	PRON
fumecheng-7385	50	11	with	with	ADP
fumecheng-7385	50	12	the	the	DET
fumecheng-7385	50	13	hpm	hpm	NOUN
fumecheng-7385	50	14	to	to	PART
fumecheng-7385	50	15	improve	improve	VERB
fumecheng-7385	50	16	it	it	PRON
fumecheng-7385	50	17	by	by	ADP
fumecheng-7385	50	18	incorporating	incorporate	VERB
fumecheng-7385	50	19	some	some	DET
fumecheng-7385	50	20	known	know	VERB
fumecheng-7385	50	21	technologies	technology	NOUN
fumecheng-7385	50	22	.	.	PUNCT
fumecheng-7385	51	1	it	it	PRON
fumecheng-7385	51	2	provides	provide	VERB
fumecheng-7385	51	3	solutions	solution	NOUN
fumecheng-7385	51	4	to	to	ADP
fumecheng-7385	51	5	nonlinear	nonlinear	ADJ
fumecheng-7385	51	6	equations	equation	NOUN
fumecheng-7385	51	7	for	for	ADP
fumecheng-7385	51	8	which	which	PRON
fumecheng-7385	51	9	the	the	DET
fumecheng-7385	51	10	classical	classical	ADJ
fumecheng-7385	51	11	perturbation	perturbation	NOUN
fumecheng-7385	51	12	method	method	NOUN
fumecheng-7385	51	13	proved	prove	VERB
fumecheng-7385	51	14	unsuccessful	unsuccessful	ADJ
fumecheng-7385	51	15	.	.	PUNCT
fumecheng-7385	52	1	a	a	DET
fumecheng-7385	52	2	modification	modification	NOUN
fumecheng-7385	52	3	of	of	ADP
fumecheng-7385	52	4	the	the	DET
fumecheng-7385	52	5	hpm	hpm	NOUN
fumecheng-7385	52	6	with	with	ADP
fumecheng-7385	52	7	the	the	DET
fumecheng-7385	52	8	so	so	ADV
fumecheng-7385	52	9	-	-	PUNCT
fumecheng-7385	52	10	called	call	VERB
fumecheng-7385	52	11	reducing	reducing	NOUN
fumecheng-7385	52	12	-	-	PUNCT
fumecheng-7385	52	13	rank	rank	NOUN
fumecheng-7385	52	14	technique	technique	NOUN
fumecheng-7385	52	15	has	have	AUX
fumecheng-7385	52	16	been	be	AUX
fumecheng-7385	52	17	introduced	introduce	VERB
fumecheng-7385	52	18	by	by	ADP
fumecheng-7385	52	19	shen	shen	PROPN
fumecheng-7385	52	20	and	and	CCONJ
fumecheng-7385	52	21	el	el	PROPN
fumecheng-7385	52	22	-	-	PROPN
fumecheng-7385	52	23	dib	dib	PROPN
fumecheng-7385	52	24	[	[	X
fumecheng-7385	52	25	31	31	NUM
fumecheng-7385	52	26	]	]	PUNCT
fumecheng-7385	52	27	and	and	CCONJ
fumecheng-7385	52	28	el	el	PROPN
fumecheng-7385	52	29	-	-	PROPN
fumecheng-7385	52	30	dib	dib	PROPN
fumecheng-7385	52	31	and	and	CCONJ
fumecheng-7385	52	32	elgazery	elgazery	NOUN
fumecheng-7385	53	1	[	[	X
fumecheng-7385	53	2	32	32	NUM
fumecheng-7385	53	3	]	]	PUNCT
fumecheng-7385	53	4	.	.	PUNCT
fumecheng-7385	54	1	in	in	ADP
fumecheng-7385	54	2	this	this	DET
fumecheng-7385	54	3	paper	paper	NOUN
fumecheng-7385	54	4	,	,	PUNCT
fumecheng-7385	54	5	we	we	PRON
fumecheng-7385	54	6	present	present	VERB
fumecheng-7385	54	7	an	an	DET
fumecheng-7385	54	8	efficient	efficient	ADJ
fumecheng-7385	54	9	method	method	NOUN
fumecheng-7385	54	10	for	for	ADP
fumecheng-7385	54	11	the	the	DET
fumecheng-7385	54	12	approximation	approximation	NOUN
fumecheng-7385	54	13	of	of	ADP
fumecheng-7385	54	14	the	the	DET
fumecheng-7385	54	15	damped	damped	PROPN
fumecheng-7385	54	16	nonlinear	nonlinear	PROPN
fumecheng-7385	54	17	klein	klein	PROPN
fumecheng-7385	54	18	–	–	PUNCT
fumecheng-7385	54	19	gordon	gordon	PROPN
fumecheng-7385	54	20	equation	equation	NOUN
fumecheng-7385	54	21	,	,	PUNCT
fumecheng-7385	54	22	with	with	ADP
fumecheng-7385	54	23	the	the	DET
fumecheng-7385	54	24	aim	aim	NOUN
fumecheng-7385	54	25	to	to	PART
fumecheng-7385	54	26	solve	solve	VERB
fumecheng-7385	54	27	and	and	CCONJ
fumecheng-7385	54	28	study	study	VERB
fumecheng-7385	54	29	the	the	DET
fumecheng-7385	54	30	stability	stability	NOUN
fumecheng-7385	54	31	of	of	ADP
fumecheng-7385	54	32	the	the	DET
fumecheng-7385	54	33	periodic	periodic	ADJ
fumecheng-7385	54	34	solution	solution	NOUN
fumecheng-7385	54	35	.	.	PUNCT
fumecheng-7385	55	1	the	the	DET
fumecheng-7385	55	2	enhanced	enhance	VERB
fumecheng-7385	55	3	homotopy	homotopy	PROPN
fumecheng-7385	55	4	perturbation	perturbation	NOUN
fumecheng-7385	55	5	method	method	NOUN
fumecheng-7385	55	6	for	for	ADP
fumecheng-7385	55	7	axial	axial	ADJ
fumecheng-7385	55	8	vibrations	vibration	NOUN
fumecheng-7385	55	9	of	of	ADP
fumecheng-7385	55	10	strings	string	NOUN
fumecheng-7385	55	11	737	737	NUM
fumecheng-7385	55	12	the	the	DET
fumecheng-7385	55	13	key	key	ADJ
fumecheng-7385	55	14	features	feature	NOUN
fumecheng-7385	55	15	of	of	ADP
fumecheng-7385	55	16	our	our	PRON
fumecheng-7385	55	17	methods	method	NOUN
fumecheng-7385	55	18	are	be	AUX
fumecheng-7385	55	19	based	base	VERB
fumecheng-7385	55	20	on	on	ADP
fumecheng-7385	55	21	the	the	DET
fumecheng-7385	55	22	coupling	coupling	NOUN
fumecheng-7385	55	23	of	of	ADP
fumecheng-7385	55	24	the	the	DET
fumecheng-7385	55	25	exponential	exponential	ADJ
fumecheng-7385	55	26	decay	decay	NOUN
fumecheng-7385	55	27	parameter	parameter	NOUN
fumecheng-7385	55	28	to	to	ADP
fumecheng-7385	55	29	the	the	DET
fumecheng-7385	55	30	homotopy	homotopy	NOUN
fumecheng-7385	55	31	perturbation	perturbation	NOUN
fumecheng-7385	55	32	method	method	NOUN
fumecheng-7385	55	33	to	to	PART
fumecheng-7385	55	34	overcome	overcome	VERB
fumecheng-7385	55	35	the	the	DET
fumecheng-7385	55	36	shortcomings	shortcoming	NOUN
fumecheng-7385	55	37	of	of	ADP
fumecheng-7385	55	38	the	the	DET
fumecheng-7385	55	39	classical	classical	ADJ
fumecheng-7385	55	40	method	method	NOUN
fumecheng-7385	55	41	.	.	PUNCT
fumecheng-7385	56	1	2	2	X
fumecheng-7385	56	2	.	.	X
fumecheng-7385	56	3	mathematical	mathematical	ADJ
fumecheng-7385	56	4	model	model	NOUN
fumecheng-7385	56	5	of	of	ADP
fumecheng-7385	56	6	the	the	DET
fumecheng-7385	56	7	damping	damp	VERB
fumecheng-7385	56	8	nonlinear	nonlinear	PROPN
fumecheng-7385	56	9	klein	klein	PROPN
fumecheng-7385	56	10	-	-	PUNCT
fumecheng-7385	56	11	gordon	gordon	PROPN
fumecheng-7385	56	12	equation	equation	NOUN
fumecheng-7385	56	13	the	the	DET
fumecheng-7385	56	14	governing	govern	VERB
fumecheng-7385	56	15	equation	equation	NOUN
fumecheng-7385	56	16	can	can	AUX
fumecheng-7385	56	17	be	be	AUX
fumecheng-7385	56	18	obtained	obtain	VERB
fumecheng-7385	56	19	from	from	ADP
fumecheng-7385	56	20	the	the	DET
fumecheng-7385	56	21	following	follow	VERB
fumecheng-7385	56	22	variational	variational	ADJ
fumecheng-7385	56	23	principle	principle	NOUN
fumecheng-7385	57	1	[	[	X
fumecheng-7385	57	2	14,15	14,15	NUM
fumecheng-7385	57	3	]	]	SYM
fumecheng-7385	57	4	:	:	PUNCT
fumecheng-7385	57	5	2	2	NUM
fumecheng-7385	57	6	1	1	NUM
fumecheng-7385	57	7	{	{	PUNCT
fumecheng-7385	57	8	}	}	PUNCT
fumecheng-7385	57	9	0	0	NUM
fumecheng-7385	58	1	t	t	NOUN
fumecheng-7385	58	2	t	t	PROPN
fumecheng-7385	59	1	k	k	PROPN
fumecheng-7385	59	2	p	p	X
fumecheng-7385	59	3	w	w	PROPN
fumecheng-7385	59	4	dt−	dt−	PROPN
fumecheng-7385	59	5	+	+	CCONJ
fumecheng-7385	59	6	=	=	NOUN
fumecheng-7385	59	7			ADP
fumecheng-7385	59	8			NUM
fumecheng-7385	59	9			NUM
fumecheng-7385	59	10			NUM
fumecheng-7385	59	11	(	(	PUNCT
fumecheng-7385	59	12	1	1	NUM
fumecheng-7385	59	13	)	)	PUNCT
fumecheng-7385	59	14	where	where	SCONJ
fumecheng-7385	59	15	k	k	NOUN
fumecheng-7385	59	16	,	,	PUNCT
fumecheng-7385	59	17	p	p	X
fumecheng-7385	59	18	,	,	PUNCT
fumecheng-7385	59	19	and	and	CCONJ
fumecheng-7385	59	20	w	w	PROPN
fumecheng-7385	59	21	represent	represent	NOUN
fumecheng-7385	59	22	,	,	PUNCT
fumecheng-7385	59	23	respectively	respectively	ADV
fumecheng-7385	59	24	,	,	PUNCT
fumecheng-7385	59	25	the	the	DET
fumecheng-7385	59	26	kinetic	kinetic	ADJ
fumecheng-7385	59	27	energy	energy	NOUN
fumecheng-7385	59	28	,	,	PUNCT
fumecheng-7385	59	29	the	the	DET
fumecheng-7385	59	30	potential	potential	ADJ
fumecheng-7385	59	31	energy	energy	NOUN
fumecheng-7385	59	32	,	,	PUNCT
fumecheng-7385	59	33	and	and	CCONJ
fumecheng-7385	59	34	the	the	DET
fumecheng-7385	59	35	work	work	NOUN
fumecheng-7385	59	36	done	do	VERB
fumecheng-7385	59	37	by	by	ADP
fumecheng-7385	59	38	the	the	DET
fumecheng-7385	59	39	external	external	ADJ
fumecheng-7385	59	40	force	force	NOUN
fumecheng-7385	59	41	;	;	PUNCT
fumecheng-7385	59	42	k	k	NOUN
fumecheng-7385	59	43	.	.	PUNCT
fumecheng-7385	60	1	p	p	NOUN
fumecheng-7385	60	2	and	and	CCONJ
fumecheng-7385	60	3	w	w	VERB
fumecheng-7385	60	4	can	can	AUX
fumecheng-7385	60	5	be	be	AUX
fumecheng-7385	60	6	expressed	express	VERB
fumecheng-7385	60	7	,	,	PUNCT
fumecheng-7385	60	8	respectively	respectively	ADV
fumecheng-7385	60	9	,	,	PUNCT
fumecheng-7385	60	10	as	as	ADP
fumecheng-7385	60	11	2	2	NUM
fumecheng-7385	60	12	0	0	NUM
fumecheng-7385	60	13	0	0	NUM
fumecheng-7385	60	14	1	1	NUM
fumecheng-7385	60	15	(	(	PUNCT
fumecheng-7385	60	16	)	)	PUNCT
fumecheng-7385	60	17	2	2	NUM
fumecheng-7385	60	18	l	l	NOUN
fumecheng-7385	60	19	ly	ly	X
fumecheng-7385	60	20	y	y	PROPN
fumecheng-7385	60	21	k	k	PROPN
fumecheng-7385	60	22	dx	dx	PROPN
fumecheng-7385	61	1	ydx	ydx	NOUN
fumecheng-7385	61	2	t	t	PROPN
fumecheng-7385	61	3	t	t	PROPN
fumecheng-7385	61	4			NUM
fumecheng-7385	61	5			NUM
fumecheng-7385	61	6			ADP
fumecheng-7385	61	7			PUNCT
fumecheng-7385	61	8			NUM
fumecheng-7385	61	9			ADJ
fumecheng-7385	61	10			NOUN
fumecheng-7385	61	11	=	=	SYM
fumecheng-7385	62	1	−	−	PROPN
fumecheng-7385	62	2			ADJ
fumecheng-7385	62	3			NOUN
fumecheng-7385	62	4			X
fumecheng-7385	62	5	(	(	PUNCT
fumecheng-7385	62	6	2	2	NUM
fumecheng-7385	62	7	)	)	PUNCT
fumecheng-7385	62	8	2	2	NUM
fumecheng-7385	62	9	0	0	NUM
fumecheng-7385	62	10	0	0	NUM
fumecheng-7385	62	11	0	0	NUM
fumecheng-7385	62	12	0	0	NUM
fumecheng-7385	62	13	1	1	NUM
fumecheng-7385	62	14	(	(	PUNCT
fumecheng-7385	62	15	)	)	PUNCT
fumecheng-7385	62	16	2	2	NUM
fumecheng-7385	62	17	l	l	NOUN
fumecheng-7385	62	18	l	l	NOUN
fumecheng-7385	62	19	l	l	NOUN
fumecheng-7385	62	20	ly	ly	X
fumecheng-7385	63	1	y	y	PROPN
fumecheng-7385	63	2	y	y	PROPN
fumecheng-7385	63	3	p	p	PROPN
fumecheng-7385	64	1	t	t	X
fumecheng-7385	64	2	dx	dx	PROPN
fumecheng-7385	65	1	ydx	ydx	PROPN
fumecheng-7385	65	2	t	t	PROPN
fumecheng-7385	65	3	dx	dx	PROPN
fumecheng-7385	65	4	ydx	ydx	NOUN
fumecheng-7385	66	1	x	x	PUNCT
fumecheng-7385	66	2	x	x	PUNCT
fumecheng-7385	66	3	x	x	X
fumecheng-7385	66	4			NUM
fumecheng-7385	66	5			NUM
fumecheng-7385	66	6			PROPN
fumecheng-7385	66	7			NOUN
fumecheng-7385	66	8			NUM
fumecheng-7385	66	9			NOUN
fumecheng-7385	66	10			NUM
fumecheng-7385	66	11			ADJ
fumecheng-7385	66	12			ADJ
fumecheng-7385	66	13			NOUN
fumecheng-7385	66	14	=	=	SYM
fumecheng-7385	66	15	−	−	PROPN
fumecheng-7385	66	16	=	=	PUNCT
fumecheng-7385	67	1	−	−	PROPN
fumecheng-7385	67	2			ADJ
fumecheng-7385	67	3			ADJ
fumecheng-7385	67	4			ADJ
fumecheng-7385	67	5			NOUN
fumecheng-7385	67	6			X
fumecheng-7385	67	7			X
fumecheng-7385	67	8	(	(	PUNCT
fumecheng-7385	67	9	3	3	NUM
fumecheng-7385	67	10	)	)	PUNCT
fumecheng-7385	67	11	0	0	NUM
fumecheng-7385	68	1	l	l	NOUN
fumecheng-7385	68	2	w	w	PROPN
fumecheng-7385	68	3	f	f	PROPN
fumecheng-7385	68	4	udx	udx	ADJ
fumecheng-7385	68	5	=	=	NOUN
fumecheng-7385	68	6			PUNCT
fumecheng-7385	68	7	(	(	PUNCT
fumecheng-7385	68	8	4	4	X
fumecheng-7385	68	9	)	)	PUNCT
fumecheng-7385	68	10	here	here	ADV
fumecheng-7385	68	11	y	y	PROPN
fumecheng-7385	68	12	is	be	AUX
fumecheng-7385	68	13	the	the	DET
fumecheng-7385	68	14	axial	axial	ADJ
fumecheng-7385	68	15	displacement	displacement	NOUN
fumecheng-7385	68	16	,	,	PUNCT
fumecheng-7385	68	17			ADP
fumecheng-7385	68	18	is	be	AUX
fumecheng-7385	68	19	the	the	DET
fumecheng-7385	68	20	density	density	NOUN
fumecheng-7385	68	21	,	,	PUNCT
fumecheng-7385	68	22	t	t	PROPN
fumecheng-7385	68	23	is	be	AUX
fumecheng-7385	68	24	the	the	DET
fumecheng-7385	68	25	surface	surface	NOUN
fumecheng-7385	68	26	tension	tension	NOUN
fumecheng-7385	68	27	of	of	ADP
fumecheng-7385	68	28	the	the	DET
fumecheng-7385	68	29	string	string	NOUN
fumecheng-7385	68	30	,	,	PUNCT
fumecheng-7385	68	31	f	f	PROPN
fumecheng-7385	68	32	is	be	AUX
fumecheng-7385	68	33	the	the	DET
fumecheng-7385	68	34	external	external	ADJ
fumecheng-7385	68	35	force	force	NOUN
fumecheng-7385	68	36	,	,	PUNCT
fumecheng-7385	68	37			PRON
fumecheng-7385	68	38	represents	represent	VERB
fumecheng-7385	68	39	the	the	DET
fumecheng-7385	68	40	temporal	temporal	ADJ
fumecheng-7385	68	41	damped	damped	ADJ
fumecheng-7385	68	42	coefficient	coefficient	NOUN
fumecheng-7385	68	43	,	,	PUNCT
fumecheng-7385	68	44			NOUN
fumecheng-7385	68	45	stands	stand	VERB
fumecheng-7385	68	46	for	for	ADP
fumecheng-7385	68	47	the	the	DET
fumecheng-7385	68	48	spatial	spatial	ADJ
fumecheng-7385	68	49	damped	damped	NOUN
fumecheng-7385	68	50	coefficient	coefficient	NOUN
fumecheng-7385	68	51	,	,	PUNCT
fumecheng-7385	68	52	+	+	CCONJ
fumecheng-7385	69	1	0tt	0tt	ADJ
fumecheng-7385	69	2	t	t	NOUN
fumecheng-7385	69	3	xx	xx	NUM
fumecheng-7385	70	1	xy	xy	INTJ
fumecheng-7385	70	2	y	y	INTJ
fumecheng-7385	70	3	ty	ty	INTJ
fumecheng-7385	70	4	y	y	PROPN
fumecheng-7385	70	5	f	f	VERB
fumecheng-7385	70	6			NUM
fumecheng-7385	70	7	−	−	PROPN
fumecheng-7385	71	1	+	+	CCONJ
fumecheng-7385	72	1	−	−	PROPN
fumecheng-7385	73	1	=	=	SYM
fumecheng-7385	74	1	(	(	PUNCT
fumecheng-7385	74	2	5	5	NUM
fumecheng-7385	74	3	)	)	PUNCT
fumecheng-7385	74	4	eq	eq	NOUN
fumecheng-7385	74	5	.	.	PUNCT
fumecheng-7385	75	1	(	(	PUNCT
fumecheng-7385	75	2	5	5	X
fumecheng-7385	75	3	)	)	PUNCT
fumecheng-7385	75	4	can	can	AUX
fumecheng-7385	75	5	be	be	AUX
fumecheng-7385	75	6	re	re	VERB
fumecheng-7385	75	7	-	-	VERB
fumecheng-7385	75	8	written	write	VERB
fumecheng-7385	75	9	as	as	ADP
fumecheng-7385	75	10	+2	+2	PROPN
fumecheng-7385	75	11	2	2	NUM
fumecheng-7385	75	12	0tt	0tt	NOUN
fumecheng-7385	76	1	xx	xx	INTJ
fumecheng-7385	77	1	t	t	NOUN
fumecheng-7385	77	2	xy	xy	INTJ
fumecheng-7385	78	1	py	py	INTJ
fumecheng-7385	78	2	y	y	PROPN
fumecheng-7385	78	3	y	y	PROPN
fumecheng-7385	78	4	f	f	NOUN
fumecheng-7385	78	5	−	−	PROPN
fumecheng-7385	79	1	+	+	CCONJ
fumecheng-7385	80	1	−	−	PUNCT
fumecheng-7385	80	2	=	=	SYM
fumecheng-7385	80	3	(	(	PUNCT
fumecheng-7385	80	4	6	6	NUM
fumecheng-7385	80	5	)	)	PUNCT
fumecheng-7385	80	6	where	where	SCONJ
fumecheng-7385	80	7	p	p	X
fumecheng-7385	80	8	=	=	NOUN
fumecheng-7385	80	9	t/	t/	NOUN
fumecheng-7385	80	10	,	,	PUNCT
fumecheng-7385	80	11	f	f	PROPN
fumecheng-7385	80	12	=	=	SYM
fumecheng-7385	80	13	f/	f/	NOUN
fumecheng-7385	80	14	,	,	PUNCT
fumecheng-7385	80	15	/	/	PUNCT
fumecheng-7385	80	16			PUNCT
fumecheng-7385	81	1	=	=	NOUN
fumecheng-7385	81	2	and	and	CCONJ
fumecheng-7385	81	3	/	/	PRON
fumecheng-7385	81	4			NOUN
fumecheng-7385	81	5	=	=	ADV
fumecheng-7385	81	6	,	,	PUNCT
fumecheng-7385	81	7	while	while	SCONJ
fumecheng-7385	81	8	y(x	y(x	PROPN
fumecheng-7385	81	9	,	,	PUNCT
fumecheng-7385	81	10	t	t	PROPN
fumecheng-7385	81	11	)	)	PUNCT
fumecheng-7385	81	12	is	be	AUX
fumecheng-7385	81	13	the	the	DET
fumecheng-7385	81	14	displacement	displacement	NOUN
fumecheng-7385	81	15	at	at	ADP
fumecheng-7385	81	16	location	location	NOUN
fumecheng-7385	81	17	x	x	PUNCT
fumecheng-7385	81	18	and	and	CCONJ
fumecheng-7385	81	19	time	time	NOUN
fumecheng-7385	81	20	t.	t.	PROPN
fumecheng-7385	81	21	when	when	SCONJ
fumecheng-7385	81	22	,	,	PUNCT
fumecheng-7385	81	23	0==	0==	NUM
fumecheng-7385	81	24			ADJ
fumecheng-7385	81	25	eq	eq	ADP
fumecheng-7385	81	26	.	.	PUNCT
fumecheng-7385	81	27	(	(	PUNCT
fumecheng-7385	81	28	6	6	NUM
fumecheng-7385	81	29	)	)	PUNCT
fumecheng-7385	81	30	,	,	PUNCT
fumecheng-7385	81	31	the	the	DET
fumecheng-7385	81	32	klein	klein	PROPN
fumecheng-7385	81	33	-	-	PUNCT
fumecheng-7385	81	34	gordon	gordon	PROPN
fumecheng-7385	81	35	equation	equation	NOUN
fumecheng-7385	81	36	becomes	become	VERB
fumecheng-7385	81	37	:	:	PUNCT
fumecheng-7385	81	38	0tt	0tt	ADJ
fumecheng-7385	81	39	xxy	xxy	PROPN
fumecheng-7385	81	40	py	py	PROPN
fumecheng-7385	82	1	f−	f−	PROPN
fumecheng-7385	82	2	−	−	PROPN
fumecheng-7385	83	1	=	=	PUNCT
fumecheng-7385	83	2	(	(	PUNCT
fumecheng-7385	83	3	7	7	NUM
fumecheng-7385	83	4	)	)	PUNCT
fumecheng-7385	83	5	when	when	SCONJ
fumecheng-7385	83	6	f	f	X
fumecheng-7385	83	7	y=	y=	NOUN
fumecheng-7385	83	8	−	−	PROPN
fumecheng-7385	83	9	(	(	PUNCT
fumecheng-7385	83	10	8)	8)	NUM
fumecheng-7385	83	11	we	we	PRON
fumecheng-7385	83	12	have	have	AUX
fumecheng-7385	83	13	a	a	DET
fumecheng-7385	83	14	linear	linear	ADJ
fumecheng-7385	83	15	damped	damp	VERB
fumecheng-7385	83	16	klein	klein	PROPN
fumecheng-7385	83	17	-	-	PUNCT
fumecheng-7385	83	18	gordon	gordon	PROPN
fumecheng-7385	83	19	equation	equation	NOUN
fumecheng-7385	83	20	+2	+2	ADP
fumecheng-7385	83	21	2	2	NUM
fumecheng-7385	84	1	+	+	CCONJ
fumecheng-7385	84	2	0tt	0tt	ADJ
fumecheng-7385	85	1	xx	xx	INTJ
fumecheng-7385	86	1	t	t	NOUN
fumecheng-7385	86	2	xy	xy	INTJ
fumecheng-7385	87	1	py	py	INTJ
fumecheng-7385	87	2	y	y	PROPN
fumecheng-7385	87	3	y	y	PROPN
fumecheng-7385	87	4	y	y	PROPN
fumecheng-7385	88	1			NOUN
fumecheng-7385	88	2	−	−	NOUN
fumecheng-7385	89	1	+	+	CCONJ
fumecheng-7385	89	2	=	=	SYM
fumecheng-7385	89	3	(	(	PUNCT
fumecheng-7385	89	4	9	9	NUM
fumecheng-7385	89	5	)	)	PUNCT
fumecheng-7385	89	6	in	in	ADP
fumecheng-7385	89	7	this	this	DET
fumecheng-7385	89	8	paper	paper	NOUN
fumecheng-7385	89	9	,	,	PUNCT
fumecheng-7385	89	10	we	we	PRON
fumecheng-7385	89	11	consider	consider	VERB
fumecheng-7385	89	12	a	a	DET
fumecheng-7385	89	13	cubic	cubic	ADJ
fumecheng-7385	89	14	nonlinear	nonlinear	NOUN
fumecheng-7385	89	15	case	case	NOUN
fumecheng-7385	89	16	3f	3f	PROPN
fumecheng-7385	89	17	y	y	PROPN
fumecheng-7385	89	18	qy=	qy=	PROPN
fumecheng-7385	90	1	−	−	PROPN
fumecheng-7385	90	2	+	+	CCONJ
fumecheng-7385	90	3	(	(	PUNCT
fumecheng-7385	90	4	10	10	NUM
fumecheng-7385	90	5	)	)	PUNCT
fumecheng-7385	90	6	we	we	PRON
fumecheng-7385	90	7	have	have	VERB
fumecheng-7385	90	8	the	the	DET
fumecheng-7385	90	9	following	follow	VERB
fumecheng-7385	90	10	one	one	NUM
fumecheng-7385	90	11	-	-	PUNCT
fumecheng-7385	90	12	dimensional	dimensional	ADJ
fumecheng-7385	90	13	nonlinear	nonlinear	ADJ
fumecheng-7385	90	14	wave	wave	NOUN
fumecheng-7385	90	15	equation	equation	NOUN
fumecheng-7385	90	16	with	with	ADP
fumecheng-7385	90	17	linear	linear	ADJ
fumecheng-7385	90	18	damping	damp	VERB
fumecheng-7385	90	19	parameters	parameter	NOUN
fumecheng-7385	90	20	:	:	PUNCT
fumecheng-7385	90	21	)	)	PUNCT
fumecheng-7385	90	22	.,(;22	.,(;22	NOUN
fumecheng-7385	90	23	3	3	NUM
fumecheng-7385	90	24	txyyqyyyypyy	txyyqyyyypyy	NOUN
fumecheng-7385	90	25	xtxxtt	xtxxtt	PUNCT
fumecheng-7385	91	1	=	=	PUNCT
fumecheng-7385	91	2	=	=	SYM
fumecheng-7385	91	3	+	+	ADJ
fumecheng-7385	91	4	+	+	ADJ
fumecheng-7385	91	5	+	+	ADJ
fumecheng-7385	91	6	−	−	PROPN
fumecheng-7385	91	7			PROPN
fumecheng-7385	91	8	(	(	PUNCT
fumecheng-7385	91	9	11	11	NUM
fumecheng-7385	91	10	)	)	PUNCT
fumecheng-7385	91	11	where	where	SCONJ
fumecheng-7385	91	12			PROPN
fumecheng-7385	91	13	refers	refer	VERB
fumecheng-7385	91	14	to	to	ADP
fumecheng-7385	91	15	the	the	DET
fumecheng-7385	91	16	natural	natural	ADJ
fumecheng-7385	91	17	frequency	frequency	NOUN
fumecheng-7385	91	18	,	,	PUNCT
fumecheng-7385	91	19	and	and	CCONJ
fumecheng-7385	91	20	q	q	PROPN
fumecheng-7385	91	21	stands	stand	VERB
fumecheng-7385	91	22	for	for	ADP
fumecheng-7385	91	23	the	the	DET
fumecheng-7385	91	24	cubic	cubic	ADJ
fumecheng-7385	91	25	-	-	PUNCT
fumecheng-7385	91	26	stiffness	stiffness	NOUN
fumecheng-7385	91	27	parameter	parameter	NOUN
fumecheng-7385	91	28	.	.	PUNCT
fumecheng-7385	92	1	738	738	NUM
fumecheng-7385	92	2	j.-h	j.-h	NOUN
fumecheng-7385	92	3	.	.	PUNCT
fumecheng-7385	93	1	he	he	PRON
fumecheng-7385	93	2	,	,	PUNCT
fumecheng-7385	93	3	y.	y.	PROPN
fumecheng-7385	93	4	o.	o.	PROPN
fumecheng-7385	93	5	el	el	PROPN
fumecheng-7385	93	6	-	-	PROPN
fumecheng-7385	93	7	dib	dib	PROPN
fumecheng-7385	93	8	eq	eq	NOUN
fumecheng-7385	93	9	.	.	PUNCT
fumecheng-7385	94	1	(	(	PUNCT
fumecheng-7385	94	2	11	11	NUM
fumecheng-7385	94	3	)	)	PUNCT
fumecheng-7385	94	4	becomes	become	VERB
fumecheng-7385	94	5	the	the	DET
fumecheng-7385	94	6	classical	classical	ADJ
fumecheng-7385	94	7	nonlinear	nonlinear	PROPN
fumecheng-7385	94	8	klein	klein	PROPN
fumecheng-7385	94	9	–	–	PUNCT
fumecheng-7385	94	10	gordon	gordon	PROPN
fumecheng-7385	94	11	equation	equation	NOUN
fumecheng-7385	94	12	that	that	PRON
fumecheng-7385	94	13	appears	appear	VERB
fumecheng-7385	94	14	in	in	ADP
fumecheng-7385	94	15	various	various	ADJ
fumecheng-7385	94	16	branches	branch	NOUN
fumecheng-7385	94	17	of	of	ADP
fumecheng-7385	94	18	science	science	NOUN
fumecheng-7385	94	19	,	,	PUNCT
fumecheng-7385	94	20	including	include	VERB
fumecheng-7385	94	21	quantum	quantum	NOUN
fumecheng-7385	94	22	mechanics	mechanic	NOUN
fumecheng-7385	94	23	,	,	PUNCT
fumecheng-7385	94	24	nonlinear	nonlinear	ADJ
fumecheng-7385	94	25	optics	optic	NOUN
fumecheng-7385	94	26	fluid	fluid	ADJ
fumecheng-7385	94	27	mechanics	mechanic	NOUN
fumecheng-7385	94	28	,	,	PUNCT
fumecheng-7385	94	29	and	and	CCONJ
fumecheng-7385	94	30	solid	solid	ADJ
fumecheng-7385	94	31	physics	physics	NOUN
fumecheng-7385	94	32	.	.	PUNCT
fumecheng-7385	95	1	in	in	ADP
fumecheng-7385	95	2	the	the	DET
fumecheng-7385	95	3	case	case	NOUN
fumecheng-7385	95	4	of	of	ADP
fumecheng-7385	95	5			NUM
fumecheng-7385	95	6	>	>	SYM
fumecheng-7385	95	7	0	0	NUM
fumecheng-7385	95	8	and	and	CCONJ
fumecheng-7385	95	9			NOUN
fumecheng-7385	95	10	=	=	SYM
fumecheng-7385	95	11	0	0	NUM
fumecheng-7385	95	12	,	,	PUNCT
fumecheng-7385	95	13	with	with	ADP
fumecheng-7385	95	14	some	some	DET
fumecheng-7385	95	15	specific	specific	ADJ
fumecheng-7385	95	16	nonlinearities	nonlinearitie	NOUN
fumecheng-7385	95	17	,	,	PUNCT
fumecheng-7385	95	18	eq	eq	NOUN
fumecheng-7385	95	19	.	.	PUNCT
fumecheng-7385	95	20	(	(	PUNCT
fumecheng-7385	95	21	11	11	NUM
fumecheng-7385	95	22	)	)	PUNCT
fumecheng-7385	95	23	becomes	become	VERB
fumecheng-7385	95	24	a	a	DET
fumecheng-7385	95	25	one	one	NUM
fumecheng-7385	95	26	-	-	PUNCT
fumecheng-7385	95	27	dimensional	dimensional	ADJ
fumecheng-7385	95	28	temporal	temporal	ADJ
fumecheng-7385	95	29	damped	damped	NOUN
fumecheng-7385	95	30	nonlinear	nonlinear	PROPN
fumecheng-7385	95	31	klein	klein	PROPN
fumecheng-7385	95	32	-	-	PUNCT
fumecheng-7385	95	33	gordon	gordon	PROPN
fumecheng-7385	95	34	equation	equation	NOUN
fumecheng-7385	95	35	[	[	X
fumecheng-7385	95	36	33	33	NUM
fumecheng-7385	95	37	]	]	PUNCT
fumecheng-7385	95	38	.	.	PUNCT
fumecheng-7385	96	1	el	el	PROPN
fumecheng-7385	96	2	-	-	PROPN
fumecheng-7385	96	3	dib	dib	PROPN
fumecheng-7385	96	4	et	et	NOUN
fumecheng-7385	96	5	al	al	PROPN
fumecheng-7385	96	6	.	.	PUNCT
fumecheng-7385	97	1	[	[	X
fumecheng-7385	97	2	34	34	NUM
fumecheng-7385	97	3	]	]	PUNCT
fumecheng-7385	97	4	discussed	discuss	VERB
fumecheng-7385	97	5	the	the	DET
fumecheng-7385	97	6	time	time	NOUN
fumecheng-7385	97	7	fraction	fraction	NOUN
fumecheng-7385	97	8	of	of	ADP
fumecheng-7385	97	9	the	the	DET
fumecheng-7385	97	10	damped	damped	NOUN
fumecheng-7385	97	11	kg	kg	X
fumecheng-7385	97	12	equation	equation	NOUN
fumecheng-7385	97	13	to	to	PART
fumecheng-7385	97	14	overcome	overcome	VERB
fumecheng-7385	97	15	the	the	DET
fumecheng-7385	97	16	presence	presence	NOUN
fumecheng-7385	97	17	of	of	ADP
fumecheng-7385	97	18	the	the	DET
fumecheng-7385	97	19	non	non	ADJ
fumecheng-7385	97	20	-	-	ADJ
fumecheng-7385	97	21	zero	zero	ADJ
fumecheng-7385	97	22	damping	damp	VERB
fumecheng-7385	97	23	coefficients	coefficient	NOUN
fumecheng-7385	97	24	.	.	PUNCT
fumecheng-7385	98	1	besides	besides	SCONJ
fumecheng-7385	98	2	,	,	PUNCT
fumecheng-7385	98	3	they	they	PRON
fumecheng-7385	98	4	applied	apply	VERB
fumecheng-7385	98	5	the	the	DET
fumecheng-7385	98	6	modified	modify	VERB
fumecheng-7385	98	7	multiple	multiple	ADJ
fumecheng-7385	98	8	scales	scale	NOUN
fumecheng-7385	98	9	method	method	NOUN
fumecheng-7385	98	10	for	for	ADP
fumecheng-7385	98	11	the	the	DET
fumecheng-7385	98	12	same	same	ADJ
fumecheng-7385	98	13	aims	aim	NOUN
fumecheng-7385	98	14	.	.	PUNCT
fumecheng-7385	99	1	if	if	SCONJ
fumecheng-7385	99	2	the	the	DET
fumecheng-7385	99	3	cubic	cubic	ADJ
fumecheng-7385	99	4	term	term	NOUN
fumecheng-7385	99	5	in	in	ADP
fumecheng-7385	99	6	eq	eq	ADP
fumecheng-7385	99	7	.	.	PUNCT
fumecheng-7385	100	1	(	(	PUNCT
fumecheng-7385	100	2	11	11	NUM
fumecheng-7385	100	3	)	)	PUNCT
fumecheng-7385	100	4	becomes	becomes	AUX
fumecheng-7385	100	5	vanishing	vanish	VERB
fumecheng-7385	100	6	because	because	SCONJ
fumecheng-7385	100	7	it	it	PRON
fumecheng-7385	100	8	is	be	AUX
fumecheng-7385	100	9	small	small	ADJ
fumecheng-7385	100	10	compared	compare	VERB
fumecheng-7385	100	11	to	to	ADP
fumecheng-7385	100	12	the	the	DET
fumecheng-7385	100	13	linear	linear	ADJ
fumecheng-7385	100	14	term	term	NOUN
fumecheng-7385	100	15	,	,	PUNCT
fumecheng-7385	100	16	then	then	ADV
fumecheng-7385	100	17	the	the	DET
fumecheng-7385	100	18	right	right	ADJ
fumecheng-7385	100	19	-	-	PUNCT
fumecheng-7385	100	20	hand	hand	NOUN
fumecheng-7385	100	21	side	side	NOUN
fumecheng-7385	100	22	term	term	NOUN
fumecheng-7385	100	23	contributes	contribute	VERB
fumecheng-7385	100	24	to	to	ADP
fumecheng-7385	100	25	the	the	DET
fumecheng-7385	100	26	order	order	NOUN
fumecheng-7385	100	27	of	of	ADP
fumecheng-7385	100	28	y3	y3	NOUN
fumecheng-7385	100	29	and	and	CCONJ
fumecheng-7385	100	30	thus	thus	ADV
fumecheng-7385	100	31	can	can	AUX
fumecheng-7385	100	32	be	be	AUX
fumecheng-7385	100	33	neglected	neglect	VERB
fumecheng-7385	100	34	.	.	PUNCT
fumecheng-7385	101	1	in	in	ADP
fumecheng-7385	101	2	the	the	DET
fumecheng-7385	101	3	linear	linear	PROPN
fumecheng-7385	101	4	limit	limit	NOUN
fumecheng-7385	101	5	,	,	PUNCT
fumecheng-7385	101	6	eq	eq	NOUN
fumecheng-7385	101	7	.	.	PUNCT
fumecheng-7385	102	1	(	(	PUNCT
fumecheng-7385	102	2	11	11	NUM
fumecheng-7385	102	3	)	)	PUNCT
fumecheng-7385	102	4	has	have	VERB
fumecheng-7385	102	5	the	the	DET
fumecheng-7385	102	6	well	well	ADV
fumecheng-7385	102	7	-	-	PUNCT
fumecheng-7385	102	8	known	know	VERB
fumecheng-7385	102	9	exact	exact	ADJ
fumecheng-7385	102	10	temporal	temporal	ADJ
fumecheng-7385	102	11	solution	solution	NOUN
fumecheng-7385	102	12	for	for	ADP
fumecheng-7385	102	13	the	the	DET
fumecheng-7385	102	14	damped	damped	NOUN
fumecheng-7385	102	15	system	system	NOUN
fumecheng-7385	102	16	given	give	VERB
fumecheng-7385	102	17	by	by	ADP
fumecheng-7385	102	18	:	:	PUNCT
fumecheng-7385	102	19	(	(	PUNCT
fumecheng-7385	102	20	)	)	PUNCT
fumecheng-7385	102	21	cos	cos	PROPN
fumecheng-7385	102	22	(	(	PUNCT
fumecheng-7385	102	23	)	)	PUNCT
fumecheng-7385	102	24	,	,	PUNCT
fumecheng-7385	102	25	t	t	PROPN
fumecheng-7385	102	26	x	x	X
fumecheng-7385	102	27	py	py	PROPN
fumecheng-7385	102	28	t	t	PROPN
fumecheng-7385	102	29	ae	ae	PROPN
fumecheng-7385	102	30	t	t	PROPN
fumecheng-7385	103	1	−	−	PROPN
fumecheng-7385	104	1	−	−	PROPN
fumecheng-7385	105	1	=	=	SYM
fumecheng-7385	106	1	+	+	NUM
fumecheng-7385	106	2			NOUN
fumecheng-7385	106	3			NUM
fumecheng-7385	106	4			X
fumecheng-7385	106	5			X
fumecheng-7385	106	6	(	(	PUNCT
fumecheng-7385	106	7	12	12	NUM
fumecheng-7385	106	8	)	)	PUNCT
fumecheng-7385	106	9	where	where	SCONJ
fumecheng-7385	106	10	a	a	PRON
fumecheng-7385	106	11	and	and	CCONJ
fumecheng-7385	106	12			NOUN
fumecheng-7385	106	13	are	be	AUX
fumecheng-7385	106	14	real	real	ADJ
fumecheng-7385	106	15	constants	constant	NOUN
fumecheng-7385	106	16	determined	determine	VERB
fumecheng-7385	106	17	by	by	ADP
fumecheng-7385	106	18	the	the	DET
fumecheng-7385	106	19	initial	initial	ADJ
fumecheng-7385	106	20	conditions	condition	NOUN
fumecheng-7385	106	21	.	.	PUNCT
fumecheng-7385	107	1	linear	linear	PROPN
fumecheng-7385	107	2	frequency	frequency	PROPN
fumecheng-7385	107	3	is	be	AUX
fumecheng-7385	107	4	given	give	VERB
fumecheng-7385	107	5	by	by	ADP
fumecheng-7385	107	6	.	.	PUNCT
fumecheng-7385	108	1	3	3	NUM
fumecheng-7385	108	2	2	2	NUM
fumecheng-7385	108	3	22	22	NUM
fumecheng-7385	108	4	p	p	NOUN
fumecheng-7385	108	5			NOUN
fumecheng-7385	108	6			NOUN
fumecheng-7385	108	7	−−=	−−=	PROPN
fumecheng-7385	108	8	(	(	PUNCT
fumecheng-7385	108	9	13	13	NUM
fumecheng-7385	108	10	)	)	PUNCT
fumecheng-7385	108	11	this	this	DET
fumecheng-7385	108	12	procedure	procedure	NOUN
fumecheng-7385	108	13	can	can	AUX
fumecheng-7385	108	14	not	not	PART
fumecheng-7385	108	15	be	be	AUX
fumecheng-7385	108	16	successfully	successfully	ADV
fumecheng-7385	108	17	used	use	VERB
fumecheng-7385	108	18	when	when	SCONJ
fumecheng-7385	108	19	the	the	DET
fumecheng-7385	108	20	nonlinear	nonlinear	ADJ
fumecheng-7385	108	21	terms	term	NOUN
fumecheng-7385	108	22	are	be	AUX
fumecheng-7385	108	23	involved	involve	VERB
fumecheng-7385	108	24	.	.	PUNCT
fumecheng-7385	109	1	the	the	DET
fumecheng-7385	109	2	solution	solution	NOUN
fumecheng-7385	109	3	of	of	ADP
fumecheng-7385	109	4	the	the	DET
fumecheng-7385	109	5	damping	damp	VERB
fumecheng-7385	109	6	nonlinear	nonlinear	PROPN
fumecheng-7385	109	7	klein	klein	PROPN
fumecheng-7385	109	8	-	-	PUNCT
fumecheng-7385	109	9	gordon	gordon	PROPN
fumecheng-7385	109	10	eq	eq	X
fumecheng-7385	109	11	.	.	PUNCT
fumecheng-7385	110	1	(	(	PUNCT
fumecheng-7385	110	2	11	11	NUM
fumecheng-7385	110	3	)	)	PUNCT
fumecheng-7385	110	4	,	,	PUNCT
fumecheng-7385	110	5	by	by	ADP
fumecheng-7385	110	6	applying	apply	VERB
fumecheng-7385	110	7	the	the	DET
fumecheng-7385	110	8	classical	classical	ADJ
fumecheng-7385	110	9	analysis	analysis	NOUN
fumecheng-7385	110	10	of	of	ADP
fumecheng-7385	110	11	the	the	DET
fumecheng-7385	110	12	homotopy	homotopy	NOUN
fumecheng-7385	110	13	perturbation	perturbation	NOUN
fumecheng-7385	110	14	method	method	NOUN
fumecheng-7385	111	1	[	[	X
fumecheng-7385	111	2	26	26	NUM
fumecheng-7385	111	3	]	]	PUNCT
fumecheng-7385	111	4	,	,	PUNCT
fumecheng-7385	111	5	leads	lead	VERB
fumecheng-7385	111	6	to	to	ADP
fumecheng-7385	111	7	the	the	DET
fumecheng-7385	111	8	disappearance	disappearance	NOUN
fumecheng-7385	111	9	of	of	ADP
fumecheng-7385	111	10	the	the	DET
fumecheng-7385	111	11	damping	damp	VERB
fumecheng-7385	111	12	coefficient	coefficient	NOUN
fumecheng-7385	111	13	.	.	PUNCT
fumecheng-7385	112	1	in	in	ADP
fumecheng-7385	112	2	what	what	PRON
fumecheng-7385	112	3	follows	follow	VERB
fumecheng-7385	112	4	the	the	DET
fumecheng-7385	112	5	homotopy	homotopy	NOUN
fumecheng-7385	112	6	perturbation	perturbation	NOUN
fumecheng-7385	112	7	with	with	ADP
fumecheng-7385	112	8	the	the	DET
fumecheng-7385	112	9	exponential	exponential	ADJ
fumecheng-7385	112	10	decay	decay	NOUN
fumecheng-7385	112	11	of	of	ADP
fumecheng-7385	112	12	the	the	DET
fumecheng-7385	112	13	slow	slow	ADJ
fumecheng-7385	112	14	variable	variable	NOUN
fumecheng-7385	112	15	is	be	AUX
fumecheng-7385	112	16	elaborated	elaborate	VERB
fumecheng-7385	112	17	[	[	X
fumecheng-7385	112	18	3,35	3,35	NOUN
fumecheng-7385	112	19	]	]	X
fumecheng-7385	112	20	:	:	PUNCT
fumecheng-7385	112	21	2.1	2.1	NUM
fumecheng-7385	112	22	.	.	PUNCT
fumecheng-7385	112	23	solution	solution	NOUN
fumecheng-7385	112	24	with	with	ADP
fumecheng-7385	112	25	the	the	DET
fumecheng-7385	112	26	modified	modify	VERB
fumecheng-7385	112	27	hpm	hpm	NOUN
fumecheng-7385	112	28	by	by	ADP
fumecheng-7385	112	29	exponential	exponential	ADJ
fumecheng-7385	112	30	decay	decay	NOUN
fumecheng-7385	112	31	description	description	NOUN
fumecheng-7385	112	32	to	to	PART
fumecheng-7385	112	33	build	build	VERB
fumecheng-7385	112	34	the	the	DET
fumecheng-7385	112	35	homotopy	homotopy	NOUN
fumecheng-7385	112	36	equation	equation	NOUN
fumecheng-7385	112	37	,	,	PUNCT
fumecheng-7385	112	38	we	we	PRON
fumecheng-7385	112	39	select	select	VERB
fumecheng-7385	112	40	the	the	DET
fumecheng-7385	112	41	linear	linear	ADJ
fumecheng-7385	112	42	partial	partial	ADJ
fumecheng-7385	112	43	differential	differential	NOUN
fumecheng-7385	112	44	operator	operator	NOUN
fumecheng-7385	112	45	and	and	CCONJ
fumecheng-7385	112	46	the	the	DET
fumecheng-7385	112	47	nonlinear	nonlinear	ADJ
fumecheng-7385	112	48	operator	operator	NOUN
fumecheng-7385	112	49	as	as	ADP
fumecheng-7385	112	50	:	:	PUNCT
fumecheng-7385	112	51	yyyl	yyyl	NOUN
fumecheng-7385	112	52	ttt	ttt	PROPN
fumecheng-7385	112	53	+=	+=	PUNCT
fumecheng-7385	112	54	and	and	CCONJ
fumecheng-7385	112	55	.22	.22	NUM
fumecheng-7385	112	56	3qyyypyny	3qyyypyny	NUM
fumecheng-7385	112	57	xtxx	xtxx	X
fumecheng-7385	112	58	−++−=	−++−=	NUM
fumecheng-7385	112	59			X
fumecheng-7385	112	60	(	(	PUNCT
fumecheng-7385	112	61	14	14	NUM
fumecheng-7385	112	62	)	)	PUNCT
fumecheng-7385	112	63	the	the	DET
fumecheng-7385	112	64	corresponding	correspond	VERB
fumecheng-7385	112	65	temporal	temporal	ADJ
fumecheng-7385	112	66	homotopy	homotopy	NOUN
fumecheng-7385	112	67	equation	equation	NOUN
fumecheng-7385	112	68	may	may	AUX
fumecheng-7385	112	69	be	be	AUX
fumecheng-7385	112	70	constructed	construct	VERB
fumecheng-7385	112	71	as	as	ADP
fumecheng-7385	112	72	3	3	NUM
fumecheng-7385	112	73	(	(	PUNCT
fumecheng-7385	112	74	;	;	PUNCT
fumecheng-7385	112	75	)	)	PUNCT
fumecheng-7385	112	76	(	(	PUNCT
fumecheng-7385	112	77	)	)	PUNCT
fumecheng-7385	112	78	(	(	PUNCT
fumecheng-7385	112	79	2	2	NUM
fumecheng-7385	112	80	2	2	NUM
fumecheng-7385	112	81	)	)	PUNCT
fumecheng-7385	112	82	0	0	NUM
fumecheng-7385	112	83	;	;	PUNCT
fumecheng-7385	113	1	[	[	X
fumecheng-7385	113	2	0,1],tt	0,1],tt	X
fumecheng-7385	113	3	xx	xx	NUM
fumecheng-7385	114	1	t	t	PROPN
fumecheng-7385	114	2	xh	xh	PROPN
fumecheng-7385	115	1	y	y	PROPN
fumecheng-7385	115	2	q	q	PROPN
fumecheng-7385	115	3	y	y	PROPN
fumecheng-7385	115	4	y	y	PROPN
fumecheng-7385	115	5	q	q	PROPN
fumecheng-7385	115	6	py	py	INTJ
fumecheng-7385	115	7	y	y	PROPN
fumecheng-7385	115	8	y	y	PROPN
fumecheng-7385	115	9	qy	qy	PROPN
fumecheng-7385	115	10	q=	q=	ADV
fumecheng-7385	115	11	+	+	CCONJ
fumecheng-7385	116	1	+	+	CCONJ
fumecheng-7385	116	2	−	−	X
fumecheng-7385	116	3	+	+	CCONJ
fumecheng-7385	117	1	+	+	CCONJ
fumecheng-7385	117	2	−	−	PROPN
fumecheng-7385	117	3	=	=	SYM
fumecheng-7385	117	4			PRON
fumecheng-7385	117	5			NUM
fumecheng-7385	117	6			NOUN
fumecheng-7385	117	7	(	(	PUNCT
fumecheng-7385	117	8	15	15	NUM
fumecheng-7385	117	9	)	)	PUNCT
fumecheng-7385	117	10	where	where	SCONJ
fumecheng-7385	117	11	function	function	NOUN
fumecheng-7385	117	12	y(x	y(x	PROPN
fumecheng-7385	117	13	,	,	PUNCT
fumecheng-7385	117	14	t	t	PROPN
fumecheng-7385	117	15	)	)	PUNCT
fumecheng-7385	117	16	becomes	become	VERB
fumecheng-7385	117	17	(	(	PUNCT
fumecheng-7385	117	18	,	,	PUNCT
fumecheng-7385	117	19	;	;	PUNCT
fumecheng-7385	117	20	)	)	PUNCT
fumecheng-7385	117	21	(	(	PUNCT
fumecheng-7385	117	22	,	,	PUNCT
fumecheng-7385	117	23	;	;	PUNCT
fumecheng-7385	117	24	)	)	PUNCT
fumecheng-7385	117	25	.q	.q	PROPN
fumecheng-7385	118	1	ty	ty	INTJ
fumecheng-7385	119	1	x	x	X
fumecheng-7385	119	2	t	t	PROPN
fumecheng-7385	119	3	q	q	X
fumecheng-7385	119	4	u	u	PROPN
fumecheng-7385	119	5	x	x	X
fumecheng-7385	119	6	t	t	NOUN
fumecheng-7385	119	7	q	q	NOUN
fumecheng-7385	119	8	e−	e−	PROPN
fumecheng-7385	119	9	=	=	PUNCT
fumecheng-7385	119	10	)	)	PUNCT
fumecheng-7385	119	11	;	;	PUNCT
fumecheng-7385	119	12	(	(	PUNCT
fumecheng-7385	119	13	qyh	qyh	INTJ
fumecheng-7385	119	14	is	be	AUX
fumecheng-7385	119	15	the	the	DET
fumecheng-7385	119	16	homotopy	homotopy	NOUN
fumecheng-7385	119	17	function	function	NOUN
fumecheng-7385	119	18	.	.	PUNCT
fumecheng-7385	120	1	as	as	SCONJ
fumecheng-7385	120	2	the	the	DET
fumecheng-7385	120	3	primary	primary	ADJ
fumecheng-7385	120	4	solution	solution	NOUN
fumecheng-7385	120	5	can	can	AUX
fumecheng-7385	120	6	be	be	AUX
fumecheng-7385	120	7	obtained	obtain	VERB
fumecheng-7385	120	8	by	by	ADP
fumecheng-7385	120	9	making	make	VERB
fumecheng-7385	120	10	parameter	parameter	NOUN
fumecheng-7385	120	11	q	q	PROPN
fumecheng-7385	120	12	tend	tend	VERB
fumecheng-7385	120	13	to	to	PART
fumecheng-7385	120	14	zero	zero	NUM
fumecheng-7385	120	15	,	,	PUNCT
fumecheng-7385	120	16	we	we	PRON
fumecheng-7385	120	17	find	find	VERB
fumecheng-7385	120	18	)	)	PUNCT
fumecheng-7385	120	19	.;,(lim	.;,(lim	NUM
fumecheng-7385	120	20	)	)	PUNCT
fumecheng-7385	120	21	,	,	PUNCT
fumecheng-7385	120	22	(	(	PUNCT
fumecheng-7385	120	23	0	0	NUM
fumecheng-7385	120	24	0	0	NUM
fumecheng-7385	120	25	qtxutxy	qtxutxy	PROPN
fumecheng-7385	120	26	q→	q→	PROPN
fumecheng-7385	120	27	=	=	SYM
fumecheng-7385	120	28	(	(	PUNCT
fumecheng-7385	120	29	16	16	NUM
fumecheng-7385	120	30	)	)	PUNCT
fumecheng-7385	120	31	the	the	DET
fumecheng-7385	120	32	final	final	ADJ
fumecheng-7385	120	33	form	form	NOUN
fumecheng-7385	120	34	of	of	ADP
fumecheng-7385	120	35	the	the	DET
fumecheng-7385	120	36	approximate	approximate	ADJ
fumecheng-7385	120	37	solution	solution	NOUN
fumecheng-7385	120	38	of	of	ADP
fumecheng-7385	120	39	the	the	DET
fumecheng-7385	120	40	original	original	ADJ
fumecheng-7385	120	41	eq	eq	X
fumecheng-7385	120	42	.	.	PUNCT
fumecheng-7385	121	1	(	(	PUNCT
fumecheng-7385	121	2	11	11	NUM
fumecheng-7385	121	3	)	)	PUNCT
fumecheng-7385	121	4	has	have	VERB
fumecheng-7385	121	5	the	the	DET
fumecheng-7385	121	6	form	form	NOUN
fumecheng-7385	121	7	)	)	PUNCT
fumecheng-7385	121	8	.;,(lim	.;,(lim	NUM
fumecheng-7385	121	9	)	)	PUNCT
fumecheng-7385	121	10	,	,	PUNCT
fumecheng-7385	121	11	(	(	PUNCT
fumecheng-7385	121	12	1	1	NUM
fumecheng-7385	121	13	qtxuetxy	qtxuetxy	PROPN
fumecheng-7385	121	14	q	q	PROPN
fumecheng-7385	121	15	t	t	PROPN
fumecheng-7385	121	16	→	→	SYM
fumecheng-7385	121	17	−=	−=	X
fumecheng-7385	121	18			NUM
fumecheng-7385	121	19	(	(	PUNCT
fumecheng-7385	121	20	17	17	NUM
fumecheng-7385	121	21	)	)	PUNCT
fumecheng-7385	121	22	assuming	assume	VERB
fumecheng-7385	121	23	that	that	SCONJ
fumecheng-7385	121	24	eq	eq	ADP
fumecheng-7385	121	25	.	.	PUNCT
fumecheng-7385	122	1	(	(	PUNCT
fumecheng-7385	122	2	15	15	NUM
fumecheng-7385	122	3	)	)	PUNCT
fumecheng-7385	122	4	admits	admit	VERB
fumecheng-7385	122	5	the	the	DET
fumecheng-7385	122	6	solution	solution	NOUN
fumecheng-7385	122	7	[	[	X
fumecheng-7385	122	8	3	3	X
fumecheng-7385	122	9	]	]	PUNCT
fumecheng-7385	122	10	.	.	PUNCT
fumecheng-7385	122	11	)	)	PUNCT
fumecheng-7385	123	1	,	,	PUNCT
fumecheng-7385	123	2	,	,	PUNCT
fumecheng-7385	123	3	(	(	PUNCT
fumecheng-7385	123	4	)	)	PUNCT
fumecheng-7385	123	5	;	;	PUNCT
fumecheng-7385	123	6	,	,	PUNCT
fumecheng-7385	123	7	(	(	PUNCT
fumecheng-7385	123	8	tqeqtxuqtxy	tqeqtxuqtxy	PROPN
fumecheng-7385	123	9	−=	−=	PROPN
fumecheng-7385	123	10	(	(	PUNCT
fumecheng-7385	123	11	18	18	NUM
fumecheng-7385	123	12	)	)	PUNCT
fumecheng-7385	123	13	the	the	DET
fumecheng-7385	123	14	enhanced	enhance	VERB
fumecheng-7385	123	15	homotopy	homotopy	NOUN
fumecheng-7385	123	16	perturbation	perturbation	NOUN
fumecheng-7385	123	17	method	method	NOUN
fumecheng-7385	123	18	for	for	ADP
fumecheng-7385	123	19	axial	axial	ADJ
fumecheng-7385	123	20	vibrations	vibration	NOUN
fumecheng-7385	123	21	of	of	ADP
fumecheng-7385	123	22	strings	string	NOUN
fumecheng-7385	123	23	739	739	NUM
fumecheng-7385	123	24	function	function	NOUN
fumecheng-7385	123	25	u(x	u(x	NOUN
fumecheng-7385	123	26	,	,	PUNCT
fumecheng-7385	123	27	t	t	PROPN
fumecheng-7385	123	28	,	,	PUNCT
fumecheng-7385	123	29	q	q	NOUN
fumecheng-7385	123	30	)	)	PUNCT
fumecheng-7385	123	31	is	be	AUX
fumecheng-7385	123	32	expanded	expand	VERB
fumecheng-7385	123	33	as	as	ADP
fumecheng-7385	123	34	...	...	PUNCT
fumecheng-7385	123	35	)	)	PUNCT
fumecheng-7385	123	36	,	,	PUNCT
fumecheng-7385	123	37	(	(	PUNCT
fumecheng-7385	123	38	)	)	PUNCT
fumecheng-7385	123	39	,	,	PUNCT
fumecheng-7385	123	40	(	(	PUNCT
fumecheng-7385	123	41	)	)	PUNCT
fumecheng-7385	123	42	,	,	PUNCT
fumecheng-7385	123	43	(	(	PUNCT
fumecheng-7385	123	44	)	)	PUNCT
fumecheng-7385	123	45	,	,	PUNCT
fumecheng-7385	123	46	,	,	PUNCT
fumecheng-7385	123	47	(	(	PUNCT
fumecheng-7385	123	48	2	2	NUM
fumecheng-7385	123	49	2	2	NUM
fumecheng-7385	123	50	10	10	NUM
fumecheng-7385	124	1	+	+	ADJ
fumecheng-7385	124	2	+	+	ADJ
fumecheng-7385	124	3	+	+	ADJ
fumecheng-7385	124	4	=	=	ADJ
fumecheng-7385	124	5	txuqtxqutxuqtxu	txuqtxqutxuqtxu	NOUN
fumecheng-7385	124	6	(	(	PUNCT
fumecheng-7385	124	7	19	19	NUM
fumecheng-7385	124	8	)	)	PUNCT
fumecheng-7385	124	9	also	also	ADV
fumecheng-7385	124	10	,	,	PUNCT
fumecheng-7385	124	11	one	one	PRON
fumecheng-7385	124	12	can	can	AUX
fumecheng-7385	124	13	use	use	VERB
fumecheng-7385	124	14	the	the	DET
fumecheng-7385	124	15	expanded	expand	VERB
fumecheng-7385	124	16	frequency	frequency	NOUN
fumecheng-7385	124	17	as	as	ADP
fumecheng-7385	124	18	...	...	PUNCT
fumecheng-7385	124	19	,	,	PUNCT
fumecheng-7385	124	20	2	2	NUM
fumecheng-7385	124	21	2	2	NUM
fumecheng-7385	124	22	1	1	NUM
fumecheng-7385	124	23	2	2	NUM
fumecheng-7385	124	24	+	+	NOUN
fumecheng-7385	124	25	++=	++=	X
fumecheng-7385	124	26	qq	qq	PROPN
fumecheng-7385	124	27	(	(	PUNCT
fumecheng-7385	124	28	20	20	NUM
fumecheng-7385	124	29	)	)	PUNCT
fumecheng-7385	124	30	where	where	SCONJ
fumecheng-7385	124	31	i	i	NOUN
fumecheng-7385	124	32	is	be	AUX
fumecheng-7385	124	33	unknown	unknown	ADJ
fumecheng-7385	124	34	in	in	ADP
fumecheng-7385	124	35	total	total	ADJ
fumecheng-7385	124	36	frequency	frequency	NOUN
fumecheng-7385	124	37	2	2	PUNCT
fumecheng-7385	124	38	and	and	CCONJ
fumecheng-7385	124	39	determined	determine	VERB
fumecheng-7385	124	40	by	by	ADP
fumecheng-7385	124	41	the	the	DET
fumecheng-7385	124	42	disappearance	disappearance	NOUN
fumecheng-7385	124	43	of	of	ADP
fumecheng-7385	124	44	the	the	DET
fumecheng-7385	124	45	secular	secular	ADJ
fumecheng-7385	124	46	term	term	NOUN
fumecheng-7385	124	47	.	.	PUNCT
fumecheng-7385	125	1	employing	employ	VERB
fumecheng-7385	125	2	eq	eq	ADP
fumecheng-7385	125	3	.	.	PUNCT
fumecheng-7385	126	1	(	(	PUNCT
fumecheng-7385	126	2	18	18	NUM
fumecheng-7385	126	3	)	)	PUNCT
fumecheng-7385	126	4	with	with	ADP
fumecheng-7385	126	5	eq	eq	NOUN
fumecheng-7385	126	6	.	.	PUNCT
fumecheng-7385	127	1	(	(	PUNCT
fumecheng-7385	127	2	15	15	NUM
fumecheng-7385	127	3	)	)	PUNCT
fumecheng-7385	127	4	,	,	PUNCT
fumecheng-7385	127	5	and	and	CCONJ
fumecheng-7385	127	6	using	use	VERB
fumecheng-7385	127	7	expansions	expansion	NOUN
fumecheng-7385	127	8	(	(	PUNCT
fumecheng-7385	127	9	19	19	NUM
fumecheng-7385	127	10	)	)	PUNCT
fumecheng-7385	127	11	and	and	CCONJ
fumecheng-7385	127	12	(	(	PUNCT
fumecheng-7385	127	13	20	20	NUM
fumecheng-7385	127	14	)	)	PUNCT
fumecheng-7385	127	15	,	,	PUNCT
fumecheng-7385	127	16	we	we	PRON
fumecheng-7385	127	17	obtain	obtain	VERB
fumecheng-7385	127	18	homotopy	homotopy	NOUN
fumecheng-7385	127	19	function	function	NOUN
fumecheng-7385	127	20	h(u;q	h(u;q	PROPN
fumecheng-7385	127	21	)	)	PUNCT
fumecheng-7385	127	22	arranged	arrange	VERB
fumecheng-7385	127	23	in	in	ADP
fumecheng-7385	127	24	the	the	DET
fumecheng-7385	127	25	form	form	NOUN
fumecheng-7385	127	26	.0	.0	NUM
fumecheng-7385	127	27	...	...	PUNCT
fumecheng-7385	127	28	)	)	PUNCT
fumecheng-7385	127	29	,	,	PUNCT
fumecheng-7385	127	30	,	,	PUNCT
fumecheng-7385	127	31	(	(	PUNCT
fumecheng-7385	127	32	)	)	PUNCT
fumecheng-7385	127	33	,	,	PUNCT
fumecheng-7385	127	34	(	(	PUNCT
fumecheng-7385	127	35	)	)	PUNCT
fumecheng-7385	127	36	(	(	PUNCT
fumecheng-7385	127	37	)	)	PUNCT
fumecheng-7385	127	38	;	;	PUNCT
fumecheng-7385	127	39	(	(	PUNCT
fumecheng-7385	127	40	0122	0122	NUM
fumecheng-7385	127	41	2	2	NUM
fumecheng-7385	127	42	01100	01100	NUM
fumecheng-7385	127	43	=	=	SYM
fumecheng-7385	127	44	+	+	ADJ
fumecheng-7385	127	45	+	+	ADJ
fumecheng-7385	127	46	+	+	ADJ
fumecheng-7385	127	47	=	=	ADJ
fumecheng-7385	127	48	uuuhquuqhuhquh	uuuhquuqhuhquh	ADJ
fumecheng-7385	127	49	(	(	PUNCT
fumecheng-7385	127	50	21	21	NUM
fumecheng-7385	127	51	)	)	PUNCT
fumecheng-7385	127	52	the	the	DET
fumecheng-7385	127	53	estimation	estimation	NOUN
fumecheng-7385	127	54	of	of	ADP
fumecheng-7385	127	55	;	;	PUNCT
fumecheng-7385	127	56	0,1,2,	0,1,2,	NUM
fumecheng-7385	127	57	...	...	PUNCT
fumecheng-7385	127	58	nh	nh	PROPN
fumecheng-7385	127	59	n	n	CCONJ
fumecheng-7385	127	60	=	=	PUNCT
fumecheng-7385	127	61	is	be	AUX
fumecheng-7385	127	62	as	as	SCONJ
fumecheng-7385	127	63	follows	follow	VERB
fumecheng-7385	127	64	:	:	PUNCT
fumecheng-7385	127	65	0	0	NUM
fumecheng-7385	127	66	0	0	NUM
fumecheng-7385	127	67	0	0	NUM
fumecheng-7385	128	1	(	(	PUNCT
fumecheng-7385	128	2	)	)	PUNCT
fumecheng-7385	128	3	lim	lim	PROPN
fumecheng-7385	128	4	(	(	PUNCT
fumecheng-7385	128	5	;	;	PUNCT
fumecheng-7385	128	6	)	)	PUNCT
fumecheng-7385	128	7	,	,	PUNCT
fumecheng-7385	128	8	q	q	PROPN
fumecheng-7385	128	9	h	h	NOUN
fumecheng-7385	128	10	u	u	NOUN
fumecheng-7385	128	11	h	h	NOUN
fumecheng-7385	128	12	y	y	NOUN
fumecheng-7385	128	13	q	q	PROPN
fumecheng-7385	128	14	→	→	SYM
fumecheng-7385	128	15	=	=	SYM
fumecheng-7385	128	16	(	(	PUNCT
fumecheng-7385	128	17	22	22	NUM
fumecheng-7385	128	18	)	)	PUNCT
fumecheng-7385	128	19	1	1	NUM
fumecheng-7385	128	20	1	1	NUM
fumecheng-7385	128	21	0	0	NUM
fumecheng-7385	128	22	0	0	NUM
fumecheng-7385	128	23	(	(	PUNCT
fumecheng-7385	128	24	,	,	PUNCT
fumecheng-7385	128	25	)	)	PUNCT
fumecheng-7385	128	26	lim	lim	PROPN
fumecheng-7385	128	27	(	(	PUNCT
fumecheng-7385	128	28	;	;	PUNCT
fumecheng-7385	128	29	)	)	PUNCT
fumecheng-7385	128	30	,	,	PUNCT
fumecheng-7385	128	31	q	q	NOUN
fumecheng-7385	128	32	h	h	NOUN
fumecheng-7385	128	33	u	u	NOUN
fumecheng-7385	128	34	u	u	NOUN
fumecheng-7385	128	35	h	h	NOUN
fumecheng-7385	128	36	y	y	PROPN
fumecheng-7385	128	37	q	q	PROPN
fumecheng-7385	128	38	q→	q→	NUM
fumecheng-7385	128	39			NOUN
fumecheng-7385	128	40	=	=	SYM
fumecheng-7385	128	41			ADJ
fumecheng-7385	128	42	(	(	PUNCT
fumecheng-7385	128	43	23	23	NUM
fumecheng-7385	128	44	)	)	PUNCT
fumecheng-7385	128	45	1	1	NUM
fumecheng-7385	128	46	0	0	NUM
fumecheng-7385	128	47	0	0	NUM
fumecheng-7385	128	48	1	1	NUM
fumecheng-7385	128	49	(	(	PUNCT
fumecheng-7385	128	50	,	,	PUNCT
fumecheng-7385	128	51	,	,	PUNCT
fumecheng-7385	128	52	...	...	PUNCT
fumecheng-7385	128	53	,	,	PUNCT
fumecheng-7385	128	54	,	,	PUNCT
fumecheng-7385	128	55	)	)	PUNCT
fumecheng-7385	128	56	lim	lim	PROPN
fumecheng-7385	128	57	(	(	PUNCT
fumecheng-7385	128	58	;	;	PUNCT
fumecheng-7385	128	59	)	)	PUNCT
fumecheng-7385	128	60	.	.	PUNCT
fumecheng-7385	128	61	!	!	PUNCT
fumecheng-7385	129	1	r	r	NOUN
fumecheng-7385	129	2	r	r	NOUN
fumecheng-7385	129	3	r	r	NOUN
fumecheng-7385	129	4	rq	rq	NOUN
fumecheng-7385	129	5	h	h	NOUN
fumecheng-7385	129	6	u	u	NOUN
fumecheng-7385	129	7	u	u	NOUN
fumecheng-7385	129	8	u	u	NOUN
fumecheng-7385	129	9	h	h	NOUN
fumecheng-7385	129	10	y	y	NOUN
fumecheng-7385	129	11	q	q	NOUN
fumecheng-7385	129	12	r	r	NOUN
fumecheng-7385	129	13	q→	q→	NUM
fumecheng-7385	129	14			NOUN
fumecheng-7385	129	15	=	=	SYM
fumecheng-7385	129	16			PROPN
fumecheng-7385	129	17	(	(	PUNCT
fumecheng-7385	129	18	24	24	NUM
fumecheng-7385	129	19	)	)	PUNCT
fumecheng-7385	129	20	according	accord	VERB
fumecheng-7385	129	21	to	to	ADP
fumecheng-7385	129	22	eqs	eqs	PROPN
fumecheng-7385	129	23	.	.	PUNCT
fumecheng-7385	130	1	(	(	PUNCT
fumecheng-7385	130	2	12	12	NUM
fumecheng-7385	130	3	-	-	SYM
fumecheng-7385	130	4	14	14	NUM
fumecheng-7385	130	5	)	)	PUNCT
fumecheng-7385	130	6	and	and	CCONJ
fumecheng-7385	130	7	equating	equate	VERB
fumecheng-7385	130	8	each	each	DET
fumecheng-7385	130	9	hi	hi	INTJ
fumecheng-7385	130	10	to	to	ADP
fumecheng-7385	130	11	zero	zero	NUM
fumecheng-7385	130	12	,	,	PUNCT
fumecheng-7385	130	13	we	we	PRON
fumecheng-7385	130	14	obtain	obtain	VERB
fumecheng-7385	130	15	2	2	NUM
fumecheng-7385	130	16	0	0	NUM
fumecheng-7385	130	17	0	0	NUM
fumecheng-7385	130	18	0	0	NUM
fumecheng-7385	130	19	(	(	PUNCT
fumecheng-7385	130	20	)	)	PUNCT
fumecheng-7385	130	21	(	(	PUNCT
fumecheng-7385	130	22	)	)	PUNCT
fumecheng-7385	130	23	(	(	PUNCT
fumecheng-7385	130	24	,	,	PUNCT
fumecheng-7385	130	25	)	)	PUNCT
fumecheng-7385	130	26	0,tth	0,tth	NUM
fumecheng-7385	130	27	u	u	NOUN
fumecheng-7385	130	28	u	u	NOUN
fumecheng-7385	130	29	x	x	ADP
fumecheng-7385	130	30	t=	t=	PRON
fumecheng-7385	130	31			ADJ
fumecheng-7385	130	32	+	+	SYM
fumecheng-7385	130	33			X
fumecheng-7385	130	34	=	=	PUNCT
fumecheng-7385	130	35	(	(	PUNCT
fumecheng-7385	130	36	25	25	NUM
fumecheng-7385	130	37	)	)	SYM
fumecheng-7385	130	38	2	2	NUM
fumecheng-7385	130	39	2	2	NUM
fumecheng-7385	130	40	2	2	NUM
fumecheng-7385	130	41	1	1	NUM
fumecheng-7385	130	42	1	1	NUM
fumecheng-7385	130	43	0	0	NUM
fumecheng-7385	130	44	1	1	NUM
fumecheng-7385	130	45	0	0	NUM
fumecheng-7385	130	46	1	1	NUM
fumecheng-7385	130	47	0	0	NUM
fumecheng-7385	130	48	0	0	NUM
fumecheng-7385	130	49	(	(	PUNCT
fumecheng-7385	130	50	,	,	PUNCT
fumecheng-7385	130	51	)	)	PUNCT
fumecheng-7385	130	52	(	(	PUNCT
fumecheng-7385	130	53	)	)	PUNCT
fumecheng-7385	130	54	(	(	PUNCT
fumecheng-7385	130	55	,	,	PUNCT
fumecheng-7385	130	56	)	)	PUNCT
fumecheng-7385	130	57	(	(	PUNCT
fumecheng-7385	130	58	)	)	PUNCT
fumecheng-7385	130	59	(	(	PUNCT
fumecheng-7385	130	60	2	2	X
fumecheng-7385	130	61	)	)	PUNCT
fumecheng-7385	130	62	0,tt	0,tt	NOUN
fumecheng-7385	130	63	tt	tt	PROPN
fumecheng-7385	130	64	xx	xx	NUM
fumecheng-7385	130	65	xh	xh	PROPN
fumecheng-7385	130	66	u	u	PROPN
fumecheng-7385	130	67	u	u	PROPN
fumecheng-7385	130	68	u	u	X
fumecheng-7385	130	69	x	x	PROPN
fumecheng-7385	130	70	t	t	PROPN
fumecheng-7385	130	71	t	t	X
fumecheng-7385	130	72	u	u	PROPN
fumecheng-7385	130	73	p	p	PROPN
fumecheng-7385	130	74	qu	qu	PROPN
fumecheng-7385	130	75	u=	u=	ADV
fumecheng-7385	130	76			PROPN
fumecheng-7385	130	77	+	+	PROPN
fumecheng-7385	130	78			PROPN
fumecheng-7385	130	79	−	−	ADP
fumecheng-7385	130	80			PROPN
fumecheng-7385	130	81	+	+	PRON
fumecheng-7385	130	82			PROPN
fumecheng-7385	131	1	+	+	CCONJ
fumecheng-7385	131	2	−	−	PROPN
fumecheng-7385	131	3			ADJ
fumecheng-7385	131	4	+	+	NUM
fumecheng-7385	131	5			ADJ
fumecheng-7385	131	6	−	−	NOUN
fumecheng-7385	131	7	−	−	NOUN
fumecheng-7385	131	8	=	=	NOUN
fumecheng-7385	131	9			NUM
fumecheng-7385	131	10			NOUN
fumecheng-7385	131	11	(	(	PUNCT
fumecheng-7385	131	12	26	26	NUM
fumecheng-7385	131	13	)	)	SYM
fumecheng-7385	131	14	2	2	NUM
fumecheng-7385	131	15	2	2	NUM
fumecheng-7385	131	16	2	2	NUM
fumecheng-7385	131	17	2	2	NUM
fumecheng-7385	131	18	2	2	NUM
fumecheng-7385	131	19	1	1	NUM
fumecheng-7385	131	20	0	0	NUM
fumecheng-7385	131	21	2	2	NUM
fumecheng-7385	131	22	1	1	NUM
fumecheng-7385	131	23	1	1	NUM
fumecheng-7385	131	24	1	1	NUM
fumecheng-7385	131	25	0	0	NUM
fumecheng-7385	131	26	1	1	NUM
fumecheng-7385	131	27	2	2	NUM
fumecheng-7385	131	28	2	2	NUM
fumecheng-7385	131	29	2	2	NUM
fumecheng-7385	131	30	2	2	NUM
fumecheng-7385	131	31	21	21	NUM
fumecheng-7385	131	32	0	0	NUM
fumecheng-7385	131	33	0	0	NUM
fumecheng-7385	131	34	2	2	NUM
fumecheng-7385	131	35	0	0	NUM
fumecheng-7385	131	36	1	1	NUM
fumecheng-7385	131	37	0	0	NUM
fumecheng-7385	131	38	0	0	NUM
fumecheng-7385	131	39	02	02	NUM
fumecheng-7385	131	40	(	(	PUNCT
fumecheng-7385	131	41	,	,	PUNCT
fumecheng-7385	131	42	,	,	PUNCT
fumecheng-7385	131	43	)	)	PUNCT
fumecheng-7385	131	44	(	(	PUNCT
fumecheng-7385	131	45	)	)	PUNCT
fumecheng-7385	131	46	(	(	PUNCT
fumecheng-7385	131	47	,	,	PUNCT
fumecheng-7385	131	48	)	)	PUNCT
fumecheng-7385	131	49	(	(	PUNCT
fumecheng-7385	131	50	)	)	PUNCT
fumecheng-7385	131	51	(	(	PUNCT
fumecheng-7385	131	52	2	2	NUM
fumecheng-7385	131	53	3	3	NUM
fumecheng-7385	131	54	)	)	PUNCT
fumecheng-7385	131	55	(	(	PUNCT
fumecheng-7385	131	56	)	)	PUNCT
fumecheng-7385	131	57	(	(	PUNCT
fumecheng-7385	131	58	2	2	NUM
fumecheng-7385	131	59	3	3	NUM
fumecheng-7385	131	60	)	)	PUNCT
fumecheng-7385	131	61	0	0	NUM
fumecheng-7385	131	62	.	.	PUNCT
fumecheng-7385	132	1	tt	tt	PROPN
fumecheng-7385	132	2	tt	tt	PROPN
fumecheng-7385	133	1	xx	xx	INTJ
fumecheng-7385	133	2	x	x	PUNCT
fumecheng-7385	133	3	tt	tt	PROPN
fumecheng-7385	133	4	xx	xx	NUM
fumecheng-7385	133	5	x	x	SYM
fumecheng-7385	133	6	h	h	NOUN
fumecheng-7385	133	7	u	u	NOUN
fumecheng-7385	133	8	u	u	VERB
fumecheng-7385	133	9	u	u	X
fumecheng-7385	133	10	u	u	X
fumecheng-7385	133	11	x	x	PROPN
fumecheng-7385	133	12	t	t	PROPN
fumecheng-7385	133	13	t	t	X
fumecheng-7385	133	14	u	u	NOUN
fumecheng-7385	133	15	p	p	X
fumecheng-7385	133	16	u	u	PROPN
fumecheng-7385	133	17	qu	qu	X
fumecheng-7385	133	18	u	u	NOUN
fumecheng-7385	133	19	t	t	PROPN
fumecheng-7385	133	20	u	u	NOUN
fumecheng-7385	133	21	p	p	X
fumecheng-7385	133	22	u	u	X
fumecheng-7385	133	23	u	u	NOUN
fumecheng-7385	133	24	t	t	PROPN
fumecheng-7385	133	25	qu	qu	NOUN
fumecheng-7385	133	26	u	u	PROPN
fumecheng-7385	133	27	u	u	NOUN
fumecheng-7385	133	28	=	=	SYM
fumecheng-7385	133	29			PROPN
fumecheng-7385	133	30	+	+	PRON
fumecheng-7385	133	31			X
fumecheng-7385	133	32	−	−	ADP
fumecheng-7385	133	33			PROPN
fumecheng-7385	133	34	+	+	PRON
fumecheng-7385	133	35			PROPN
fumecheng-7385	133	36	−	−	ADP
fumecheng-7385	133	37			ADJ
fumecheng-7385	133	38	+	+	NUM
fumecheng-7385	133	39			ADJ
fumecheng-7385	133	40	−	−	NOUN
fumecheng-7385	133	41	−	−	PROPN
fumecheng-7385	133	42	+	+	NUM
fumecheng-7385	133	43			ADJ
fumecheng-7385	133	44	+	+	PRON
fumecheng-7385	133	45			X
fumecheng-7385	134	1	+	+	NUM
fumecheng-7385	134	2			ADJ
fumecheng-7385	134	3	−	−	NOUN
fumecheng-7385	134	4	−	−	NOUN
fumecheng-7385	134	5			ADJ
fumecheng-7385	134	6	−	−	NOUN
fumecheng-7385	134	7	−	−	NOUN
fumecheng-7385	134	8	−	−	NOUN
fumecheng-7385	134	9	=	=	SYM
fumecheng-7385	134	10			NUM
fumecheng-7385	134	11			NOUN
fumecheng-7385	134	12			NUM
fumecheng-7385	134	13			NUM
fumecheng-7385	134	14			NOUN
fumecheng-7385	134	15			NUM
fumecheng-7385	134	16	(	(	PUNCT
fumecheng-7385	134	17	27	27	NUM
fumecheng-7385	134	18	)	)	PUNCT
fumecheng-7385	134	19	handling	handle	VERB
fumecheng-7385	134	20	eq	eq	NOUN
fumecheng-7385	134	21	.	.	PUNCT
fumecheng-7385	135	1	(	(	PUNCT
fumecheng-7385	135	2	25	25	NUM
fumecheng-7385	135	3	)	)	PUNCT
fumecheng-7385	135	4	with	with	ADP
fumecheng-7385	135	5	eq	eq	NOUN
fumecheng-7385	135	6	.	.	PUNCT
fumecheng-7385	136	1	(	(	PUNCT
fumecheng-7385	136	2	26	26	NUM
fumecheng-7385	136	3	)	)	PUNCT
fumecheng-7385	136	4	yields	yield	VERB
fumecheng-7385	136	5	2	2	NUM
fumecheng-7385	136	6	3	3	NUM
fumecheng-7385	136	7	1	1	NUM
fumecheng-7385	136	8	0	0	NUM
fumecheng-7385	136	9	0	0	NUM
fumecheng-7385	136	10	1	1	NUM
fumecheng-7385	136	11	0	0	NUM
fumecheng-7385	136	12	0	0	NUM
fumecheng-7385	136	13	(	(	PUNCT
fumecheng-7385	136	14	)	)	PUNCT
fumecheng-7385	136	15	(	(	PUNCT
fumecheng-7385	136	16	,	,	PUNCT
fumecheng-7385	136	17	)	)	PUNCT
fumecheng-7385	136	18	2	2	NUM
fumecheng-7385	136	19	.tt	.tt	NUM
fumecheng-7385	136	20	xx	xx	NUM
fumecheng-7385	137	1	xu	xu	NUM
fumecheng-7385	137	2	x	x	PUNCT
fumecheng-7385	138	1	t	t	PROPN
fumecheng-7385	138	2	p	p	X
fumecheng-7385	138	3	u	u	X
fumecheng-7385	138	4	u	u	X
fumecheng-7385	138	5	u	u	NOUN
fumecheng-7385	138	6	qu	qu	VERB
fumecheng-7385	138	7	+	+	NOUN
fumecheng-7385	138	8			X
fumecheng-7385	138	9	=	=	NOUN
fumecheng-7385	138	10			ADJ
fumecheng-7385	138	11	−	−	ADP
fumecheng-7385	138	12			PROPN
fumecheng-7385	138	13	+	+	PRON
fumecheng-7385	138	14			X
fumecheng-7385	138	15	+	+	ADJ
fumecheng-7385	138	16			NOUN
fumecheng-7385	138	17	(	(	PUNCT
fumecheng-7385	138	18	28	28	NUM
fumecheng-7385	138	19	)	)	PUNCT
fumecheng-7385	138	20	eq	eq	NOUN
fumecheng-7385	138	21	.	.	PUNCT
fumecheng-7385	139	1	(	(	PUNCT
fumecheng-7385	139	2	27	27	NUM
fumecheng-7385	139	3	)	)	PUNCT
fumecheng-7385	139	4	will	will	AUX
fumecheng-7385	139	5	be	be	AUX
fumecheng-7385	139	6	simplified	simplify	VERB
fumecheng-7385	139	7	by	by	ADP
fumecheng-7385	139	8	using	use	VERB
fumecheng-7385	139	9	eqs	eqs	PROPN
fumecheng-7385	139	10	.	.	PUNCT
fumecheng-7385	140	1	(	(	PUNCT
fumecheng-7385	140	2	25	25	NUM
fumecheng-7385	140	3	)	)	PUNCT
fumecheng-7385	140	4	and	and	CCONJ
fumecheng-7385	140	5	(	(	PUNCT
fumecheng-7385	140	6	28	28	NUM
fumecheng-7385	140	7	)	)	PUNCT
fumecheng-7385	140	8	,	,	PUNCT
fumecheng-7385	140	9	to	to	PART
fumecheng-7385	140	10	become	become	VERB
fumecheng-7385	140	11	2	2	NUM
fumecheng-7385	140	12	2	2	NUM
fumecheng-7385	140	13	2	2	NUM
fumecheng-7385	140	14	3	3	NUM
fumecheng-7385	140	15	2	2	NUM
fumecheng-7385	140	16	1	1	NUM
fumecheng-7385	140	17	0	0	NUM
fumecheng-7385	140	18	1	1	NUM
fumecheng-7385	140	19	2	2	NUM
fumecheng-7385	140	20	0	0	NUM
fumecheng-7385	140	21	0	0	NUM
fumecheng-7385	140	22	0	0	NUM
fumecheng-7385	140	23	(	(	PUNCT
fumecheng-7385	140	24	)	)	PUNCT
fumecheng-7385	140	25	(	(	PUNCT
fumecheng-7385	140	26	,	,	PUNCT
fumecheng-7385	140	27	)	)	PUNCT
fumecheng-7385	140	28	(	(	PUNCT
fumecheng-7385	140	29	2	2	NUM
fumecheng-7385	140	30	3	3	NUM
fumecheng-7385	140	31	)	)	PUNCT
fumecheng-7385	140	32	(	(	PUNCT
fumecheng-7385	140	33	)	)	PUNCT
fumecheng-7385	140	34	2	2	NUM
fumecheng-7385	140	35	.tt	.tt	SYM
fumecheng-7385	141	1	xx	xx	NUM
fumecheng-7385	142	1	x	x	PUNCT
fumecheng-7385	142	2	xxu	xxu	PROPN
fumecheng-7385	142	3	x	x	X
fumecheng-7385	142	4	t	t	PROPN
fumecheng-7385	142	5	p	p	X
fumecheng-7385	142	6	qu	qu	PROPN
fumecheng-7385	142	7	u	u	PROPN
fumecheng-7385	142	8	p	p	PROPN
fumecheng-7385	142	9	u	u	X
fumecheng-7385	142	10	u	u	X
fumecheng-7385	142	11	tqu	tqu	PROPN
fumecheng-7385	142	12	+	+	PROPN
fumecheng-7385	142	13			X
fumecheng-7385	142	14	=	=	NOUN
fumecheng-7385	142	15			ADJ
fumecheng-7385	142	16	−	−	ADP
fumecheng-7385	142	17			PROPN
fumecheng-7385	142	18	+	+	PRON
fumecheng-7385	142	19			PROPN
fumecheng-7385	142	20	+	+	CCONJ
fumecheng-7385	142	21	+	+	NUM
fumecheng-7385	142	22			X
fumecheng-7385	143	1	+	+	CCONJ
fumecheng-7385	143	2	+	+	NUM
fumecheng-7385	143	3			ADJ
fumecheng-7385	143	4	−	−	ADJ
fumecheng-7385	143	5			NUM
fumecheng-7385	143	6			NUM
fumecheng-7385	143	7	(	(	PUNCT
fumecheng-7385	143	8	29	29	NUM
fumecheng-7385	143	9	)	)	PUNCT
fumecheng-7385	143	10	suppose	suppose	VERB
fumecheng-7385	143	11	the	the	DET
fumecheng-7385	143	12	solution	solution	NOUN
fumecheng-7385	143	13	of	of	ADP
fumecheng-7385	143	14	eq	eq	PROPN
fumecheng-7385	143	15	.	.	PUNCT
fumecheng-7385	144	1	(	(	PUNCT
fumecheng-7385	144	2	25	25	NUM
fumecheng-7385	144	3	)	)	PUNCT
fumecheng-7385	144	4	has	have	VERB
fumecheng-7385	144	5	the	the	DET
fumecheng-7385	144	6	form	form	NOUN
fumecheng-7385	144	7	0	0	NUM
fumecheng-7385	145	1	(	(	PUNCT
fumecheng-7385	145	2	,	,	PUNCT
fumecheng-7385	145	3	)	)	PUNCT
fumecheng-7385	145	4	cos	cos	PROPN
fumecheng-7385	145	5	(	(	PUNCT
fumecheng-7385	145	6	)	)	PUNCT
fumecheng-7385	145	7	,	,	PUNCT
fumecheng-7385	145	8	x	x	X
fumecheng-7385	145	9	pu	pu	PROPN
fumecheng-7385	145	10	x	x	PROPN
fumecheng-7385	145	11	t	t	PROPN
fumecheng-7385	145	12	ae	ae	INTJ
fumecheng-7385	145	13	t	t	PROPN
fumecheng-7385	145	14	−	−	PROPN
fumecheng-7385	145	15	=	=	SYM
fumecheng-7385	145	16			PROPN
fumecheng-7385	146	1	+	+	NUM
fumecheng-7385	146	2			NOUN
fumecheng-7385	146	3			X
fumecheng-7385	146	4	(	(	PUNCT
fumecheng-7385	146	5	30	30	NUM
fumecheng-7385	146	6	)	)	PUNCT
fumecheng-7385	146	7	where	where	SCONJ
fumecheng-7385	146	8	unknown	unknown	ADJ
fumecheng-7385	146	9	arbitrary	arbitrary	ADJ
fumecheng-7385	146	10	function	function	NOUN
fumecheng-7385	146	11	b(x	b(x	NOUN
fumecheng-7385	146	12	)	)	PUNCT
fumecheng-7385	146	13	is	be	AUX
fumecheng-7385	146	14	chosen	choose	VERB
fumecheng-7385	146	15	to	to	PART
fumecheng-7385	146	16	be	be	AUX
fumecheng-7385	146	17	(	(	PUNCT
fumecheng-7385	146	18	)	)	PUNCT
fumecheng-7385	146	19	,	,	PUNCT
fumecheng-7385	146	20	x	x	PUNCT
fumecheng-7385	146	21	pb	pb	ADP
fumecheng-7385	146	22	x	x	PUNCT
fumecheng-7385	146	23	ae	ae	PROPN
fumecheng-7385	146	24			NOUN
fumecheng-7385	146	25	−	−	NOUN
fumecheng-7385	146	26	=	=	PUNCT
fumecheng-7385	146	27	with	with	ADP
fumecheng-7385	146	28	constant	constant	ADJ
fumecheng-7385	146	29	a.	a.	NOUN
fumecheng-7385	146	30	by	by	ADP
fumecheng-7385	146	31	making	make	VERB
fumecheng-7385	146	32	use	use	NOUN
fumecheng-7385	146	33	of	of	ADP
fumecheng-7385	146	34	(	(	PUNCT
fumecheng-7385	146	35	20	20	NUM
fumecheng-7385	146	36	)	)	PUNCT
fumecheng-7385	146	37	into	into	ADP
fumecheng-7385	146	38	(	(	PUNCT
fumecheng-7385	146	39	18	18	NUM
fumecheng-7385	146	40	)	)	PUNCT
fumecheng-7385	146	41	,	,	PUNCT
fumecheng-7385	146	42	we	we	PRON
fumecheng-7385	146	43	transformed	transform	VERB
fumecheng-7385	146	44	the	the	DET
fumecheng-7385	146	45	right	right	ADJ
fumecheng-7385	146	46	-	-	PUNCT
fumecheng-7385	146	47	hand	hand	NOUN
fumecheng-7385	146	48	side	side	NOUN
fumecheng-7385	146	49	into	into	ADP
fumecheng-7385	146	50	a	a	DET
fumecheng-7385	146	51	polynomial	polynomial	NOUN
fumecheng-7385	146	52	in	in	ADP
fumecheng-7385	146	53	exp	exp	NOUN
fumecheng-7385	146	54	(	(	PUNCT
fumecheng-7385	146	55	)	)	PUNCT
fumecheng-7385	146	56	.x	.x	PROPN
fumecheng-7385	146	57	p	p	NOUN
fumecheng-7385	146	58			NOUN
fumecheng-7385	146	59	−	−	NOUN
fumecheng-7385	146	60	740	740	NUM
fumecheng-7385	146	61	j.-h	j.-h	NOUN
fumecheng-7385	146	62	.	.	PUNCT
fumecheng-7385	147	1	he	he	PRON
fumecheng-7385	147	2	,	,	PUNCT
fumecheng-7385	147	3	y.	y.	PROPN
fumecheng-7385	147	4	o.	o.	PROPN
fumecheng-7385	147	5	el	el	PROPN
fumecheng-7385	147	6	-	-	PROPN
fumecheng-7385	147	7	dib	dib	PROPN
fumecheng-7385	147	8	(	(	PUNCT
fumecheng-7385	147	9	)	)	PUNCT
fumecheng-7385	147	10	(	(	PUNCT
fumecheng-7385	147	11	)	)	PUNCT
fumecheng-7385	147	12	(	(	PUNCT
fumecheng-7385	147	13	)	)	PUNCT
fumecheng-7385	147	14	22	22	NUM
fumecheng-7385	147	15	2	2	NUM
fumecheng-7385	147	16	2	2	NUM
fumecheng-7385	147	17	1	1	NUM
fumecheng-7385	147	18	1	1	NUM
fumecheng-7385	147	19	3	3	NUM
fumecheng-7385	147	20	3	3	NUM
fumecheng-7385	147	21	3	3	NUM
fumecheng-7385	147	22	3	3	NUM
fumecheng-7385	147	23	(	(	PUNCT
fumecheng-7385	147	24	,	,	PUNCT
fumecheng-7385	147	25	)	)	PUNCT
fumecheng-7385	147	26	cos	cos	ADP
fumecheng-7385	147	27	4	4	NUM
fumecheng-7385	147	28	1	1	NUM
fumecheng-7385	147	29	cos	cos	NOUN
fumecheng-7385	147	30	3	3	NUM
fumecheng-7385	147	31	3	3	NUM
fumecheng-7385	147	32	4	4	NUM
fumecheng-7385	147	33	x	x	SYM
fumecheng-7385	147	34	x	x	X
fumecheng-7385	147	35	p	p	X
fumecheng-7385	147	36	p	p	X
fumecheng-7385	147	37	tt	tt	PROPN
fumecheng-7385	147	38	x	x	X
fumecheng-7385	147	39	p	p	X
fumecheng-7385	147	40	u	u	X
fumecheng-7385	147	41	x	x	PROPN
fumecheng-7385	147	42	t	t	PROPN
fumecheng-7385	147	43	a	a	DET
fumecheng-7385	147	44	qe	qe	PROPN
fumecheng-7385	147	45	e	e	PROPN
fumecheng-7385	147	46	a	a	PROPN
fumecheng-7385	147	47	t	t	NOUN
fumecheng-7385	147	48	p	p	X
fumecheng-7385	147	49	e	e	PROPN
fumecheng-7385	147	50	a	a	DET
fumecheng-7385	147	51	q	q	PROPN
fumecheng-7385	147	52	t	t	NOUN
fumecheng-7385	147	53			NOUN
fumecheng-7385	147	54			NOUN
fumecheng-7385	147	55			NOUN
fumecheng-7385	147	56			NOUN
fumecheng-7385	147	57			NOUN
fumecheng-7385	147	58			X
fumecheng-7385	148	1	−	−	PROPN
fumecheng-7385	149	1	−	−	PROPN
fumecheng-7385	149	2	−	−	PROPN
fumecheng-7385	149	3			NOUN
fumecheng-7385	149	4			PROPN
fumecheng-7385	149	5			PROPN
fumecheng-7385	149	6	+	+	PRON
fumecheng-7385	149	7			PROPN
fumecheng-7385	149	8	=	=	SYM
fumecheng-7385	149	9			PROPN
fumecheng-7385	150	1	+	+	CCONJ
fumecheng-7385	150	2	+	+	NUM
fumecheng-7385	150	3			X
fumecheng-7385	151	1	+	+	ADJ
fumecheng-7385	151	2			PROPN
fumecheng-7385	151	3			CCONJ
fumecheng-7385	151	4			PROPN
fumecheng-7385	151	5			PROPN
fumecheng-7385	151	6	+	+	CCONJ
fumecheng-7385	151	7			NUM
fumecheng-7385	151	8	+	+	CCONJ
fumecheng-7385	151	9	(	(	PUNCT
fumecheng-7385	151	10	31	31	NUM
fumecheng-7385	151	11	)	)	PUNCT
fumecheng-7385	151	12	avoiding	avoid	VERB
fumecheng-7385	151	13	the	the	DET
fumecheng-7385	151	14	secular	secular	ADJ
fumecheng-7385	151	15	term	term	NOUN
fumecheng-7385	151	16	that	that	PRON
fumecheng-7385	151	17	appeared	appear	VERB
fumecheng-7385	151	18	in	in	ADP
fumecheng-7385	151	19	eq	eq	ADP
fumecheng-7385	151	20	.	.	PUNCT
fumecheng-7385	152	1	(	(	PUNCT
fumecheng-7385	152	2	31	31	NUM
fumecheng-7385	152	3	)	)	PUNCT
fumecheng-7385	152	4	gives	give	VERB
fumecheng-7385	152	5	.	.	PUNCT
fumecheng-7385	153	1	4	4	NUM
fumecheng-7385	153	2	33	33	NUM
fumecheng-7385	153	3	2	2	NUM
fumecheng-7385	153	4	2	2	NUM
fumecheng-7385	153	5	2	2	NUM
fumecheng-7385	153	6	1	1	NUM
fumecheng-7385	153	7	x	x	NOUN
fumecheng-7385	153	8	pqea	pqea	NOUN
fumecheng-7385	153	9	p	p	NOUN
fumecheng-7385	153	10			NOUN
fumecheng-7385	153	11			NOUN
fumecheng-7385	153	12	−	−	NOUN
fumecheng-7385	153	13	−−=	−−=	CCONJ
fumecheng-7385	153	14	(	(	PUNCT
fumecheng-7385	153	15	32	32	NUM
fumecheng-7385	153	16	)	)	PUNCT
fumecheng-7385	153	17	consequently	consequently	ADV
fumecheng-7385	153	18	,	,	PUNCT
fumecheng-7385	153	19	the	the	DET
fumecheng-7385	153	20	total	total	ADJ
fumecheng-7385	153	21	solution	solution	NOUN
fumecheng-7385	153	22	of	of	ADP
fumecheng-7385	153	23	eq	eq	PROPN
fumecheng-7385	153	24	.	.	PUNCT
fumecheng-7385	154	1	(	(	PUNCT
fumecheng-7385	154	2	31	31	NUM
fumecheng-7385	154	3	)	)	PUNCT
fumecheng-7385	154	4	becomes	become	VERB
fumecheng-7385	154	5	33	33	NUM
fumecheng-7385	154	6	1	1	NUM
fumecheng-7385	154	7	2	2	NUM
fumecheng-7385	154	8	(	(	PUNCT
fumecheng-7385	154	9	,	,	PUNCT
fumecheng-7385	154	10	)	)	PUNCT
fumecheng-7385	154	11	cos(3	cos(3	NOUN
fumecheng-7385	154	12	3	3	NUM
fumecheng-7385	154	13	)	)	PUNCT
fumecheng-7385	154	14	.	.	PUNCT
fumecheng-7385	155	1	32	32	NUM
fumecheng-7385	155	2	x	x	SYM
fumecheng-7385	155	3	p	p	X
fumecheng-7385	155	4	qa	qa	PROPN
fumecheng-7385	155	5	u	u	NOUN
fumecheng-7385	155	6	x	x	PROPN
fumecheng-7385	155	7	t	t	NOUN
fumecheng-7385	155	8	e	e	X
fumecheng-7385	155	9	t	t	NOUN
fumecheng-7385	155	10	−	−	PROPN
fumecheng-7385	155	11	=	=	SYM
fumecheng-7385	156	1	−	−	PROPN
fumecheng-7385	156	2			PROPN
fumecheng-7385	156	3	+	+	CCONJ
fumecheng-7385	156	4			PROPN
fumecheng-7385	156	5			NOUN
fumecheng-7385	156	6			NOUN
fumecheng-7385	156	7	(	(	PUNCT
fumecheng-7385	156	8	33	33	NUM
fumecheng-7385	156	9	)	)	PUNCT
fumecheng-7385	156	10	employing	employ	VERB
fumecheng-7385	156	11	eqs	eqs	PROPN
fumecheng-7385	156	12	.	.	PUNCT
fumecheng-7385	156	13	(	(	PUNCT
fumecheng-7385	156	14	30	30	NUM
fumecheng-7385	156	15	)	)	PUNCT
fumecheng-7385	156	16	and	and	CCONJ
fumecheng-7385	156	17	(	(	PUNCT
fumecheng-7385	156	18	33	33	NUM
fumecheng-7385	156	19	)	)	PUNCT
fumecheng-7385	156	20	into	into	ADP
fumecheng-7385	156	21	eq	eq	NOUN
fumecheng-7385	156	22	.	.	PUNCT
fumecheng-7385	156	23	(	(	PUNCT
fumecheng-7385	156	24	29	29	NUM
fumecheng-7385	156	25	)	)	PUNCT
fumecheng-7385	156	26	,	,	PUNCT
fumecheng-7385	156	27	and	and	CCONJ
fumecheng-7385	156	28	using	use	VERB
fumecheng-7385	156	29	eq	eq	X
fumecheng-7385	156	30	.	.	PUNCT
fumecheng-7385	156	31	(	(	PUNCT
fumecheng-7385	156	32	32	32	NUM
fumecheng-7385	156	33	)	)	PUNCT
fumecheng-7385	156	34	,	,	PUNCT
fumecheng-7385	156	35	the	the	DET
fumecheng-7385	156	36	result	result	NOUN
fumecheng-7385	156	37	reduces	reduce	VERB
fumecheng-7385	156	38	to	to	ADP
fumecheng-7385	156	39	42	42	NUM
fumecheng-7385	156	40	4	4	NUM
fumecheng-7385	156	41	2	2	NUM
fumecheng-7385	156	42	2	2	NUM
fumecheng-7385	156	43	2	2	NUM
fumecheng-7385	156	44	2	2	NUM
fumecheng-7385	156	45	2	2	NUM
fumecheng-7385	156	46	2	2	NUM
fumecheng-7385	156	47	2	2	NUM
fumecheng-7385	156	48	22	22	NUM
fumecheng-7385	156	49	3	3	NUM
fumecheng-7385	156	50	3	3	NUM
fumecheng-7385	156	51	2	2	NUM
fumecheng-7385	156	52	2	2	NUM
fumecheng-7385	156	53	2	2	NUM
fumecheng-7385	156	54	52	52	NUM
fumecheng-7385	156	55	5	5	NUM
fumecheng-7385	156	56	2	2	NUM
fumecheng-7385	156	57	3	3	NUM
fumecheng-7385	156	58	3	3	NUM
fumecheng-7385	156	59	(	(	PUNCT
fumecheng-7385	156	60	)	)	PUNCT
fumecheng-7385	156	61	(	(	PUNCT
fumecheng-7385	156	62	,	,	PUNCT
fumecheng-7385	156	63	)	)	PUNCT
fumecheng-7385	156	64	cos	cos	PROPN
fumecheng-7385	156	65	(	(	PUNCT
fumecheng-7385	156	66	)	)	PUNCT
fumecheng-7385	156	67	2	2	NUM
fumecheng-7385	156	68	128	128	NUM
fumecheng-7385	156	69	1	1	NUM
fumecheng-7385	156	70	3	3	NUM
fumecheng-7385	156	71	3	3	NUM
fumecheng-7385	156	72	cos(3	cos(3	NOUN
fumecheng-7385	156	73	3	3	NUM
fumecheng-7385	156	74	)	)	PUNCT
fumecheng-7385	156	75	2	2	NUM
fumecheng-7385	156	76	8	8	NUM
fumecheng-7385	156	77	128	128	NUM
fumecheng-7385	156	78	3	3	NUM
fumecheng-7385	156	79	cos(5	cos(5	PROPN
fumecheng-7385	156	80	5	5	NUM
fumecheng-7385	156	81	)	)	PUNCT
fumecheng-7385	156	82	.	.	PUNCT
fumecheng-7385	157	1	128	128	NUM
fumecheng-7385	157	2	x	x	SYM
fumecheng-7385	157	3	x	x	PUNCT
fumecheng-7385	157	4	x	x	X
fumecheng-7385	157	5	p	p	X
fumecheng-7385	157	6	p	p	X
fumecheng-7385	157	7	p	p	X
fumecheng-7385	157	8	tt	tt	PROPN
fumecheng-7385	157	9	x	x	PUNCT
fumecheng-7385	157	10	x	x	X
fumecheng-7385	157	11	p	p	X
fumecheng-7385	157	12	p	p	X
fumecheng-7385	157	13	x	x	X
fumecheng-7385	157	14	p	p	X
fumecheng-7385	157	15	q	q	X
fumecheng-7385	157	16	a	a	DET
fumecheng-7385	157	17	u	u	NOUN
fumecheng-7385	157	18	x	x	NOUN
fumecheng-7385	157	19	t	t	NOUN
fumecheng-7385	157	20	tqa	tqa	NOUN
fumecheng-7385	157	21	e	e	PROPN
fumecheng-7385	157	22	e	e	PROPN
fumecheng-7385	157	23	ae	ae	PROPN
fumecheng-7385	157	24	t	t	PROPN
fumecheng-7385	157	25	qa	qa	PROPN
fumecheng-7385	157	26	t	t	PROPN
fumecheng-7385	157	27	a	a	DET
fumecheng-7385	157	28	qe	qe	PROPN
fumecheng-7385	157	29	e	e	PROPN
fumecheng-7385	157	30	t	t	PROPN
fumecheng-7385	157	31	p	p	X
fumecheng-7385	157	32	q	q	PROPN
fumecheng-7385	157	33	a	a	DET
fumecheng-7385	157	34	e	e	NOUN
fumecheng-7385	157	35	t	t	NOUN
fumecheng-7385	157	36	−	−	PROPN
fumecheng-7385	157	37	−	−	PROPN
fumecheng-7385	157	38	−	−	PROPN
fumecheng-7385	157	39	−	−	PROPN
fumecheng-7385	157	40	−	−	PROPN
fumecheng-7385	157	41	−	−	PROPN
fumecheng-7385	157	42			NOUN
fumecheng-7385	157	43			PROPN
fumecheng-7385	157	44			PROPN
fumecheng-7385	157	45	+	+	PRON
fumecheng-7385	157	46			PROPN
fumecheng-7385	157	47	=	=	PUNCT
fumecheng-7385	157	48			PROPN
fumecheng-7385	158	1	+	+	CCONJ
fumecheng-7385	158	2	−	−	PROPN
fumecheng-7385	158	3	−	−	NUM
fumecheng-7385	158	4			PROPN
fumecheng-7385	159	1	+	+	CCONJ
fumecheng-7385	159	2			PROPN
fumecheng-7385	159	3			PROPN
fumecheng-7385	159	4			NOUN
fumecheng-7385	159	5			NOUN
fumecheng-7385	159	6			NOUN
fumecheng-7385	159	7			NOUN
fumecheng-7385	159	8	+	+	CCONJ
fumecheng-7385	160	1	−	−	PROPN
fumecheng-7385	160	2	−	−	PROPN
fumecheng-7385	160	3	−	−	PROPN
fumecheng-7385	160	4			PROPN
fumecheng-7385	161	1	+	+	CCONJ
fumecheng-7385	161	2			PROPN
fumecheng-7385	161	3			PROPN
fumecheng-7385	161	4			PROPN
fumecheng-7385	161	5			NOUN
fumecheng-7385	161	6			NOUN
fumecheng-7385	161	7	−	−	PROPN
fumecheng-7385	161	8			PROPN
fumecheng-7385	161	9	+	+	CCONJ
fumecheng-7385	161	10			PROPN
fumecheng-7385	161	11			NOUN
fumecheng-7385	161	12			NOUN
fumecheng-7385	161	13			NOUN
fumecheng-7385	161	14			NOUN
fumecheng-7385	161	15			NOUN
fumecheng-7385	161	16			NOUN
fumecheng-7385	161	17			NUM
fumecheng-7385	161	18			NUM
fumecheng-7385	161	19			NOUN
fumecheng-7385	161	20			NOUN
fumecheng-7385	161	21			NUM
fumecheng-7385	161	22			X
fumecheng-7385	161	23			PROPN
fumecheng-7385	161	24	(	(	PUNCT
fumecheng-7385	161	25	34	34	NUM
fumecheng-7385	161	26	)	)	PUNCT
fumecheng-7385	161	27	avoiding	avoid	VERB
fumecheng-7385	161	28	the	the	DET
fumecheng-7385	161	29	secular	secular	ADJ
fumecheng-7385	161	30	terms	term	NOUN
fumecheng-7385	161	31	from	from	ADP
fumecheng-7385	161	32	eq	eq	ADP
fumecheng-7385	161	33	.	.	PUNCT
fumecheng-7385	162	1	(	(	PUNCT
fumecheng-7385	162	2	34	34	NUM
fumecheng-7385	162	3	)	)	PUNCT
fumecheng-7385	162	4	requires	require	VERB
fumecheng-7385	162	5	that	that	SCONJ
fumecheng-7385	162	6	.0	.0	NUM
fumecheng-7385	162	7	128	128	NUM
fumecheng-7385	162	8	3	3	NUM
fumecheng-7385	162	9	2	2	NUM
fumecheng-7385	162	10	3	3	NUM
fumecheng-7385	162	11	4	4	NUM
fumecheng-7385	162	12	2	2	NUM
fumecheng-7385	162	13	422	422	NUM
fumecheng-7385	162	14	22	22	NUM
fumecheng-7385	162	15	2	2	NUM
fumecheng-7385	162	16	=	=	SYM
fumecheng-7385	162	17			PROPN
fumecheng-7385	162	18	−−+	−−+	NOUN
fumecheng-7385	162	19	−−	−−	PROPN
fumecheng-7385	162	20	x	x	PUNCT
fumecheng-7385	163	1	p	p	X
fumecheng-7385	163	2	x	x	X
fumecheng-7385	163	3	p	p	X
fumecheng-7385	163	4	e	e	X
fumecheng-7385	163	5	aq	aq	X
fumecheng-7385	163	6	eqat	eqat	NOUN
fumecheng-7385	163	7			ADP
fumecheng-7385	163	8			NOUN
fumecheng-7385	163	9	(	(	PUNCT
fumecheng-7385	163	10	35	35	NUM
fumecheng-7385	163	11	)	)	PUNCT
fumecheng-7385	163	12	according	accord	VERB
fumecheng-7385	163	13	to	to	ADP
fumecheng-7385	163	14	the	the	DET
fumecheng-7385	163	15	solvability	solvability	NOUN
fumecheng-7385	163	16	condition	condition	NOUN
fumecheng-7385	163	17	of	of	ADP
fumecheng-7385	163	18	eq	eq	PROPN
fumecheng-7385	163	19	.	.	PUNCT
fumecheng-7385	164	1	(	(	PUNCT
fumecheng-7385	164	2	35	35	NUM
fumecheng-7385	164	3	)	)	PUNCT
fumecheng-7385	164	4	,	,	PUNCT
fumecheng-7385	164	5	the	the	DET
fumecheng-7385	164	6	solution	solution	NOUN
fumecheng-7385	164	7	of	of	ADP
fumecheng-7385	164	8	eq	eq	PROPN
fumecheng-7385	164	9	.	.	PUNCT
fumecheng-7385	165	1	(	(	PUNCT
fumecheng-7385	165	2	34	34	NUM
fumecheng-7385	165	3	)	)	PUNCT
fumecheng-7385	165	4	becomes	become	VERB
fumecheng-7385	165	5	22	22	NUM
fumecheng-7385	165	6	3	3	NUM
fumecheng-7385	165	7	3	3	NUM
fumecheng-7385	165	8	2	2	NUM
fumecheng-7385	165	9	2	2	NUM
fumecheng-7385	165	10	2	2	NUM
fumecheng-7385	165	11	4	4	NUM
fumecheng-7385	165	12	53	53	NUM
fumecheng-7385	165	13	2	2	NUM
fumecheng-7385	165	14	3	3	NUM
fumecheng-7385	165	15	5	5	NUM
fumecheng-7385	165	16	2	2	NUM
fumecheng-7385	165	17	4	4	NUM
fumecheng-7385	165	18	1	1	NUM
fumecheng-7385	165	19	1	1	NUM
fumecheng-7385	165	20	3	3	NUM
fumecheng-7385	165	21	3	3	NUM
fumecheng-7385	165	22	(	(	PUNCT
fumecheng-7385	165	23	,	,	PUNCT
fumecheng-7385	165	24	)	)	PUNCT
fumecheng-7385	165	25	cos(3	cos(3	NOUN
fumecheng-7385	165	26	3	3	NUM
fumecheng-7385	165	27	)	)	PUNCT
fumecheng-7385	165	28	1616	1616	NUM
fumecheng-7385	165	29	256	256	NUM
fumecheng-7385	165	30	3	3	NUM
fumecheng-7385	165	31	sin(3	sin(3	NOUN
fumecheng-7385	165	32	3	3	NUM
fumecheng-7385	165	33	)	)	PUNCT
fumecheng-7385	165	34	cos(5	cos(5	ADJ
fumecheng-7385	165	35	5	5	NUM
fumecheng-7385	165	36	)	)	PUNCT
fumecheng-7385	165	37	.	.	PUNCT
fumecheng-7385	166	1	32	32	NUM
fumecheng-7385	166	2	1024	1024	NUM
fumecheng-7385	166	3	x	x	SYM
fumecheng-7385	167	1	x	x	X
fumecheng-7385	167	2	p	p	X
fumecheng-7385	167	3	p	p	X
fumecheng-7385	167	4	x	x	X
fumecheng-7385	167	5	x	x	X
fumecheng-7385	167	6	p	p	X
fumecheng-7385	167	7	p	p	X
fumecheng-7385	167	8	u	u	X
fumecheng-7385	167	9	x	x	PROPN
fumecheng-7385	167	10	t	t	NOUN
fumecheng-7385	167	11	qa	qa	PROPN
fumecheng-7385	167	12	t	t	PROPN
fumecheng-7385	167	13	a	a	DET
fumecheng-7385	167	14	qe	qe	PROPN
fumecheng-7385	167	15	e	e	PROPN
fumecheng-7385	167	16	t	t	PROPN
fumecheng-7385	167	17	p	p	X
fumecheng-7385	167	18	qa	qa	PROPN
fumecheng-7385	167	19	q	q	PROPN
fumecheng-7385	167	20	e	e	PROPN
fumecheng-7385	167	21	t	t	PROPN
fumecheng-7385	167	22	a	a	DET
fumecheng-7385	167	23	e	e	NOUN
fumecheng-7385	167	24	t	t	NOUN
fumecheng-7385	167	25	−	−	PROPN
fumecheng-7385	167	26	−	−	PROPN
fumecheng-7385	167	27	−	−	PROPN
fumecheng-7385	167	28	−	−	PROPN
fumecheng-7385	167	29			PROPN
fumecheng-7385	167	30			PROPN
fumecheng-7385	167	31			NOUN
fumecheng-7385	167	32	=	=	PUNCT
fumecheng-7385	168	1	+	+	PUNCT
fumecheng-7385	168	2	+	+	CCONJ
fumecheng-7385	168	3			X
fumecheng-7385	169	1	+	+	SYM
fumecheng-7385	169	2			NOUN
fumecheng-7385	169	3			NOUN
fumecheng-7385	169	4			X
fumecheng-7385	169	5			NOUN
fumecheng-7385	169	6			X
fumecheng-7385	169	7			NOUN
fumecheng-7385	169	8			PROPN
fumecheng-7385	169	9			PROPN
fumecheng-7385	169	10	+	+	CCONJ
fumecheng-7385	169	11			PROPN
fumecheng-7385	170	1	+	+	CCONJ
fumecheng-7385	171	1	+	+	NUM
fumecheng-7385	171	2			PRON
fumecheng-7385	171	3	+	+	CCONJ
fumecheng-7385	171	4			PROPN
fumecheng-7385	171	5			PROPN
fumecheng-7385	171	6			NOUN
fumecheng-7385	171	7			NOUN
fumecheng-7385	171	8			NOUN
fumecheng-7385	171	9			NOUN
fumecheng-7385	171	10			NOUN
fumecheng-7385	171	11			NUM
fumecheng-7385	171	12			NOUN
fumecheng-7385	171	13			NUM
fumecheng-7385	171	14			PROPN
fumecheng-7385	171	15			PROPN
fumecheng-7385	171	16	(	(	PUNCT
fumecheng-7385	171	17	36	36	NUM
fumecheng-7385	171	18	)	)	PUNCT
fumecheng-7385	171	19	the	the	DET
fumecheng-7385	171	20	approximate	approximate	ADJ
fumecheng-7385	171	21	second	second	ADJ
fumecheng-7385	171	22	-	-	PUNCT
fumecheng-7385	171	23	order	order	NOUN
fumecheng-7385	171	24	solution	solution	NOUN
fumecheng-7385	171	25	can	can	AUX
fumecheng-7385	171	26	be	be	AUX
fumecheng-7385	171	27	performed	perform	VERB
fumecheng-7385	171	28	by	by	ADP
fumecheng-7385	171	29	inserting	insert	VERB
fumecheng-7385	171	30	eqs	eqs	PROPN
fumecheng-7385	171	31	.	.	PUNCT
fumecheng-7385	172	1	(	(	PUNCT
fumecheng-7385	172	2	30	30	NUM
fumecheng-7385	172	3	)	)	PUNCT
fumecheng-7385	172	4	,	,	PUNCT
fumecheng-7385	172	5	(	(	PUNCT
fumecheng-7385	172	6	33	33	NUM
fumecheng-7385	172	7	)	)	PUNCT
fumecheng-7385	172	8	,	,	PUNCT
fumecheng-7385	172	9	and	and	CCONJ
fumecheng-7385	172	10	(	(	PUNCT
fumecheng-7385	172	11	36	36	NUM
fumecheng-7385	172	12	)	)	PUNCT
fumecheng-7385	172	13	into	into	ADP
fumecheng-7385	172	14	eq	eq	NOUN
fumecheng-7385	172	15	.	.	PUNCT
fumecheng-7385	173	1	(	(	PUNCT
fumecheng-7385	173	2	18	18	NUM
fumecheng-7385	173	3	)	)	PUNCT
fumecheng-7385	173	4	,	,	PUNCT
fumecheng-7385	173	5	and	and	CCONJ
fumecheng-7385	173	6	taking	take	VERB
fumecheng-7385	173	7	q	q	NOUN
fumecheng-7385	173	8	=	=	SYM
fumecheng-7385	173	9	1	1	NUM
fumecheng-7385	173	10	yields	yield	NOUN
fumecheng-7385	173	11	:	:	PUNCT
fumecheng-7385	173	12	3	3	NUM
fumecheng-7385	173	13	3	3	NUM
fumecheng-7385	173	14	2	2	NUM
fumecheng-7385	173	15	33	33	NUM
fumecheng-7385	173	16	2	2	NUM
fumecheng-7385	173	17	323	323	NUM
fumecheng-7385	173	18	2	2	NUM
fumecheng-7385	173	19	2	2	NUM
fumecheng-7385	173	20	4	4	NUM
fumecheng-7385	173	21	52	52	NUM
fumecheng-7385	173	22	5	5	NUM
fumecheng-7385	173	23	4	4	NUM
fumecheng-7385	173	24	(	(	PUNCT
fumecheng-7385	173	25	,	,	PUNCT
fumecheng-7385	173	26	)	)	PUNCT
fumecheng-7385	173	27	cos	cos	PROPN
fumecheng-7385	173	28	(	(	PUNCT
fumecheng-7385	173	29	)	)	PUNCT
fumecheng-7385	173	30	cos(3	cos(3	NOUN
fumecheng-7385	173	31	3	3	NUM
fumecheng-7385	173	32	)	)	PUNCT
fumecheng-7385	173	33	32	32	NUM
fumecheng-7385	173	34	3	3	NUM
fumecheng-7385	173	35	sin(3	sin(3	NOUN
fumecheng-7385	173	36	3	3	NUM
fumecheng-7385	173	37	)	)	PUNCT
fumecheng-7385	173	38	32	32	NUM
fumecheng-7385	173	39	3	3	NUM
fumecheng-7385	173	40	3	3	NUM
fumecheng-7385	173	41	cos(3	cos(3	NOUN
fumecheng-7385	173	42	3	3	NUM
fumecheng-7385	173	43	)	)	PUNCT
fumecheng-7385	173	44	16256	16256	NUM
fumecheng-7385	173	45	cos(5	cos(5	PROPN
fumecheng-7385	173	46	5	5	NUM
fumecheng-7385	173	47	)	)	PUNCT
fumecheng-7385	173	48	.	.	PUNCT
fumecheng-7385	174	1	1024	1024	NUM
fumecheng-7385	174	2	t	t	NOUN
fumecheng-7385	174	3	x	x	SYM
fumecheng-7385	174	4	t	t	NOUN
fumecheng-7385	174	5	x	x	PROPN
fumecheng-7385	174	6	p	p	X
fumecheng-7385	174	7	p	p	X
fumecheng-7385	174	8	t	t	X
fumecheng-7385	174	9	x	x	X
fumecheng-7385	174	10	p	p	NOUN
fumecheng-7385	174	11	t	t	NOUN
fumecheng-7385	174	12	xx	xx	NUM
fumecheng-7385	175	1	pp	pp	ADV
fumecheng-7385	175	2	t	t	PROPN
fumecheng-7385	176	1	x	x	PUNCT
fumecheng-7385	176	2	p	p	X
fumecheng-7385	176	3	qa	qa	PROPN
fumecheng-7385	176	4	y	y	PROPN
fumecheng-7385	176	5	x	x	PROPN
fumecheng-7385	176	6	t	t	PROPN
fumecheng-7385	176	7	ae	ae	PROPN
fumecheng-7385	176	8	t	t	PROPN
fumecheng-7385	176	9	e	e	PROPN
fumecheng-7385	176	10	t	t	PROPN
fumecheng-7385	176	11	qa	qa	PROPN
fumecheng-7385	176	12	e	e	PROPN
fumecheng-7385	176	13	t	t	PROPN
fumecheng-7385	176	14	qa	qa	PROPN
fumecheng-7385	176	15	a	a	DET
fumecheng-7385	176	16	qe	qe	PROPN
fumecheng-7385	176	17	e	e	PROPN
fumecheng-7385	176	18	t	t	PROPN
fumecheng-7385	176	19	p	p	X
fumecheng-7385	176	20	q	q	PROPN
fumecheng-7385	176	21	a	a	DET
fumecheng-7385	176	22	e	e	NOUN
fumecheng-7385	176	23	t	t	PROPN
fumecheng-7385	176	24			NOUN
fumecheng-7385	176	25			PROPN
fumecheng-7385	176	26			NOUN
fumecheng-7385	176	27			NOUN
fumecheng-7385	176	28	−	−	PROPN
fumecheng-7385	177	1	+	+	CCONJ
fumecheng-7385	177	2	−	−	PROPN
fumecheng-7385	178	1	+	+	ADJ
fumecheng-7385	178	2			PROPN
fumecheng-7385	179	1			PROPN
fumecheng-7385	180	1			PROPN
fumecheng-7385	180	2			PROPN
fumecheng-7385	181	1			ADJ
fumecheng-7385	181	2			PROPN
fumecheng-7385	181	3			PROPN
fumecheng-7385	181	4			NOUN
fumecheng-7385	181	5			NOUN
fumecheng-7385	181	6			NOUN
fumecheng-7385	181	7	−	−	PROPN
fumecheng-7385	182	1	+	+	ADJ
fumecheng-7385	182	2			PROPN
fumecheng-7385	182	3			PROPN
fumecheng-7385	182	4			PROPN
fumecheng-7385	182	5			NOUN
fumecheng-7385	182	6			VERB
fumecheng-7385	182	7			NOUN
fumecheng-7385	182	8	−	−	PUNCT
fumecheng-7385	183	1	+	+	NOUN
fumecheng-7385	183	2	−	−	PROPN
fumecheng-7385	183	3			PROPN
fumecheng-7385	183	4			PROPN
fumecheng-7385	184	1			PROPN
fumecheng-7385	184	2			NOUN
fumecheng-7385	184	3			VERB
fumecheng-7385	184	4			NOUN
fumecheng-7385	184	5	−	−	PROPN
fumecheng-7385	185	1	+	+	ADJ
fumecheng-7385	185	2			PROPN
fumecheng-7385	185	3			PROPN
fumecheng-7385	186	1			PROPN
fumecheng-7385	186	2			PROPN
fumecheng-7385	186	3	=	=	SYM
fumecheng-7385	186	4			PROPN
fumecheng-7385	187	1	+	+	CCONJ
fumecheng-7385	187	2	−	−	PROPN
fumecheng-7385	187	3			PROPN
fumecheng-7385	188	1	+	+	CCONJ
fumecheng-7385	188	2			PROPN
fumecheng-7385	189	1	+	+	CCONJ
fumecheng-7385	189	2			PROPN
fumecheng-7385	189	3	+	+	CCONJ
fumecheng-7385	189	4			PROPN
fumecheng-7385	189	5			NOUN
fumecheng-7385	189	6			NOUN
fumecheng-7385	189	7	+	+	CCONJ
fumecheng-7385	190	1	+	+	NUM
fumecheng-7385	190	2			X
fumecheng-7385	191	1	+	+	ADJ
fumecheng-7385	191	2			PROPN
fumecheng-7385	191	3			PRON
fumecheng-7385	191	4			PROPN
fumecheng-7385	191	5			ADJ
fumecheng-7385	191	6			PROPN
fumecheng-7385	191	7	+	+	CCONJ
fumecheng-7385	191	8			PROPN
fumecheng-7385	191	9	+	+	CCONJ
fumecheng-7385	191	10			NOUN
fumecheng-7385	191	11			NOUN
fumecheng-7385	191	12			NOUN
fumecheng-7385	191	13			NUM
fumecheng-7385	191	14			NUM
fumecheng-7385	191	15			NOUN
fumecheng-7385	191	16			NUM
fumecheng-7385	191	17			ADP
fumecheng-7385	191	18			NUM
fumecheng-7385	191	19			NOUN
fumecheng-7385	191	20			NUM
fumecheng-7385	191	21			X
fumecheng-7385	191	22			PROPN
fumecheng-7385	191	23			CCONJ
fumecheng-7385	191	24			SYM
fumecheng-7385	191	25			NOUN
fumecheng-7385	191	26			NOUN
fumecheng-7385	191	27			PROPN
fumecheng-7385	191	28	(	(	PUNCT
fumecheng-7385	191	29	37	37	NUM
fumecheng-7385	191	30	)	)	PUNCT
fumecheng-7385	191	31	the	the	DET
fumecheng-7385	191	32	enhanced	enhance	VERB
fumecheng-7385	191	33	homotopy	homotopy	NOUN
fumecheng-7385	191	34	perturbation	perturbation	NOUN
fumecheng-7385	191	35	method	method	NOUN
fumecheng-7385	191	36	for	for	ADP
fumecheng-7385	191	37	axial	axial	ADJ
fumecheng-7385	191	38	vibrations	vibration	NOUN
fumecheng-7385	191	39	of	of	ADP
fumecheng-7385	191	40	strings	string	NOUN
fumecheng-7385	191	41	741	741	NUM
fumecheng-7385	191	42	if	if	SCONJ
fumecheng-7385	191	43	the	the	DET
fumecheng-7385	191	44	higher	high	ADJ
fumecheng-7385	191	45	orders	order	NOUN
fumecheng-7385	191	46	of	of	ADP
fumecheng-7385	191	47	the	the	DET
fumecheng-7385	191	48	perturbation	perturbation	NOUN
fumecheng-7385	191	49	are	be	AUX
fumecheng-7385	191	50	done	do	VERB
fumecheng-7385	191	51	,	,	PUNCT
fumecheng-7385	191	52	the	the	DET
fumecheng-7385	191	53	compact	compact	ADJ
fumecheng-7385	191	54	form	form	NOUN
fumecheng-7385	191	55	of	of	ADP
fumecheng-7385	191	56	(	(	PUNCT
fumecheng-7385	191	57	1	1	NUM
fumecheng-7385	191	58	–	–	PUNCT
fumecheng-7385	191	59	2t	2t	PROPN
fumecheng-7385	191	60	+	+	CCONJ
fumecheng-7385	191	61	…	…	PUNCT
fumecheng-7385	191	62	)	)	PUNCT
fumecheng-7385	191	63	becomes	become	VERB
fumecheng-7385	191	64	2	2	NUM
fumecheng-7385	191	65	te	te	PROPN
fumecheng-7385	191	66	−	−	NOUN
fumecheng-7385	191	67	[	[	X
fumecheng-7385	191	68	3	3	NUM
fumecheng-7385	191	69	]	]	PUNCT
fumecheng-7385	191	70	.	.	PUNCT
fumecheng-7385	192	1	this	this	DET
fumecheng-7385	192	2	solution	solution	NOUN
fumecheng-7385	192	3	still	still	ADV
fumecheng-7385	192	4	contains	contain	VERB
fumecheng-7385	192	5	unknown	unknown	ADJ
fumecheng-7385	192	6	frequency	frequency	NOUN
fumecheng-7385	192	7	.	.	PUNCT
fumecheng-7385	192	8	its	its	PRON
fumecheng-7385	192	9	determination	determination	NOUN
fumecheng-7385	192	10	is	be	AUX
fumecheng-7385	192	11	the	the	DET
fumecheng-7385	192	12	subject	subject	NOUN
fumecheng-7385	192	13	of	of	ADP
fumecheng-7385	192	14	the	the	DET
fumecheng-7385	192	15	following	follow	VERB
fumecheng-7385	192	16	section	section	NOUN
fumecheng-7385	192	17	.	.	PUNCT
fumecheng-7385	193	1	2.2	2.2	NUM
fumecheng-7385	193	2	.	.	PUNCT
fumecheng-7385	194	1	the	the	DET
fumecheng-7385	194	2	nonlinear	nonlinear	ADJ
fumecheng-7385	194	3	frequency	frequency	NOUN
fumecheng-7385	194	4	in	in	ADP
fumecheng-7385	194	5	the	the	DET
fumecheng-7385	194	6	perturbed	perturb	VERB
fumecheng-7385	194	7	form	form	NOUN
fumecheng-7385	194	8	to	to	PART
fumecheng-7385	194	9	get	get	VERB
fumecheng-7385	194	10	stability	stability	NOUN
fumecheng-7385	194	11	condition	condition	NOUN
fumecheng-7385	194	12	the	the	DET
fumecheng-7385	194	13	two	two	NUM
fumecheng-7385	194	14	solvability	solvability	NOUN
fumecheng-7385	194	15	conditions	condition	NOUN
fumecheng-7385	194	16	(	(	PUNCT
fumecheng-7385	194	17	32	32	NUM
fumecheng-7385	194	18	)	)	PUNCT
fumecheng-7385	194	19	and	and	CCONJ
fumecheng-7385	194	20	(	(	PUNCT
fumecheng-7385	194	21	35	35	NUM
fumecheng-7385	194	22	)	)	PUNCT
fumecheng-7385	194	23	can	can	AUX
fumecheng-7385	194	24	be	be	AUX
fumecheng-7385	194	25	used	use	VERB
fumecheng-7385	194	26	to	to	PART
fumecheng-7385	194	27	establish	establish	VERB
fumecheng-7385	194	28	the	the	DET
fumecheng-7385	194	29	frequency	frequency	NOUN
fumecheng-7385	194	30	formula	formula	NOUN
fumecheng-7385	194	31	by	by	ADP
fumecheng-7385	194	32	inserting	insert	VERB
fumecheng-7385	194	33	them	they	PRON
fumecheng-7385	194	34	into	into	ADP
fumecheng-7385	194	35	the	the	DET
fumecheng-7385	194	36	expansion	expansion	NOUN
fumecheng-7385	194	37	(	(	PUNCT
fumecheng-7385	194	38	20	20	NUM
fumecheng-7385	194	39	)	)	PUNCT
fumecheng-7385	194	40	,	,	PUNCT
fumecheng-7385	194	41	and	and	CCONJ
fumecheng-7385	194	42	making	make	VERB
fumecheng-7385	194	43	q	q	NOUN
fumecheng-7385	194	44	=	=	SYM
fumecheng-7385	194	45	1	1	NUM
fumecheng-7385	194	46	yields	yield	NOUN
fumecheng-7385	194	47	:	:	PUNCT
fumecheng-7385	194	48	.	.	PUNCT
fumecheng-7385	195	1	128	128	NUM
fumecheng-7385	195	2	3	3	NUM
fumecheng-7385	195	3	4	4	NUM
fumecheng-7385	195	4	3	3	NUM
fumecheng-7385	195	5	4	4	NUM
fumecheng-7385	195	6	2	2	NUM
fumecheng-7385	195	7	422	422	NUM
fumecheng-7385	195	8	222	222	NUM
fumecheng-7385	195	9	x	x	NOUN
fumecheng-7385	195	10	p	p	X
fumecheng-7385	195	11	x	x	X
fumecheng-7385	195	12	p	p	NOUN
fumecheng-7385	195	13	t	t	X
fumecheng-7385	195	14	e	e	NOUN
fumecheng-7385	195	15	aq	aq	VERB
fumecheng-7385	195	16	qea	qea	PROPN
fumecheng-7385	195	17			ADV
fumecheng-7385	195	18			AUX
fumecheng-7385	195	19			NOUN
fumecheng-7385	195	20	−	−	PRON
fumecheng-7385	195	21			NOUN
fumecheng-7385	195	22			PRON
fumecheng-7385	195	23			PROPN
fumecheng-7385	195	24			PROPN
fumecheng-7385	195	25			NOUN
fumecheng-7385	196	1	+	+	ADP
fumecheng-7385	196	2	−	−	PROPN
fumecheng-7385	196	3			PROPN
fumecheng-7385	196	4	−−=	−−=	X
fumecheng-7385	196	5	(	(	PUNCT
fumecheng-7385	196	6	38	38	NUM
fumecheng-7385	196	7	)	)	PUNCT
fumecheng-7385	196	8	without	without	ADP
fumecheng-7385	196	9	upgrading	upgrade	VERB
fumecheng-7385	196	10	the	the	DET
fumecheng-7385	196	11	power	power	NOUN
fumecheng-7385	196	12	of	of	ADP
fumecheng-7385	196	13	the	the	DET
fumecheng-7385	196	14	frequency	frequency	NOUN
fumecheng-7385	196	15	,	,	PUNCT
fumecheng-7385	196	16	we	we	PRON
fumecheng-7385	196	17	need	need	VERB
fumecheng-7385	196	18	to	to	PART
fumecheng-7385	196	19	obtain	obtain	VERB
fumecheng-7385	196	20	an	an	DET
fumecheng-7385	196	21	approximate	approximate	ADJ
fumecheng-7385	196	22	solution	solution	NOUN
fumecheng-7385	196	23	of	of	ADP
fumecheng-7385	196	24	the	the	DET
fumecheng-7385	196	25	above	above	ADJ
fumecheng-7385	196	26	frequency	frequency	NOUN
fumecheng-7385	196	27	equation	equation	NOUN
fumecheng-7385	196	28	.	.	PUNCT
fumecheng-7385	197	1	to	to	PART
fumecheng-7385	197	2	accomplish	accomplish	VERB
fumecheng-7385	197	3	this	this	DET
fumecheng-7385	197	4	solution	solution	NOUN
fumecheng-7385	197	5	,	,	PUNCT
fumecheng-7385	197	6	we	we	PRON
fumecheng-7385	197	7	put	put	VERB
fumecheng-7385	197	8	eq	eq	ADP
fumecheng-7385	197	9	.	.	PUNCT
fumecheng-7385	198	1	(	(	PUNCT
fumecheng-7385	198	2	38	38	NUM
fumecheng-7385	198	3	)	)	PUNCT
fumecheng-7385	198	4	in	in	ADP
fumecheng-7385	198	5	the	the	DET
fumecheng-7385	198	6	perturbed	perturb	VERB
fumecheng-7385	198	7	form	form	NOUN
fumecheng-7385	198	8	by	by	ADP
fumecheng-7385	198	9	introducing	introduce	VERB
fumecheng-7385	198	10	an	an	DET
fumecheng-7385	198	11	artificial	artificial	ADJ
fumecheng-7385	198	12	small	small	ADJ
fumecheng-7385	198	13	parameter	parameter	NOUN
fumecheng-7385	198	14			PROPN
fumecheng-7385	198	15	[0	[0	NOUN
fumecheng-7385	198	16	,	,	PUNCT
fumecheng-7385	198	17	1	1	NUM
fumecheng-7385	198	18	]	]	PUNCT
fumecheng-7385	198	19	.	.	PUNCT
fumecheng-7385	199	1	thus	thus	ADV
fumecheng-7385	199	2	,	,	PUNCT
fumecheng-7385	199	3	we	we	PRON
fumecheng-7385	199	4	have	have	VERB
fumecheng-7385	199	5	42	42	NUM
fumecheng-7385	199	6	42	42	NUM
fumecheng-7385	199	7	2	2	NUM
fumecheng-7385	199	8	2	2	NUM
fumecheng-7385	199	9	2	2	NUM
fumecheng-7385	199	10	2	2	NUM
fumecheng-7385	199	11	3	3	NUM
fumecheng-7385	199	12	3	3	NUM
fumecheng-7385	199	13	(	(	PUNCT
fumecheng-7385	199	14	)	)	PUNCT
fumecheng-7385	199	15	.	.	PUNCT
fumecheng-7385	200	1	4	4	NUM
fumecheng-7385	200	2	128	128	NUM
fumecheng-7385	200	3	(	(	PUNCT
fumecheng-7385	200	4	)	)	PUNCT
fumecheng-7385	200	5	t	t	NOUN
fumecheng-7385	200	6	x	x	PUNCT
fumecheng-7385	201	1	x	x	X
fumecheng-7385	201	2	p	p	X
fumecheng-7385	201	3	p	p	X
fumecheng-7385	201	4	q	q	X
fumecheng-7385	201	5	a	a	DET
fumecheng-7385	201	6	a	a	DET
fumecheng-7385	201	7	qe	qe	X
fumecheng-7385	201	8	e	e	PROPN
fumecheng-7385	201	9			NOUN
fumecheng-7385	201	10			NOUN
fumecheng-7385	201	11	−	−	PROPN
fumecheng-7385	202	1	+	+	CCONJ
fumecheng-7385	202	2	−	−	PROPN
fumecheng-7385	202	3			PROPN
fumecheng-7385	203	1			ADJ
fumecheng-7385	203	2			NUM
fumecheng-7385	203	3	=	=	SYM
fumecheng-7385	203	4	−	−	PROPN
fumecheng-7385	203	5	−	−	PROPN
fumecheng-7385	203	6			NOUN
fumecheng-7385	203	7			NOUN
fumecheng-7385	203	8			NUM
fumecheng-7385	203	9			NUM
fumecheng-7385	203	10			PROPN
fumecheng-7385	203	11			PROPN
fumecheng-7385	203	12			PROPN
fumecheng-7385	203	13			PROPN
fumecheng-7385	203	14			PROPN
fumecheng-7385	203	15			PROPN
fumecheng-7385	203	16	(	(	PUNCT
fumecheng-7385	203	17	39	39	NUM
fumecheng-7385	203	18	)	)	PUNCT
fumecheng-7385	203	19	consider	consider	VERB
fumecheng-7385	203	20	the	the	DET
fumecheng-7385	203	21	following	follow	VERB
fumecheng-7385	203	22	expansion	expansion	NOUN
fumecheng-7385	203	23	:	:	PUNCT
fumecheng-7385	203	24	...	...	PUNCT
fumecheng-7385	203	25	2	2	NUM
fumecheng-7385	203	26	2	2	NUM
fumecheng-7385	203	27	1	1	NUM
fumecheng-7385	203	28	22	22	NUM
fumecheng-7385	203	29	+	+	ADJ
fumecheng-7385	203	30	+	+	ADJ
fumecheng-7385	203	31	+	+	ADJ
fumecheng-7385	203	32	=	=	ADJ
fumecheng-7385	203	33			X
fumecheng-7385	204	1			X
fumecheng-7385	204	2	(	(	PUNCT
fumecheng-7385	204	3	40	40	NUM
fumecheng-7385	204	4	)	)	PUNCT
fumecheng-7385	204	5	inserting	insert	VERB
fumecheng-7385	204	6	eq	eq	X
fumecheng-7385	204	7	.	.	PUNCT
fumecheng-7385	204	8	(	(	PUNCT
fumecheng-7385	204	9	30	30	NUM
fumecheng-7385	204	10	)	)	PUNCT
fumecheng-7385	204	11	into	into	ADP
fumecheng-7385	204	12	eq	eq	NOUN
fumecheng-7385	204	13	.	.	PUNCT
fumecheng-7385	205	1	(	(	PUNCT
fumecheng-7385	205	2	29	29	NUM
fumecheng-7385	205	3	)	)	PUNCT
fumecheng-7385	205	4	and	and	CCONJ
fumecheng-7385	205	5	equating	equate	VERB
fumecheng-7385	205	6	the	the	DET
fumecheng-7385	205	7	identical	identical	ADJ
fumecheng-7385	205	8	power	power	NOUN
fumecheng-7385	205	9	of	of	ADP
fumecheng-7385	205	10			PROPN
fumecheng-7385	205	11	to	to	ADP
fumecheng-7385	205	12	zero	zero	NUM
fumecheng-7385	205	13	,	,	PUNCT
fumecheng-7385	205	14	we	we	PRON
fumecheng-7385	205	15	obtain	obtain	VERB
fumecheng-7385	205	16	.	.	PUNCT
fumecheng-7385	206	1	128	128	NUM
fumecheng-7385	206	2	3	3	NUM
fumecheng-7385	206	3	4	4	NUM
fumecheng-7385	206	4	3	3	NUM
fumecheng-7385	206	5	2	2	NUM
fumecheng-7385	206	6	42	42	NUM
fumecheng-7385	206	7	2	2	NUM
fumecheng-7385	206	8	1	1	NUM
fumecheng-7385	206	9			NOUN
fumecheng-7385	206	10			X
fumecheng-7385	206	11	aq	aq	NUM
fumecheng-7385	206	12	qa	qa	NOUN
fumecheng-7385	206	13	−−=	−−=	PROPN
fumecheng-7385	206	14	(	(	PUNCT
fumecheng-7385	206	15	41	41	NUM
fumecheng-7385	206	16	)	)	PUNCT
fumecheng-7385	206	17	to	to	PART
fumecheng-7385	206	18	perform	perform	VERB
fumecheng-7385	206	19	the	the	DET
fumecheng-7385	206	20	first	first	ADJ
fumecheng-7385	206	21	-	-	PUNCT
fumecheng-7385	206	22	order	order	NOUN
fumecheng-7385	206	23	approximate	approximate	ADJ
fumecheng-7385	206	24	solution	solution	NOUN
fumecheng-7385	206	25	of	of	ADP
fumecheng-7385	206	26	eq	eq	PROPN
fumecheng-7385	206	27	.	.	PUNCT
fumecheng-7385	207	1	(	(	PUNCT
fumecheng-7385	207	2	39	39	NUM
fumecheng-7385	207	3	)	)	PUNCT
fumecheng-7385	207	4	,	,	PUNCT
fumecheng-7385	207	5	we	we	PRON
fumecheng-7385	207	6	employ	employ	VERB
fumecheng-7385	207	7	eqs	eqs	PROPN
fumecheng-7385	207	8	.	.	PUNCT
fumecheng-7385	208	1	(	(	PUNCT
fumecheng-7385	208	2	13	13	NUM
fumecheng-7385	208	3	)	)	PUNCT
fumecheng-7385	208	4	and	and	CCONJ
fumecheng-7385	208	5	(	(	PUNCT
fumecheng-7385	208	6	41	41	NUM
fumecheng-7385	208	7	)	)	PUNCT
fumecheng-7385	208	8	in	in	ADP
fumecheng-7385	208	9	eq	eq	ADP
fumecheng-7385	208	10	.	.	PUNCT
fumecheng-7385	209	1	(	(	PUNCT
fumecheng-7385	209	2	40	40	NUM
fumecheng-7385	209	3	)	)	PUNCT
fumecheng-7385	209	4	,	,	PUNCT
fumecheng-7385	209	5	which	which	PRON
fumecheng-7385	209	6	yields	yield	VERB
fumecheng-7385	209	7	.	.	PUNCT
fumecheng-7385	210	1	128	128	NUM
fumecheng-7385	210	2	3	3	NUM
fumecheng-7385	210	3	4	4	NUM
fumecheng-7385	210	4	3	3	NUM
fumecheng-7385	210	5	2	2	NUM
fumecheng-7385	210	6	42	42	NUM
fumecheng-7385	210	7	222	222	NUM
fumecheng-7385	210	8			NOUN
fumecheng-7385	210	9			NOUN
fumecheng-7385	210	10	aq	aq	NOUN
fumecheng-7385	210	11	qa	qa	PROPN
fumecheng-7385	211	1	−−=	−−=	CCONJ
fumecheng-7385	211	2	(	(	PUNCT
fumecheng-7385	211	3	42	42	NUM
fumecheng-7385	211	4	)	)	PUNCT
fumecheng-7385	211	5	the	the	DET
fumecheng-7385	211	6	stability	stability	NOUN
fumecheng-7385	211	7	requires	require	VERB
fumecheng-7385	211	8			PROPN
fumecheng-7385	211	9	to	to	PART
fumecheng-7385	211	10	be	be	AUX
fumecheng-7385	211	11	real	real	ADJ
fumecheng-7385	211	12	,	,	PUNCT
fumecheng-7385	211	13	which	which	PRON
fumecheng-7385	211	14	needs	need	VERB
fumecheng-7385	211	15	the	the	DET
fumecheng-7385	211	16	following	follow	VERB
fumecheng-7385	211	17	condition	condition	NOUN
fumecheng-7385	211	18	:	:	PUNCT
fumecheng-7385	211	19	.0	.0	NUM
fumecheng-7385	211	20	128	128	NUM
fumecheng-7385	211	21	3	3	NUM
fumecheng-7385	211	22	4	4	NUM
fumecheng-7385	211	23	3	3	NUM
fumecheng-7385	211	24	2	2	NUM
fumecheng-7385	211	25	42	42	NUM
fumecheng-7385	211	26	22	22	NUM
fumecheng-7385	211	27	−−	−−	PROPN
fumecheng-7385	211	28			NOUN
fumecheng-7385	212	1			NOUN
fumecheng-7385	212	2	aq	aq	PROPN
fumecheng-7385	212	3	qa	qa	PROPN
fumecheng-7385	212	4	(	(	PUNCT
fumecheng-7385	212	5	43	43	NUM
fumecheng-7385	212	6	)	)	PUNCT
fumecheng-7385	212	7	employing	employ	VERB
fumecheng-7385	212	8	the	the	DET
fumecheng-7385	212	9	linear	linear	ADJ
fumecheng-7385	212	10	frequency	frequency	NOUN
fumecheng-7385	212	11	as	as	SCONJ
fumecheng-7385	212	12	defined	define	VERB
fumecheng-7385	212	13	by	by	ADP
fumecheng-7385	212	14	eq	eq	PROPN
fumecheng-7385	212	15	.	.	PUNCT
fumecheng-7385	213	1	(	(	PUNCT
fumecheng-7385	213	2	13	13	NUM
fumecheng-7385	213	3	)	)	PUNCT
fumecheng-7385	213	4	,	,	PUNCT
fumecheng-7385	213	5	we	we	PRON
fumecheng-7385	213	6	obtain	obtain	VERB
fumecheng-7385	213	7	.0	.0	NUM
fumecheng-7385	213	8	128	128	NUM
fumecheng-7385	213	9	33	33	NUM
fumecheng-7385	213	10	4	4	NUM
fumecheng-7385	213	11	33	33	NUM
fumecheng-7385	213	12	422	422	NUM
fumecheng-7385	213	13	22	22	NUM
fumecheng-7385	213	14	2	2	NUM
fumecheng-7385	213	15	2	2	NUM
fumecheng-7385	213	16	2	2	NUM
fumecheng-7385	213	17	−	−	NUM
fumecheng-7385	213	18			PROPN
fumecheng-7385	213	19			PROPN
fumecheng-7385	214	1			NOUN
fumecheng-7385	215	1			PROPN
fumecheng-7385	215	2			PROPN
fumecheng-7385	215	3			PROPN
fumecheng-7385	216	1			PROPN
fumecheng-7385	216	2			NOUN
fumecheng-7385	216	3	−−−	−−−	PUNCT
fumecheng-7385	217	1			PROPN
fumecheng-7385	218	1			PROPN
fumecheng-7385	218	2			NOUN
fumecheng-7385	219	1			PROPN
fumecheng-7385	219	2			PROPN
fumecheng-7385	219	3			PROPN
fumecheng-7385	220	1			PROPN
fumecheng-7385	220	2			NOUN
fumecheng-7385	220	3	−−	−−	PROPN
fumecheng-7385	220	4	aq	aq	X
fumecheng-7385	221	1	p	p	NOUN
fumecheng-7385	221	2	qa	qa	PROPN
fumecheng-7385	221	3	p	p	NOUN
fumecheng-7385	221	4			NOUN
fumecheng-7385	221	5			ADJ
fumecheng-7385	221	6			NOUN
fumecheng-7385	221	7			PROPN
fumecheng-7385	221	8	(	(	PUNCT
fumecheng-7385	221	9	44	44	NUM
fumecheng-7385	221	10	)	)	PUNCT
fumecheng-7385	221	11	2.3	2.3	NUM
fumecheng-7385	221	12	.	.	PUNCT
fumecheng-7385	222	1	numerical	numerical	PROPN
fumecheng-7385	222	2	illustrations	illustration	NOUN
fumecheng-7385	222	3	the	the	DET
fumecheng-7385	222	4	numerical	numerical	ADJ
fumecheng-7385	222	5	solution	solution	NOUN
fumecheng-7385	222	6	of	of	ADP
fumecheng-7385	222	7	the	the	DET
fumecheng-7385	222	8	damped	damped	NOUN
fumecheng-7385	222	9	nonlinear	nonlinear	ADJ
fumecheng-7385	222	10	kg	kg	NOUN
fumecheng-7385	222	11	-	-	PUNCT
fumecheng-7385	222	12	equation	equation	NOUN
fumecheng-7385	222	13	(	(	PUNCT
fumecheng-7385	222	14	11	11	NUM
fumecheng-7385	222	15	)	)	PUNCT
fumecheng-7385	222	16	is	be	AUX
fumecheng-7385	222	17	obtained	obtain	VERB
fumecheng-7385	222	18	by	by	ADP
fumecheng-7385	222	19	using	use	VERB
fumecheng-7385	222	20	a	a	DET
fumecheng-7385	222	21	mathematical	mathematical	ADJ
fumecheng-7385	222	22	software	software	NOUN
fumecheng-7385	222	23	for	for	ADP
fumecheng-7385	222	24	the	the	DET
fumecheng-7385	222	25	system	system	NOUN
fumecheng-7385	222	26	of	of	ADP
fumecheng-7385	222	27	p=1	p=1	PROPN
fumecheng-7385	222	28	,	,	PUNCT
fumecheng-7385	222	29	=3	=3	PROPN
fumecheng-7385	222	30	,	,	PUNCT
fumecheng-7385	222	31	q=0.3	q=0.3	ADJ
fumecheng-7385	222	32	,	,	PUNCT
fumecheng-7385	222	33	a=1	a=1	ADP
fumecheng-7385	222	34	,	,	PUNCT
fumecheng-7385	222	35	=0.1	=0.1	PROPN
fumecheng-7385	222	36	,	,	PUNCT
fumecheng-7385	222	37	=0.1	=0.1	PROPN
fumecheng-7385	222	38	.	.	PUNCT
fumecheng-7385	223	1	the	the	DET
fumecheng-7385	223	2	results	result	NOUN
fumecheng-7385	223	3	are	be	AUX
fumecheng-7385	223	4	displayed	display	VERB
fumecheng-7385	223	5	in	in	ADP
fumecheng-7385	223	6	fig	fig	NOUN
fumecheng-7385	223	7	.	.	PUNCT
fumecheng-7385	224	1	1	1	X
fumecheng-7385	224	2	.	.	X
fumecheng-7385	225	1	it	it	PRON
fumecheng-7385	225	2	is	be	AUX
fumecheng-7385	225	3	noted	note	VERB
fumecheng-7385	225	4	that	that	SCONJ
fumecheng-7385	225	5	the	the	DET
fumecheng-7385	225	6	small	small	ADJ
fumecheng-7385	225	7	values	value	NOUN
fumecheng-7385	225	8	in	in	ADP
fumecheng-7385	225	9	damping	damp	VERB
fumecheng-7385	225	10	coefficients	coefficient	NOUN
fumecheng-7385	225	11			NUM
fumecheng-7385	225	12	742	742	NUM
fumecheng-7385	225	13	j.-h	j.-h	NOUN
fumecheng-7385	225	14	.	.	PUNCT
fumecheng-7385	226	1	he	he	PRON
fumecheng-7385	226	2	,	,	PUNCT
fumecheng-7385	226	3	y.	y.	PROPN
fumecheng-7385	226	4	o.	o.	PROPN
fumecheng-7385	226	5	el	el	PROPN
fumecheng-7385	226	6	-	-	PROPN
fumecheng-7385	226	7	dib	dib	NOUN
fumecheng-7385	226	8	and	and	CCONJ
fumecheng-7385	226	9			NOUN
fumecheng-7385	226	10	lead	lead	NOUN
fumecheng-7385	226	11	to	to	ADP
fumecheng-7385	226	12	the	the	DET
fumecheng-7385	226	13	gradual	gradual	ADJ
fumecheng-7385	226	14	damping	damping	NOUN
fumecheng-7385	226	15	in	in	ADP
fumecheng-7385	226	16	the	the	DET
fumecheng-7385	226	17	periodic	periodic	ADJ
fumecheng-7385	226	18	wave	wave	NOUN
fumecheng-7385	226	19	solution	solution	NOUN
fumecheng-7385	226	20	.	.	PUNCT
fumecheng-7385	227	1	the	the	DET
fumecheng-7385	227	2	analytical	analytical	ADJ
fumecheng-7385	227	3	solution	solution	NOUN
fumecheng-7385	227	4	as	as	SCONJ
fumecheng-7385	227	5	given	give	VERB
fumecheng-7385	227	6	by	by	ADP
fumecheng-7385	227	7	eq	eq	PROPN
fumecheng-7385	227	8	.	.	PUNCT
fumecheng-7385	228	1	(	(	PUNCT
fumecheng-7385	228	2	37	37	NUM
fumecheng-7385	228	3	)	)	PUNCT
fumecheng-7385	228	4	is	be	AUX
fumecheng-7385	228	5	also	also	ADV
fumecheng-7385	228	6	calculated	calculate	VERB
fumecheng-7385	228	7	numerically	numerically	ADV
fumecheng-7385	228	8	for	for	ADP
fumecheng-7385	228	9	the	the	DET
fumecheng-7385	228	10	same	same	ADJ
fumecheng-7385	228	11	system	system	NOUN
fumecheng-7385	228	12	as	as	SCONJ
fumecheng-7385	228	13	used	use	VERB
fumecheng-7385	228	14	in	in	ADP
fumecheng-7385	228	15	the	the	DET
fumecheng-7385	228	16	numerical	numerical	ADJ
fumecheng-7385	228	17	solution	solution	NOUN
fumecheng-7385	228	18	,	,	PUNCT
fumecheng-7385	228	19	assuming	assume	VERB
fumecheng-7385	228	20	that	that	SCONJ
fumecheng-7385	228	21	=0	=0	PROPN
fumecheng-7385	228	22	.	.	PUNCT
fumecheng-7385	229	1	the	the	DET
fumecheng-7385	229	2	results	result	NOUN
fumecheng-7385	229	3	are	be	AUX
fumecheng-7385	229	4	located	locate	VERB
fumecheng-7385	229	5	in	in	ADP
fumecheng-7385	229	6	fig	fig	NOUN
fumecheng-7385	229	7	.	.	PUNCT
fumecheng-7385	230	1	2	2	X
fumecheng-7385	230	2	.	.	X
fumecheng-7385	230	3	fig	fig	NOUN
fumecheng-7385	230	4	.	.	PUNCT
fumecheng-7385	231	1	1	1	NUM
fumecheng-7385	232	1	the	the	DET
fumecheng-7385	232	2	numerical	numerical	ADJ
fumecheng-7385	232	3	solution	solution	NOUN
fumecheng-7385	232	4	of	of	ADP
fumecheng-7385	232	5	eq	eq	PROPN
fumecheng-7385	232	6	.	.	PUNCT
fumecheng-7385	233	1	(	(	PUNCT
fumecheng-7385	233	2	11	11	NUM
fumecheng-7385	233	3	)	)	PUNCT
fumecheng-7385	233	4	for	for	ADP
fumecheng-7385	233	5	a	a	DET
fumecheng-7385	233	6	system	system	NOUN
fumecheng-7385	233	7	having	have	VERB
fumecheng-7385	233	8	p=1	p=1	NOUN
fumecheng-7385	233	9	,	,	PUNCT
fumecheng-7385	233	10	=3	=3	PROPN
fumecheng-7385	233	11	,	,	PUNCT
fumecheng-7385	233	12	q=0.3	q=0.3	ADJ
fumecheng-7385	233	13	,	,	PUNCT
fumecheng-7385	233	14	a=1	a=1	ADP
fumecheng-7385	233	15	,	,	PUNCT
fumecheng-7385	233	16	=0.1	=0.1	ADP
fumecheng-7385	233	17	,	,	PUNCT
fumecheng-7385	233	18	=0.1	=0.1	ADJ
fumecheng-7385	233	19	fig	fig	NOUN
fumecheng-7385	233	20	.	.	PUNCT
fumecheng-7385	234	1	2	2	NUM
fumecheng-7385	235	1	the	the	DET
fumecheng-7385	235	2	analytical	analytical	ADJ
fumecheng-7385	235	3	approximate	approximate	ADJ
fumecheng-7385	235	4	solution	solution	NOUN
fumecheng-7385	235	5	of	of	ADP
fumecheng-7385	235	6	eq	eq	PROPN
fumecheng-7385	235	7	.	.	PUNCT
fumecheng-7385	236	1	(	(	PUNCT
fumecheng-7385	236	2	11	11	NUM
fumecheng-7385	236	3	)	)	PUNCT
fumecheng-7385	236	4	as	as	SCONJ
fumecheng-7385	236	5	given	give	VERB
fumecheng-7385	236	6	by	by	ADP
fumecheng-7385	236	7	eq	eq	PROPN
fumecheng-7385	236	8	.	.	PUNCT
fumecheng-7385	237	1	(	(	PUNCT
fumecheng-7385	237	2	37	37	NUM
fumecheng-7385	237	3	)	)	PUNCT
fumecheng-7385	237	4	using	use	VERB
fumecheng-7385	237	5	the	the	DET
fumecheng-7385	237	6	full	full	ADJ
fumecheng-7385	237	7	frequency	frequency	NOUN
fumecheng-7385	237	8	as	as	SCONJ
fumecheng-7385	237	9	given	give	VERB
fumecheng-7385	237	10	by	by	ADP
fumecheng-7385	237	11	eq	eq	PROPN
fumecheng-7385	237	12	.	.	PUNCT
fumecheng-7385	238	1	(	(	PUNCT
fumecheng-7385	238	2	39	39	NUM
fumecheng-7385	238	3	)	)	PUNCT
fumecheng-7385	238	4	.	.	PUNCT
fumecheng-7385	239	1	the	the	DET
fumecheng-7385	239	2	system	system	NOUN
fumecheng-7385	239	3	is	be	AUX
fumecheng-7385	239	4	considered	consider	VERB
fumecheng-7385	239	5	as	as	SCONJ
fumecheng-7385	239	6	given	give	VERB
fumecheng-7385	239	7	in	in	ADP
fumecheng-7385	239	8	fig	fig	NOUN
fumecheng-7385	239	9	.	.	PUNCT
fumecheng-7385	240	1	(	(	PUNCT
fumecheng-7385	240	2	1	1	X
fumecheng-7385	240	3	)	)	PUNCT
fumecheng-7385	240	4	for	for	ADP
fumecheng-7385	240	5	comparison	comparison	NOUN
fumecheng-7385	240	6	,	,	PUNCT
fumecheng-7385	240	7	the	the	DET
fumecheng-7385	240	8	two	two	NUM
fumecheng-7385	240	9	kinds	kind	NOUN
fumecheng-7385	240	10	of	of	ADP
fumecheng-7385	240	11	solutions	solution	NOUN
fumecheng-7385	240	12	of	of	ADP
fumecheng-7385	240	13	eq	eq	PROPN
fumecheng-7385	240	14	.	.	PUNCT
fumecheng-7385	241	1	(	(	PUNCT
fumecheng-7385	241	2	11	11	NUM
fumecheng-7385	241	3	)	)	PUNCT
fumecheng-7385	241	4	are	be	AUX
fumecheng-7385	241	5	collected	collect	VERB
fumecheng-7385	241	6	together	together	ADV
fumecheng-7385	241	7	in	in	ADP
fumecheng-7385	241	8	one	one	NUM
fumecheng-7385	241	9	graph	graph	NOUN
fumecheng-7385	241	10	as	as	SCONJ
fumecheng-7385	241	11	shown	show	VERB
fumecheng-7385	241	12	in	in	ADP
fumecheng-7385	241	13	fig	fig	NOUN
fumecheng-7385	241	14	.	.	PUNCT
fumecheng-7385	242	1	3	3	X
fumecheng-7385	242	2	.	.	X
fumecheng-7385	243	1	it	it	PRON
fumecheng-7385	243	2	is	be	AUX
fumecheng-7385	243	3	observed	observe	VERB
fumecheng-7385	243	4	that	that	SCONJ
fumecheng-7385	243	5	there	there	PRON
fumecheng-7385	243	6	is	be	VERB
fumecheng-7385	243	7	an	an	DET
fumecheng-7385	243	8	excellent	excellent	ADJ
fumecheng-7385	243	9	agreement	agreement	NOUN
fumecheng-7385	243	10	between	between	ADP
fumecheng-7385	243	11	the	the	DET
fumecheng-7385	243	12	numerical	numerical	ADJ
fumecheng-7385	243	13	and	and	CCONJ
fumecheng-7385	243	14	analytical	analytical	ADJ
fumecheng-7385	243	15	solutions	solution	NOUN
fumecheng-7385	243	16	along	along	ADP
fumecheng-7385	243	17	the	the	DET
fumecheng-7385	243	18	time	time	NOUN
fumecheng-7385	243	19	.	.	PUNCT
fumecheng-7385	244	1	the	the	DET
fumecheng-7385	244	2	enhanced	enhance	VERB
fumecheng-7385	244	3	homotopy	homotopy	PROPN
fumecheng-7385	244	4	perturbation	perturbation	NOUN
fumecheng-7385	244	5	method	method	NOUN
fumecheng-7385	244	6	for	for	ADP
fumecheng-7385	244	7	axial	axial	ADJ
fumecheng-7385	244	8	vibrations	vibration	NOUN
fumecheng-7385	244	9	of	of	ADP
fumecheng-7385	244	10	strings	string	NOUN
fumecheng-7385	244	11	743	743	NUM
fumecheng-7385	244	12	fig	fig	NOUN
fumecheng-7385	244	13	.	.	PUNCT
fumecheng-7385	245	1	3	3	NUM
fumecheng-7385	245	2	the	the	DET
fumecheng-7385	245	3	comparison	comparison	NOUN
fumecheng-7385	245	4	between	between	ADP
fumecheng-7385	245	5	the	the	DET
fumecheng-7385	245	6	numerical	numerical	ADJ
fumecheng-7385	245	7	and	and	CCONJ
fumecheng-7385	245	8	analytical	analytical	ADJ
fumecheng-7385	245	9	solutions	solution	NOUN
fumecheng-7385	245	10	of	of	ADP
fumecheng-7385	245	11	eq	eq	PROPN
fumecheng-7385	245	12	.	.	PUNCT
fumecheng-7385	246	1	(	(	PUNCT
fumecheng-7385	246	2	11	11	NUM
fumecheng-7385	246	3	)	)	PUNCT
fumecheng-7385	246	4	for	for	ADP
fumecheng-7385	246	5	the	the	DET
fumecheng-7385	246	6	same	same	ADJ
fumecheng-7385	246	7	system	system	NOUN
fumecheng-7385	246	8	as	as	SCONJ
fumecheng-7385	246	9	given	give	VERB
fumecheng-7385	246	10	in	in	ADP
fumecheng-7385	246	11	fig	fig	NOUN
fumecheng-7385	246	12	.	.	PUNCT
fumecheng-7385	247	1	1	1	NUM
fumecheng-7385	247	2	the	the	DET
fumecheng-7385	247	3	examination	examination	NOUN
fumecheng-7385	247	4	of	of	ADP
fumecheng-7385	247	5	the	the	DET
fumecheng-7385	247	6	impact	impact	NOUN
fumecheng-7385	247	7	of	of	ADP
fumecheng-7385	247	8	temporal	temporal	ADJ
fumecheng-7385	247	9	damping	damp	VERB
fumecheng-7385	247	10	coefficient	coefficient	NOUN
fumecheng-7385	247	11			NUM
fumecheng-7385	247	12	on	on	ADP
fumecheng-7385	247	13	the	the	DET
fumecheng-7385	247	14	picture	picture	NOUN
fumecheng-7385	247	15	of	of	ADP
fumecheng-7385	247	16	the	the	DET
fumecheng-7385	247	17	periodic	periodic	ADJ
fumecheng-7385	247	18	wave	wave	NOUN
fumecheng-7385	247	19	solution	solution	NOUN
fumecheng-7385	247	20	of	of	ADP
fumecheng-7385	247	21	the	the	DET
fumecheng-7385	247	22	modified	modified	ADJ
fumecheng-7385	247	23	analytical	analytical	ADJ
fumecheng-7385	247	24	solution	solution	NOUN
fumecheng-7385	247	25	of	of	ADP
fumecheng-7385	247	26	eq	eq	PROPN
fumecheng-7385	247	27	.	.	PUNCT
fumecheng-7385	248	1	(	(	PUNCT
fumecheng-7385	248	2	37	37	NUM
fumecheng-7385	248	3	)	)	PUNCT
fumecheng-7385	248	4	is	be	AUX
fumecheng-7385	248	5	displayed	display	VERB
fumecheng-7385	248	6	in	in	ADP
fumecheng-7385	248	7	fig	fig	NOUN
fumecheng-7385	248	8	.	.	PUNCT
fumecheng-7385	249	1	4	4	X
fumecheng-7385	249	2	.	.	X
fumecheng-7385	250	1	the	the	DET
fumecheng-7385	250	2	numerical	numerical	ADJ
fumecheng-7385	250	3	values	value	NOUN
fumecheng-7385	250	4	are	be	AUX
fumecheng-7385	250	5	the	the	DET
fumecheng-7385	250	6	same	same	ADJ
fumecheng-7385	250	7	as	as	ADP
fumecheng-7385	250	8	those	those	PRON
fumecheng-7385	250	9	used	use	VERB
fumecheng-7385	250	10	in	in	ADP
fumecheng-7385	250	11	fig	fig	NOUN
fumecheng-7385	250	12	.	.	PUNCT
fumecheng-7385	251	1	(	(	PUNCT
fumecheng-7385	251	2	2	2	NUM
fumecheng-7385	251	3	)	)	PUNCT
fumecheng-7385	251	4	,	,	PUNCT
fumecheng-7385	251	5	except	except	SCONJ
fumecheng-7385	251	6	that	that	SCONJ
fumecheng-7385	251	7	the	the	DET
fumecheng-7385	251	8	spatial	spatial	ADJ
fumecheng-7385	251	9	variable	variable	NOUN
fumecheng-7385	251	10	is	be	AUX
fumecheng-7385	251	11	fixed	fix	VERB
fumecheng-7385	251	12	to	to	PART
fumecheng-7385	251	13	value	value	VERB
fumecheng-7385	251	14	x=1	x=1	PROPN
fumecheng-7385	251	15	.	.	PUNCT
fumecheng-7385	252	1	it	it	PRON
fumecheng-7385	252	2	is	be	AUX
fumecheng-7385	252	3	observed	observe	VERB
fumecheng-7385	252	4	that	that	SCONJ
fumecheng-7385	252	5	as	as	SCONJ
fumecheng-7385	252	6	=0	=0	VERB
fumecheng-7385	252	7	the	the	DET
fumecheng-7385	252	8	pure	pure	ADJ
fumecheng-7385	252	9	periodic	periodic	ADJ
fumecheng-7385	252	10	solution	solution	NOUN
fumecheng-7385	252	11	is	be	AUX
fumecheng-7385	252	12	found	find	VERB
fumecheng-7385	252	13	.	.	PUNCT
fumecheng-7385	253	1	by	by	ADP
fumecheng-7385	253	2	a	a	DET
fumecheng-7385	253	3	slight	slight	ADJ
fumecheng-7385	253	4	change	change	NOUN
fumecheng-7385	253	5	in	in	ADP
fumecheng-7385	253	6			NUM
fumecheng-7385	253	7	from	from	ADP
fumecheng-7385	253	8	the	the	DET
fumecheng-7385	253	9	zero	zero	NUM
fumecheng-7385	253	10	value	value	NOUN
fumecheng-7385	253	11	,	,	PUNCT
fumecheng-7385	253	12	the	the	DET
fumecheng-7385	253	13	damping	damp	VERB
fumecheng-7385	253	14	influence	influence	NOUN
fumecheng-7385	253	15	is	be	AUX
fumecheng-7385	253	16	observed	observe	VERB
fumecheng-7385	253	17	.	.	PUNCT
fumecheng-7385	254	1	the	the	DET
fumecheng-7385	254	2	damping	damp	VERB
fumecheng-7385	254	3	influence	influence	NOUN
fumecheng-7385	254	4	of	of	ADP
fumecheng-7385	254	5	the	the	DET
fumecheng-7385	254	6	increase	increase	NOUN
fumecheng-7385	254	7	of	of	ADP
fumecheng-7385	254	8	spatial	spatial	ADJ
fumecheng-7385	254	9	damping	damp	VERB
fumecheng-7385	254	10	coefficient	coefficient	NOUN
fumecheng-7385	254	11			NOUN
fumecheng-7385	254	12	is	be	AUX
fumecheng-7385	254	13	shown	show	VERB
fumecheng-7385	254	14	in	in	ADP
fumecheng-7385	254	15	fig	fig	NOUN
fumecheng-7385	254	16	.	.	PUNCT
fumecheng-7385	255	1	4	4	X
fumecheng-7385	255	2	.	.	PUNCT
fumecheng-7385	255	3	the	the	DET
fumecheng-7385	255	4	calculation	calculation	NOUN
fumecheng-7385	255	5	is	be	AUX
fumecheng-7385	255	6	made	make	VERB
fumecheng-7385	255	7	for	for	ADP
fumecheng-7385	255	8	the	the	DET
fumecheng-7385	255	9	same	same	ADJ
fumecheng-7385	255	10	system	system	NOUN
fumecheng-7385	255	11	as	as	SCONJ
fumecheng-7385	255	12	illustrated	illustrate	VERB
fumecheng-7385	255	13	in	in	ADP
fumecheng-7385	255	14	fig	fig	NOUN
fumecheng-7385	255	15	.	.	PUNCT
fumecheng-7385	255	16	4	4	NUM
fumecheng-7385	255	17	by	by	ADP
fumecheng-7385	255	18	fixing	fix	VERB
fumecheng-7385	255	19			NUM
fumecheng-7385	255	20	at	at	ADP
fumecheng-7385	255	21	the	the	DET
fumecheng-7385	255	22	zero	zero	NUM
fumecheng-7385	255	23	value	value	NOUN
fumecheng-7385	255	24	.	.	PUNCT
fumecheng-7385	256	1	it	it	PRON
fumecheng-7385	256	2	is	be	AUX
fumecheng-7385	256	3	noted	note	VERB
fumecheng-7385	256	4	that	that	SCONJ
fumecheng-7385	256	5	increase	increase	NOUN
fumecheng-7385	256	6	in	in	ADP
fumecheng-7385	256	7			NOUN
fumecheng-7385	256	8	decreases	decrease	VERB
fumecheng-7385	256	9	the	the	DET
fumecheng-7385	256	10	amplitude	amplitude	NOUN
fumecheng-7385	256	11	of	of	ADP
fumecheng-7385	256	12	the	the	DET
fumecheng-7385	256	13	wave	wave	NOUN
fumecheng-7385	256	14	solution	solution	NOUN
fumecheng-7385	256	15	.	.	PUNCT
fumecheng-7385	257	1	fig	fig	NOUN
fumecheng-7385	257	2	.	.	PUNCT
fumecheng-7385	258	1	4	4	NUM
fumecheng-7385	258	2	the	the	DET
fumecheng-7385	258	3	variation	variation	NOUN
fumecheng-7385	258	4	of	of	ADP
fumecheng-7385	258	5	temporal	temporal	ADJ
fumecheng-7385	258	6	damping	damp	VERB
fumecheng-7385	258	7	coefficient	coefficient	NOUN
fumecheng-7385	258	8			NUM
fumecheng-7385	258	9	for	for	ADP
fumecheng-7385	258	10	the	the	DET
fumecheng-7385	258	11	same	same	ADJ
fumecheng-7385	258	12	system	system	NOUN
fumecheng-7385	258	13	as	as	SCONJ
fumecheng-7385	258	14	given	give	VERB
fumecheng-7385	258	15	in	in	ADP
fumecheng-7385	258	16	fig	fig	NOUN
fumecheng-7385	258	17	.	.	PUNCT
fumecheng-7385	258	18	1	1	NUM
fumecheng-7385	258	19	except	except	SCONJ
fumecheng-7385	258	20	that	that	SCONJ
fumecheng-7385	258	21	the	the	DET
fumecheng-7385	258	22	spatial	spatial	ADJ
fumecheng-7385	258	23	variable	variable	NOUN
fumecheng-7385	258	24	is	be	AUX
fumecheng-7385	258	25	considered	consider	VERB
fumecheng-7385	258	26	fixed	fix	VERB
fumecheng-7385	258	27	at	at	ADP
fumecheng-7385	258	28	the	the	DET
fumecheng-7385	258	29	value	value	NOUN
fumecheng-7385	258	30	x=1	x=1	PROPN
fumecheng-7385	258	31	744	744	NUM
fumecheng-7385	258	32	j.-h	j.-h	NOUN
fumecheng-7385	258	33	.	.	PUNCT
fumecheng-7385	259	1	he	he	PRON
fumecheng-7385	259	2	,	,	PUNCT
fumecheng-7385	259	3	y.	y.	PROPN
fumecheng-7385	259	4	o.	o.	PROPN
fumecheng-7385	259	5	el	el	PROPN
fumecheng-7385	259	6	-	-	PROPN
fumecheng-7385	259	7	dib	dib	PROPN
fumecheng-7385	259	8	fig	fig	NOUN
fumecheng-7385	259	9	.	.	PUNCT
fumecheng-7385	260	1	5	5	NUM
fumecheng-7385	260	2	the	the	DET
fumecheng-7385	260	3	variation	variation	NOUN
fumecheng-7385	260	4	of	of	ADP
fumecheng-7385	260	5	spatial	spatial	ADJ
fumecheng-7385	260	6	damping	damp	VERB
fumecheng-7385	260	7	coefficient	coefficient	NOUN
fumecheng-7385	260	8			NOUN
fumecheng-7385	260	9	for	for	ADP
fumecheng-7385	260	10	the	the	DET
fumecheng-7385	260	11	same	same	ADJ
fumecheng-7385	260	12	system	system	NOUN
fumecheng-7385	260	13	as	as	SCONJ
fumecheng-7385	260	14	given	give	VERB
fumecheng-7385	260	15	in	in	ADP
fumecheng-7385	260	16	fig	fig	NOUN
fumecheng-7385	260	17	.	.	PUNCT
fumecheng-7385	261	1	4	4	NUM
fumecheng-7385	261	2	except	except	SCONJ
fumecheng-7385	261	3	that	that	DET
fumecheng-7385	261	4	temporal	temporal	ADJ
fumecheng-7385	261	5	damping	damp	VERB
fumecheng-7385	261	6	coefficient	coefficient	NOUN
fumecheng-7385	261	7			NUM
fumecheng-7385	261	8	is	be	AUX
fumecheng-7385	261	9	considered	consider	VERB
fumecheng-7385	261	10	fixed	fix	VERB
fumecheng-7385	261	11	at	at	ADP
fumecheng-7385	261	12	the	the	DET
fumecheng-7385	261	13	value	value	NOUN
fumecheng-7385	261	14	=0	=0	ADJ
fumecheng-7385	261	15	3	3	NUM
fumecheng-7385	261	16	.	.	NOUN
fumecheng-7385	261	17	alternative	alternative	ADJ
fumecheng-7385	261	18	process	process	NOUN
fumecheng-7385	261	19	across	across	ADP
fumecheng-7385	261	20	the	the	DET
fumecheng-7385	261	21	traveling	travel	VERB
fumecheng-7385	261	22	wave	wave	NOUN
fumecheng-7385	261	23	description	description	NOUN
fumecheng-7385	261	24	traveling	travel	VERB
fumecheng-7385	261	25	waves	wave	NOUN
fumecheng-7385	261	26	arise	arise	VERB
fumecheng-7385	261	27	naturally	naturally	ADV
fumecheng-7385	261	28	in	in	ADP
fumecheng-7385	261	29	many	many	ADJ
fumecheng-7385	261	30	physical	physical	ADJ
fumecheng-7385	261	31	systems	system	NOUN
fumecheng-7385	261	32	,	,	PUNCT
fumecheng-7385	261	33	usually	usually	ADV
fumecheng-7385	261	34	qualified	qualify	VERB
fumecheng-7385	261	35	by	by	ADP
fumecheng-7385	261	36	partial	partial	ADJ
fumecheng-7385	261	37	differential	differential	ADJ
fumecheng-7385	261	38	equations	equation	NOUN
fumecheng-7385	261	39	.	.	PUNCT
fumecheng-7385	262	1	therefore	therefore	ADV
fumecheng-7385	262	2	,	,	PUNCT
fumecheng-7385	262	3	an	an	DET
fumecheng-7385	262	4	alternative	alternative	ADJ
fumecheng-7385	262	5	homotopy	homotopy	NOUN
fumecheng-7385	262	6	equation	equation	NOUN
fumecheng-7385	262	7	can	can	AUX
fumecheng-7385	262	8	be	be	AUX
fumecheng-7385	262	9	formulated	formulate	VERB
fumecheng-7385	262	10	by	by	ADP
fumecheng-7385	262	11	introducing	introduce	VERB
fumecheng-7385	262	12	traveling	travel	VERB
fumecheng-7385	262	13	wave	wave	NOUN
fumecheng-7385	262	14	variable	variable	NOUN
fumecheng-7385	262	15	(x	(x	PROPN
fumecheng-7385	262	16	,	,	PUNCT
fumecheng-7385	262	17	t	t	PROPN
fumecheng-7385	262	18	)	)	PUNCT
fumecheng-7385	262	19	defined	define	VERB
fumecheng-7385	262	20	as	as	ADP
fumecheng-7385	262	21	(	(	PUNCT
fumecheng-7385	262	22	,	,	PUNCT
fumecheng-7385	262	23	)	)	PUNCT
fumecheng-7385	262	24	2	2	NUM
fumecheng-7385	262	25	2	2	NUM
fumecheng-7385	262	26	.x	.x	NOUN
fumecheng-7385	262	27	t	t	NOUN
fumecheng-7385	262	28	x	x	X
fumecheng-7385	263	1	p	p	X
fumecheng-7385	263	2	t=	t=	ADJ
fumecheng-7385	263	3	+	+	ADJ
fumecheng-7385	263	4			X
fumecheng-7385	263	5			NOUN
fumecheng-7385	263	6			NUM
fumecheng-7385	263	7	(	(	PUNCT
fumecheng-7385	263	8	45	45	NUM
fumecheng-7385	263	9	)	)	PUNCT
fumecheng-7385	263	10	according	accord	VERB
fumecheng-7385	263	11	to	to	ADP
fumecheng-7385	263	12	the	the	DET
fumecheng-7385	263	13	above	above	ADJ
fumecheng-7385	263	14	new	new	ADJ
fumecheng-7385	263	15	independent	independent	ADJ
fumecheng-7385	263	16	variable	variable	NOUN
fumecheng-7385	263	17	,	,	PUNCT
fumecheng-7385	263	18	we	we	PRON
fumecheng-7385	263	19	have	have	VERB
fumecheng-7385	263	20	2	2	NUM
fumecheng-7385	263	21	2	2	NUM
fumecheng-7385	263	22	22	22	NUM
fumecheng-7385	263	23	(	(	PUNCT
fumecheng-7385	263	24	)	)	PUNCT
fumecheng-7385	263	25	,	,	PUNCT
fumecheng-7385	263	26	2	2	NUM
fumecheng-7385	263	27	(	(	PUNCT
fumecheng-7385	263	28	)	)	PUNCT
fumecheng-7385	263	29	,	,	PUNCT
fumecheng-7385	263	30	4	4	NUM
fumecheng-7385	263	31	(	(	PUNCT
fumecheng-7385	263	32	)	)	PUNCT
fumecheng-7385	263	33	,	,	PUNCT
fumecheng-7385	263	34	4	4	NUM
fumecheng-7385	263	35	(	(	PUNCT
fumecheng-7385	263	36	)	)	PUNCT
fumecheng-7385	263	37	,	,	PUNCT
fumecheng-7385	263	38	t	t	PROPN
fumecheng-7385	263	39	x	x	X
fumecheng-7385	263	40	tt	tt	PROPN
fumecheng-7385	263	41	xxy	xxy	PROPN
fumecheng-7385	263	42	p	p	PROPN
fumecheng-7385	263	43	y	y	PROPN
fumecheng-7385	263	44	y	y	PROPN
fumecheng-7385	263	45	y	y	PROPN
fumecheng-7385	263	46	y	y	PROPN
fumecheng-7385	263	47	p	p	PROPN
fumecheng-7385	263	48	y	y	PROPN
fumecheng-7385	263	49	y	y	PROPN
fumecheng-7385	263	50	y	y	PROPN
fumecheng-7385	264	1			X
fumecheng-7385	264	2			NOUN
fumecheng-7385	264	3			NOUN
fumecheng-7385	264	4			NUM
fumecheng-7385	264	5			NOUN
fumecheng-7385	264	6			NOUN
fumecheng-7385	264	7			PUNCT
fumecheng-7385	264	8			CCONJ
fumecheng-7385	264	9			PROPN
fumecheng-7385	264	10	=	=	NOUN
fumecheng-7385	264	11	=	=	PUNCT
fumecheng-7385	264	12	=	=	SYM
fumecheng-7385	265	1	=	=	SYM
fumecheng-7385	265	2	(	(	PUNCT
fumecheng-7385	265	3	46	46	NUM
fumecheng-7385	265	4	)	)	PUNCT
fumecheng-7385	265	5	where	where	SCONJ
fumecheng-7385	265	6	the	the	DET
fumecheng-7385	265	7	prime	prime	ADJ
fumecheng-7385	265	8	denotes	denote	VERB
fumecheng-7385	265	9	the	the	DET
fumecheng-7385	265	10	total	total	ADJ
fumecheng-7385	265	11	derivative	derivative	NOUN
fumecheng-7385	265	12	with	with	ADP
fumecheng-7385	265	13	respect	respect	NOUN
fumecheng-7385	265	14	to	to	ADP
fumecheng-7385	265	15	variable	variable	ADJ
fumecheng-7385	265	16	.	.	NOUN
fumecheng-7385	265	17	employing	employ	VERB
fumecheng-7385	265	18	eq	eq	NOUN
fumecheng-7385	265	19	.	.	PUNCT
fumecheng-7385	266	1	(	(	PUNCT
fumecheng-7385	266	2	45	45	NUM
fumecheng-7385	266	3	)	)	PUNCT
fumecheng-7385	266	4	with	with	ADP
fumecheng-7385	266	5	eq	eq	NOUN
fumecheng-7385	266	6	.	.	PUNCT
fumecheng-7385	267	1	(	(	PUNCT
fumecheng-7385	267	2	11	11	NUM
fumecheng-7385	267	3	)	)	PUNCT
fumecheng-7385	267	4	,	,	PUNCT
fumecheng-7385	267	5	it	it	PRON
fumecheng-7385	267	6	will	will	AUX
fumecheng-7385	267	7	handle	handle	VERB
fumecheng-7385	267	8	the	the	DET
fumecheng-7385	267	9	following	follow	VERB
fumecheng-7385	267	10	damping	damp	VERB
fumecheng-7385	267	11	duffing	duffing	NOUN
fumecheng-7385	267	12	equation	equation	NOUN
fumecheng-7385	267	13	:	:	PUNCT
fumecheng-7385	267	14	2	2	NUM
fumecheng-7385	267	15	3	3	NUM
fumecheng-7385	267	16	0	0	NUM
fumecheng-7385	267	17	1	1	NUM
fumecheng-7385	267	18	(	(	PUNCT
fumecheng-7385	267	19	)	)	PUNCT
fumecheng-7385	267	20	(	(	PUNCT
fumecheng-7385	267	21	)	)	PUNCT
fumecheng-7385	267	22	(	(	PUNCT
fumecheng-7385	267	23	)	)	PUNCT
fumecheng-7385	267	24	(	(	PUNCT
fumecheng-7385	267	25	)	)	PUNCT
fumecheng-7385	267	26	,	,	PUNCT
fumecheng-7385	267	27	y	y	PROPN
fumecheng-7385	267	28	y	y	PROPN
fumecheng-7385	267	29	y	y	INTJ
fumecheng-7385	267	30	ry	ry	PROPN
fumecheng-7385	267	31	p	p	X
fumecheng-7385	267	32			PROPN
fumecheng-7385	267	33	+	+	NOUN
fumecheng-7385	267	34	+	+	CCONJ
fumecheng-7385	268	1	=	=	X
fumecheng-7385	268	2			X
fumecheng-7385	268	3			X
fumecheng-7385	269	1			X
fumecheng-7385	269	2			X
fumecheng-7385	269	3			X
fumecheng-7385	270	1	(	(	PUNCT
fumecheng-7385	270	2	47	47	NUM
fumecheng-7385	270	3	)	)	PUNCT
fumecheng-7385	270	4	where	where	SCONJ
fumecheng-7385	270	5	2	2	NUM
fumecheng-7385	270	6	0	0	NUM
fumecheng-7385	270	7	and	and	CCONJ
fumecheng-7385	270	8	r	r	NOUN
fumecheng-7385	270	9	are	be	AUX
fumecheng-7385	270	10	given	give	VERB
fumecheng-7385	270	11	by	by	ADP
fumecheng-7385	270	12	the	the	DET
fumecheng-7385	270	13	following	following	ADJ
fumecheng-7385	270	14	notations	notation	NOUN
fumecheng-7385	270	15	:	:	PUNCT
fumecheng-7385	270	16	2	2	NUM
fumecheng-7385	270	17	0	0	NUM
fumecheng-7385	270	18	2	2	NUM
fumecheng-7385	270	19	2	2	NUM
fumecheng-7385	270	20	2	2	NUM
fumecheng-7385	270	21	2	2	NUM
fumecheng-7385	270	22	,	,	PUNCT
fumecheng-7385	270	23	4	4	NUM
fumecheng-7385	270	24	(	(	PUNCT
fumecheng-7385	270	25	)	)	PUNCT
fumecheng-7385	270	26	.	.	PUNCT
fumecheng-7385	271	1	4	4	NUM
fumecheng-7385	271	2	(	(	PUNCT
fumecheng-7385	271	3	)	)	PUNCT
fumecheng-7385	272	1	p	p	X
fumecheng-7385	272	2	p	p	X
fumecheng-7385	272	3	q	q	NOUN
fumecheng-7385	272	4	r	r	NOUN
fumecheng-7385	272	5	p	p	NOUN
fumecheng-7385	272	6	p	p	X
fumecheng-7385	272	7	=	=	PUNCT
fumecheng-7385	273	1	+	+	PUNCT
fumecheng-7385	273	2	=	=	SYM
fumecheng-7385	273	3	+	+	CCONJ
fumecheng-7385	273	4			X
fumecheng-7385	273	5			X
fumecheng-7385	273	6			NUM
fumecheng-7385	274	1			NOUN
fumecheng-7385	274	2			NUM
fumecheng-7385	274	3			NOUN
fumecheng-7385	274	4	(	(	PUNCT
fumecheng-7385	274	5	48	48	NUM
fumecheng-7385	274	6	)	)	PUNCT
fumecheng-7385	274	7	accordingly	accordingly	ADV
fumecheng-7385	274	8	,	,	PUNCT
fumecheng-7385	274	9	the	the	DET
fumecheng-7385	274	10	homotopy	homotopy	NOUN
fumecheng-7385	274	11	equation	equation	NOUN
fumecheng-7385	274	12	can	can	AUX
fumecheng-7385	274	13	be	be	AUX
fumecheng-7385	274	14	built	build	VERB
fumecheng-7385	274	15	in	in	ADP
fumecheng-7385	274	16	the	the	DET
fumecheng-7385	274	17	form	form	NOUN
fumecheng-7385	274	18	2	2	NUM
fumecheng-7385	274	19	3	3	NUM
fumecheng-7385	274	20	0	0	NUM
fumecheng-7385	274	21	1	1	NUM
fumecheng-7385	274	22	(	(	PUNCT
fumecheng-7385	274	23	;	;	PUNCT
fumecheng-7385	274	24	)	)	PUNCT
fumecheng-7385	274	25	0	0	NUM
fumecheng-7385	274	26	;	;	PUNCT
fumecheng-7385	275	1	[	[	X
fumecheng-7385	275	2	0,1]h	0,1]h	NUM
fumecheng-7385	275	3	y	y	PROPN
fumecheng-7385	275	4	q	q	X
fumecheng-7385	275	5	y	y	PROPN
fumecheng-7385	275	6	y	y	PROPN
fumecheng-7385	275	7	q	q	PROPN
fumecheng-7385	275	8	y	y	PROPN
fumecheng-7385	275	9	ry	ry	PROPN
fumecheng-7385	275	10	q	q	PROPN
fumecheng-7385	275	11	p	p	PROPN
fumecheng-7385	275	12			NOUN
fumecheng-7385	275	13			NOUN
fumecheng-7385	275	14			PROPN
fumecheng-7385	275	15	=	=	PROPN
fumecheng-7385	275	16	+	+	X
fumecheng-7385	275	17	+	+	CCONJ
fumecheng-7385	275	18	−	−	NOUN
fumecheng-7385	275	19	=	=	PUNCT
fumecheng-7385	275	20			PROPN
fumecheng-7385	275	21			PROPN
fumecheng-7385	275	22			PROPN
fumecheng-7385	275	23			NOUN
fumecheng-7385	275	24			X
fumecheng-7385	275	25	(	(	PUNCT
fumecheng-7385	275	26	49	49	NUM
fumecheng-7385	275	27	)	)	PUNCT
fumecheng-7385	275	28	the	the	DET
fumecheng-7385	275	29	enhanced	enhance	VERB
fumecheng-7385	275	30	homotopy	homotopy	NOUN
fumecheng-7385	275	31	perturbation	perturbation	NOUN
fumecheng-7385	275	32	method	method	NOUN
fumecheng-7385	275	33	for	for	ADP
fumecheng-7385	275	34	axial	axial	ADJ
fumecheng-7385	275	35	vibrations	vibration	NOUN
fumecheng-7385	275	36	of	of	ADP
fumecheng-7385	275	37	strings	string	NOUN
fumecheng-7385	275	38	745	745	NUM
fumecheng-7385	275	39	the	the	DET
fumecheng-7385	275	40	homotopy	homotopy	NOUN
fumecheng-7385	275	41	expansion	expansion	NOUN
fumecheng-7385	275	42	is	be	AUX
fumecheng-7385	275	43	applied	apply	VERB
fumecheng-7385	275	44	associated	associate	VERB
fumecheng-7385	275	45	with	with	ADP
fumecheng-7385	275	46	the	the	DET
fumecheng-7385	275	47	modification	modification	NOUN
fumecheng-7385	275	48	by	by	ADP
fumecheng-7385	275	49	the	the	DET
fumecheng-7385	275	50	exponential	exponential	ADJ
fumecheng-7385	275	51	decay	decay	NOUN
fumecheng-7385	275	52	parameter	parameter	NOUN
fumecheng-7385	275	53	[	[	X
fumecheng-7385	275	54	3	3	X
fumecheng-7385	275	55	]	]	PUNCT
fumecheng-7385	275	56	as	as	SCONJ
fumecheng-7385	275	57	follows	follow	VERB
fumecheng-7385	275	58	:	:	PUNCT
fumecheng-7385	275	59	1	1	NUM
fumecheng-7385	275	60	22	22	NUM
fumecheng-7385	275	61	0	0	NUM
fumecheng-7385	275	62	1	1	NUM
fumecheng-7385	275	63	2	2	NUM
fumecheng-7385	275	64	(	(	PUNCT
fumecheng-7385	275	65	;	;	PUNCT
fumecheng-7385	275	66	)	)	PUNCT
fumecheng-7385	275	67	(	(	PUNCT
fumecheng-7385	275	68	(	(	PUNCT
fumecheng-7385	275	69	)	)	PUNCT
fumecheng-7385	275	70	(	(	PUNCT
fumecheng-7385	275	71	)	)	PUNCT
fumecheng-7385	275	72	(	(	PUNCT
fumecheng-7385	275	73	)	)	PUNCT
fumecheng-7385	275	74	...	...	PUNCT
fumecheng-7385	275	75	)	)	PUNCT
fumecheng-7385	275	76	,	,	PUNCT
fumecheng-7385	275	77	q	q	PROPN
fumecheng-7385	275	78	py	py	INTJ
fumecheng-7385	275	79	q	q	PROPN
fumecheng-7385	275	80	e	e	PROPN
fumecheng-7385	275	81	y	y	PROPN
fumecheng-7385	275	82	qy	qy	PROPN
fumecheng-7385	275	83	q	q	PROPN
fumecheng-7385	275	84	y	y	PROPN
fumecheng-7385	275	85	−	−	PROPN
fumecheng-7385	276	1	=	=	PUNCT
fumecheng-7385	277	1	+	+	PUNCT
fumecheng-7385	277	2	+	+	CCONJ
fumecheng-7385	278	1	+	+	CCONJ
fumecheng-7385	278	2			X
fumecheng-7385	278	3			X
fumecheng-7385	279	1			X
fumecheng-7385	279	2			X
fumecheng-7385	280	1			X
fumecheng-7385	280	2	(	(	PUNCT
fumecheng-7385	280	3	50	50	NUM
fumecheng-7385	280	4	)	)	PUNCT
fumecheng-7385	280	5	introducing	introduce	VERB
fumecheng-7385	280	6	modified	modify	VERB
fumecheng-7385	280	7	frequency	frequency	NOUN
fumecheng-7385	280	8			X
fumecheng-7385	280	9	which	which	PRON
fumecheng-7385	280	10	is	be	AUX
fumecheng-7385	280	11	given	give	VERB
fumecheng-7385	280	12	by	by	ADP
fumecheng-7385	280	13	,	,	PUNCT
fumecheng-7385	280	14	...	...	PUNCT
fumecheng-7385	280	15	2	2	NUM
fumecheng-7385	280	16	2	2	NUM
fumecheng-7385	280	17	1	1	NUM
fumecheng-7385	280	18	2	2	NUM
fumecheng-7385	280	19	0	0	NUM
fumecheng-7385	280	20	2	2	NUM
fumecheng-7385	281	1	+	+	ADJ
fumecheng-7385	281	2	+	+	ADJ
fumecheng-7385	281	3	+	+	NOUN
fumecheng-7385	281	4	=	=	SYM
fumecheng-7385	281	5			PROPN
fumecheng-7385	281	6	qq	qq	X
fumecheng-7385	281	7	(	(	PUNCT
fumecheng-7385	281	8	51	51	NUM
fumecheng-7385	281	9	)	)	PUNCT
fumecheng-7385	281	10	where	where	SCONJ
fumecheng-7385	281	11	i	i	VERB
fumecheng-7385	281	12	is	be	AUX
fumecheng-7385	281	13	unknown	unknown	ADJ
fumecheng-7385	281	14	,	,	PUNCT
fumecheng-7385	281	15	determined	determine	VERB
fumecheng-7385	281	16	through	through	ADP
fumecheng-7385	281	17	the	the	DET
fumecheng-7385	281	18	perturbation	perturbation	NOUN
fumecheng-7385	281	19	analysis	analysis	NOUN
fumecheng-7385	281	20	.	.	PUNCT
fumecheng-7385	282	1	substituting	substitute	VERB
fumecheng-7385	282	2	eqs	eqs	PROPN
fumecheng-7385	282	3	.	.	PUNCT
fumecheng-7385	283	1	(	(	PUNCT
fumecheng-7385	283	2	50	50	NUM
fumecheng-7385	283	3	)	)	PUNCT
fumecheng-7385	283	4	and	and	CCONJ
fumecheng-7385	283	5	(	(	PUNCT
fumecheng-7385	283	6	51	51	NUM
fumecheng-7385	283	7	)	)	PUNCT
fumecheng-7385	283	8	into	into	ADP
fumecheng-7385	283	9	eq	eq	NOUN
fumecheng-7385	283	10	.	.	PUNCT
fumecheng-7385	284	1	(	(	PUNCT
fumecheng-7385	284	2	49	49	NUM
fumecheng-7385	284	3	)	)	PUNCT
fumecheng-7385	284	4	,	,	PUNCT
fumecheng-7385	284	5	and	and	CCONJ
fumecheng-7385	284	6	proceeding	proceed	VERB
fumecheng-7385	284	7	as	as	SCONJ
fumecheng-7385	284	8	requested	request	VERB
fumecheng-7385	284	9	by	by	ADP
fumecheng-7385	284	10	the	the	DET
fumecheng-7385	284	11	homotopy	homotopy	NOUN
fumecheng-7385	284	12	perturbation	perturbation	NOUN
fumecheng-7385	284	13	method	method	NOUN
fumecheng-7385	284	14	,	,	PUNCT
fumecheng-7385	284	15	the	the	DET
fumecheng-7385	284	16	above	above	ADJ
fumecheng-7385	284	17	unknowns	unknown	NOUN
fumecheng-7385	284	18	can	can	AUX
fumecheng-7385	284	19	be	be	AUX
fumecheng-7385	284	20	determined	determine	VERB
fumecheng-7385	284	21	and	and	CCONJ
fumecheng-7385	284	22	have	have	VERB
fumecheng-7385	284	23	the	the	DET
fumecheng-7385	284	24	following	follow	VERB
fumecheng-7385	284	25	results	result	NOUN
fumecheng-7385	284	26	:	:	PUNCT
fumecheng-7385	284	27	0	0	NUM
fumecheng-7385	284	28	(	(	PUNCT
fumecheng-7385	284	29	)	)	PUNCT
fumecheng-7385	284	30	cos	cos	PROPN
fumecheng-7385	284	31	(	(	PUNCT
fumecheng-7385	284	32	)	)	PUNCT
fumecheng-7385	285	1	,	,	PUNCT
fumecheng-7385	285	2	y	y	PROPN
fumecheng-7385	285	3	a=	a=	VERB
fumecheng-7385	286	1	+	+	ADP
fumecheng-7385	286	2			X
fumecheng-7385	286	3			X
fumecheng-7385	286	4			PROPN
fumecheng-7385	286	5	(	(	PUNCT
fumecheng-7385	286	6	52	52	NUM
fumecheng-7385	286	7	)	)	PUNCT
fumecheng-7385	286	8	where	where	SCONJ
fumecheng-7385	286	9	a	a	PRON
fumecheng-7385	286	10	and	and	CCONJ
fumecheng-7385	286	11			NOUN
fumecheng-7385	286	12	are	be	AUX
fumecheng-7385	286	13	two	two	NUM
fumecheng-7385	286	14	arbitrary	arbitrary	ADJ
fumecheng-7385	286	15	constants	constant	NOUN
fumecheng-7385	286	16	determined	determine	VERB
fumecheng-7385	286	17	by	by	ADP
fumecheng-7385	286	18	the	the	DET
fumecheng-7385	286	19	initial	initial	ADJ
fumecheng-7385	286	20	conditions	condition	NOUN
fumecheng-7385	286	21	.	.	PUNCT
fumecheng-7385	287	1	besides	besides	SCONJ
fumecheng-7385	287	2	,	,	PUNCT
fumecheng-7385	287	3	we	we	PRON
fumecheng-7385	287	4	have	have	VERB
fumecheng-7385	287	5	3	3	NUM
fumecheng-7385	287	6	1	1	NUM
fumecheng-7385	287	7	2	2	NUM
fumecheng-7385	287	8	(	(	PUNCT
fumecheng-7385	287	9	)	)	PUNCT
fumecheng-7385	287	10	cos(3	cos(3	NOUN
fumecheng-7385	287	11	3	3	NUM
fumecheng-7385	287	12	)	)	PUNCT
fumecheng-7385	287	13	,	,	PUNCT
fumecheng-7385	287	14	32	32	NUM
fumecheng-7385	287	15	ra	ra	NOUN
fumecheng-7385	287	16	y	y	PROPN
fumecheng-7385	287	17	=	=	PUNCT
fumecheng-7385	287	18	−	−	PROPN
fumecheng-7385	288	1	+	+	NUM
fumecheng-7385	288	2			PROPN
fumecheng-7385	288	3			X
fumecheng-7385	288	4			X
fumecheng-7385	288	5			PROPN
fumecheng-7385	288	6	under	under	ADP
fumecheng-7385	288	7	the	the	DET
fumecheng-7385	288	8	condition	condition	NOUN
fumecheng-7385	288	9	2	2	NUM
fumecheng-7385	288	10	1	1	NUM
fumecheng-7385	288	11	3	3	NUM
fumecheng-7385	288	12	.	.	PUNCT
fumecheng-7385	288	13	4	4	NUM
fumecheng-7385	288	14	ra	ra	NOUN
fumecheng-7385	288	15	=	=	PRON
fumecheng-7385	288	16	−	−	PROPN
fumecheng-7385	288	17	(	(	PUNCT
fumecheng-7385	288	18	53	53	NUM
fumecheng-7385	288	19	)	)	PUNCT
fumecheng-7385	288	20	moreover	moreover	ADV
fumecheng-7385	288	21	,	,	PUNCT
fumecheng-7385	288	22	we	we	PRON
fumecheng-7385	288	23	get	get	VERB
fumecheng-7385	288	24	(	(	PUNCT
fumecheng-7385	288	25	)	)	PUNCT
fumecheng-7385	288	26	3	3	NUM
fumecheng-7385	288	27	2	2	NUM
fumecheng-7385	288	28	3	3	NUM
fumecheng-7385	288	29	2	2	NUM
fumecheng-7385	288	30	2	2	NUM
fumecheng-7385	288	31	2	2	NUM
fumecheng-7385	288	32	2	2	NUM
fumecheng-7385	288	33	2	2	NUM
fumecheng-7385	288	34	5	5	NUM
fumecheng-7385	288	35	4	4	NUM
fumecheng-7385	288	36	3	3	NUM
fumecheng-7385	288	37	3	3	NUM
fumecheng-7385	288	38	cos(3	cos(3	NOUN
fumecheng-7385	288	39	3	3	NUM
fumecheng-7385	288	40	)	)	PUNCT
fumecheng-7385	288	41	sin(3	sin(3	NOUN
fumecheng-7385	288	42	3	3	NUM
fumecheng-7385	288	43	)	)	PUNCT
fumecheng-7385	288	44	32	32	NUM
fumecheng-7385	288	45	32	32	NUM
fumecheng-7385	288	46	128	128	NUM
fumecheng-7385	288	47	cos(5	cos(5	ADJ
fumecheng-7385	288	48	5	5	NUM
fumecheng-7385	288	49	)	)	PUNCT
fumecheng-7385	288	50	,	,	PUNCT
fumecheng-7385	288	51	1024	1024	NUM
fumecheng-7385	288	52	ra	ra	NOUN
fumecheng-7385	289	1	ra	ra	INTJ
fumecheng-7385	289	2	ra	ra	INTJ
fumecheng-7385	290	1	y	y	PROPN
fumecheng-7385	290	2	p	p	X
fumecheng-7385	291	1	p	p	X
fumecheng-7385	291	2	r	r	NOUN
fumecheng-7385	291	3	a	a	DET
fumecheng-7385	291	4			NOUN
fumecheng-7385	291	5			X
fumecheng-7385	292	1			X
fumecheng-7385	293	1			PROPN
fumecheng-7385	293	2			ADP
fumecheng-7385	293	3			PROPN
fumecheng-7385	293	4			X
fumecheng-7385	293	5			X
fumecheng-7385	293	6			X
fumecheng-7385	293	7			X
fumecheng-7385	293	8			PROPN
fumecheng-7385	293	9			X
fumecheng-7385	293	10			NOUN
fumecheng-7385	293	11			NOUN
fumecheng-7385	293	12	=	=	PUNCT
fumecheng-7385	294	1	+	+	PUNCT
fumecheng-7385	294	2	+	+	PUNCT
fumecheng-7385	294	3	+	+	CCONJ
fumecheng-7385	294	4	+	+	ADJ
fumecheng-7385	294	5			ADJ
fumecheng-7385	294	6			CCONJ
fumecheng-7385	294	7			ADJ
fumecheng-7385	294	8			NOUN
fumecheng-7385	294	9	+	+	CCONJ
fumecheng-7385	294	10	+	+	CCONJ
fumecheng-7385	294	11	(	(	PUNCT
fumecheng-7385	294	12	54	54	NUM
fumecheng-7385	294	13	)	)	PUNCT
fumecheng-7385	294	14	under	under	ADP
fumecheng-7385	294	15	the	the	DET
fumecheng-7385	294	16	condition	condition	NOUN
fumecheng-7385	294	17	:	:	PUNCT
fumecheng-7385	294	18	2	2	NUM
fumecheng-7385	294	19	4	4	NUM
fumecheng-7385	294	20	2	2	NUM
fumecheng-7385	294	21	2	2	NUM
fumecheng-7385	294	22	2	2	NUM
fumecheng-7385	294	23	2	2	NUM
fumecheng-7385	294	24	1	1	NUM
fumecheng-7385	294	25	3	3	NUM
fumecheng-7385	294	26	3	3	NUM
fumecheng-7385	294	27	.	.	PUNCT
fumecheng-7385	295	1	44	44	NUM
fumecheng-7385	295	2	128	128	NUM
fumecheng-7385	295	3	r	r	NOUN
fumecheng-7385	295	4	a	a	DET
fumecheng-7385	295	5	ra	ra	NOUN
fumecheng-7385	296	1	pp	pp	ADV
fumecheng-7385	296	2			PROPN
fumecheng-7385	297	1			X
fumecheng-7385	297	2			X
fumecheng-7385	297	3	=	=	PUNCT
fumecheng-7385	297	4	−	−	PROPN
fumecheng-7385	298	1	+	+	CCONJ
fumecheng-7385	298	2	+	+	CCONJ
fumecheng-7385	298	3	(	(	PUNCT
fumecheng-7385	298	4	55	55	NUM
fumecheng-7385	298	5	)	)	PUNCT
fumecheng-7385	298	6	as	as	SCONJ
fumecheng-7385	298	7	known	know	VERB
fumecheng-7385	298	8	,	,	PUNCT
fumecheng-7385	298	9	the	the	DET
fumecheng-7385	298	10	approximate	approximate	ADJ
fumecheng-7385	298	11	second	second	ADJ
fumecheng-7385	298	12	-	-	PUNCT
fumecheng-7385	298	13	order	order	NOUN
fumecheng-7385	298	14	solution	solution	NOUN
fumecheng-7385	298	15	of	of	ADP
fumecheng-7385	298	16	eq	eq	PROPN
fumecheng-7385	298	17	.	.	PUNCT
fumecheng-7385	299	1	(	(	PUNCT
fumecheng-7385	299	2	47	47	NUM
fumecheng-7385	299	3	)	)	PUNCT
fumecheng-7385	299	4	is	be	AUX
fumecheng-7385	299	5	given	give	VERB
fumecheng-7385	299	6	by	by	ADP
fumecheng-7385	299	7	1	1	NUM
fumecheng-7385	299	8	22	22	NUM
fumecheng-7385	299	9	0	0	NUM
fumecheng-7385	299	10	1	1	NUM
fumecheng-7385	299	11	2	2	NUM
fumecheng-7385	299	12	1	1	NUM
fumecheng-7385	299	13	(	(	PUNCT
fumecheng-7385	299	14	)	)	PUNCT
fumecheng-7385	299	15	lim	lim	PROPN
fumecheng-7385	299	16	(	(	PUNCT
fumecheng-7385	299	17	(	(	PUNCT
fumecheng-7385	299	18	)	)	PUNCT
fumecheng-7385	299	19	(	(	PUNCT
fumecheng-7385	299	20	)	)	PUNCT
fumecheng-7385	299	21	(	(	PUNCT
fumecheng-7385	299	22	)	)	PUNCT
fumecheng-7385	299	23	...	...	PUNCT
fumecheng-7385	299	24	)	)	PUNCT
fumecheng-7385	299	25	,	,	PUNCT
fumecheng-7385	299	26	q	q	PROPN
fumecheng-7385	299	27	p	p	X
fumecheng-7385	299	28	q	q	X
fumecheng-7385	299	29	y	y	PROPN
fumecheng-7385	299	30	e	e	PROPN
fumecheng-7385	299	31	y	y	PROPN
fumecheng-7385	299	32	qy	qy	PROPN
fumecheng-7385	299	33	q	q	PROPN
fumecheng-7385	299	34	y	y	PROPN
fumecheng-7385	299	35			NOUN
fumecheng-7385	300	1			X
fumecheng-7385	300	2			X
fumecheng-7385	301	1			X
fumecheng-7385	301	2			X
fumecheng-7385	301	3	−	−	X
fumecheng-7385	302	1	→	→	SYM
fumecheng-7385	302	2			NOUN
fumecheng-7385	302	3			NOUN
fumecheng-7385	302	4	=	=	PUNCT
fumecheng-7385	303	1	+	+	PUNCT
fumecheng-7385	303	2	+	+	CCONJ
fumecheng-7385	303	3	+	+	ADJ
fumecheng-7385	303	4			ADJ
fumecheng-7385	303	5			CCONJ
fumecheng-7385	303	6			PROPN
fumecheng-7385	303	7			NOUN
fumecheng-7385	303	8	(	(	PUNCT
fumecheng-7385	303	9	56	56	NUM
fumecheng-7385	303	10	)	)	PUNCT
fumecheng-7385	303	11	also	also	ADV
fumecheng-7385	303	12	,	,	PUNCT
fumecheng-7385	303	13	the	the	DET
fumecheng-7385	303	14	approximate	approximate	ADJ
fumecheng-7385	303	15	frequency	frequency	NOUN
fumecheng-7385	303	16	is	be	AUX
fumecheng-7385	303	17	formulated	formulate	VERB
fumecheng-7385	303	18	by	by	ADP
fumecheng-7385	303	19	2	2	NUM
fumecheng-7385	303	20	2	2	NUM
fumecheng-7385	303	21	2	2	NUM
fumecheng-7385	303	22	0	0	NUM
fumecheng-7385	303	23	1	1	NUM
fumecheng-7385	303	24	2	2	NUM
fumecheng-7385	303	25	1	1	NUM
fumecheng-7385	303	26	lim	lim	PROPN
fumecheng-7385	303	27	(	(	PUNCT
fumecheng-7385	303	28	...	...	PUNCT
fumecheng-7385	303	29	)	)	PUNCT
fumecheng-7385	303	30	.	.	PUNCT
fumecheng-7385	304	1	q	q	NOUN
fumecheng-7385	305	1	q	q	X
fumecheng-7385	305	2	q	q	X
fumecheng-7385	305	3	→	→	SYM
fumecheng-7385	305	4	=	=	SYM
fumecheng-7385	306	1	+	+	PUNCT
fumecheng-7385	307	1	+	+	X
fumecheng-7385	307	2	+	+	ADJ
fumecheng-7385	307	3			X
fumecheng-7385	307	4			X
fumecheng-7385	307	5			X
fumecheng-7385	307	6			X
fumecheng-7385	307	7	(	(	PUNCT
fumecheng-7385	307	8	57	57	NUM
fumecheng-7385	307	9	)	)	PUNCT
fumecheng-7385	307	10	inserting	insert	VERB
fumecheng-7385	307	11	y0(),y1(	y0(),y1(	NUM
fumecheng-7385	307	12	)	)	PUNCT
fumecheng-7385	307	13	and	and	CCONJ
fumecheng-7385	307	14	y2(	y2(	NOUN
fumecheng-7385	307	15	)	)	PUNCT
fumecheng-7385	307	16	into	into	ADP
fumecheng-7385	307	17	eq	eq	NOUN
fumecheng-7385	307	18	.	.	PUNCT
fumecheng-7385	308	1	(	(	PUNCT
fumecheng-7385	308	2	50	50	NUM
fumecheng-7385	308	3	)	)	PUNCT
fumecheng-7385	308	4	yields	yield	VERB
fumecheng-7385	308	5	12	12	NUM
fumecheng-7385	308	6	2	2	NUM
fumecheng-7385	308	7	1	1	NUM
fumecheng-7385	308	8	2	2	NUM
fumecheng-7385	308	9	2	2	NUM
fumecheng-7385	308	10	2	2	NUM
fumecheng-7385	308	11	2	2	NUM
fumecheng-7385	308	12	2	2	NUM
fumecheng-7385	308	13	4	4	NUM
fumecheng-7385	308	14	2	2	NUM
fumecheng-7385	308	15	4	4	NUM
fumecheng-7385	308	16	(	(	PUNCT
fumecheng-7385	308	17	)	)	PUNCT
fumecheng-7385	308	18	3	3	NUM
fumecheng-7385	308	19	cos	cos	PROPN
fumecheng-7385	308	20	(	(	PUNCT
fumecheng-7385	308	21	)	)	PUNCT
fumecheng-7385	308	22	cos(3	cos(3	NOUN
fumecheng-7385	308	23	3	3	NUM
fumecheng-7385	308	24	)	)	PUNCT
fumecheng-7385	308	25	32	32	NUM
fumecheng-7385	308	26	32	32	NUM
fumecheng-7385	308	27	3	3	NUM
fumecheng-7385	308	28	sin(3	sin(3	NOUN
fumecheng-7385	308	29	3	3	NUM
fumecheng-7385	308	30	)	)	PUNCT
fumecheng-7385	308	31	cos(5	cos(5	ADJ
fumecheng-7385	308	32	5	5	NUM
fumecheng-7385	308	33	)	)	PUNCT
fumecheng-7385	308	34	.	.	PUNCT
fumecheng-7385	309	1	128	128	NUM
fumecheng-7385	309	2	1024	1024	NUM
fumecheng-7385	309	3	p	p	NOUN
fumecheng-7385	309	4	p	p	X
fumecheng-7385	309	5	y	y	PROPN
fumecheng-7385	309	6	ra	ra	INTJ
fumecheng-7385	309	7	ra	ra	PROPN
fumecheng-7385	310	1	e	e	PROPN
fumecheng-7385	310	2	ae	ae	PROPN
fumecheng-7385	310	3	ra	ra	PROPN
fumecheng-7385	310	4	r	r	NOUN
fumecheng-7385	310	5	a	a	DET
fumecheng-7385	310	6	p	p	NOUN
fumecheng-7385	310	7			NOUN
fumecheng-7385	311	1			X
fumecheng-7385	311	2			X
fumecheng-7385	311	3			X
fumecheng-7385	312	1			PROPN
fumecheng-7385	312	2			ADP
fumecheng-7385	312	3			PROPN
fumecheng-7385	312	4			X
fumecheng-7385	312	5			X
fumecheng-7385	312	6			X
fumecheng-7385	312	7			PROPN
fumecheng-7385	312	8			PROPN
fumecheng-7385	312	9			PROPN
fumecheng-7385	312	10			X
fumecheng-7385	312	11			X
fumecheng-7385	312	12	−	−	NOUN
fumecheng-7385	312	13	−	−	PROPN
fumecheng-7385	312	14			NOUN
fumecheng-7385	312	15			NOUN
fumecheng-7385	312	16	=	=	PUNCT
fumecheng-7385	313	1	+	+	PUNCT
fumecheng-7385	314	1	+	+	CCONJ
fumecheng-7385	314	2	−	−	X
fumecheng-7385	315	1	+	+	CCONJ
fumecheng-7385	315	2	+	+	ADJ
fumecheng-7385	315	3			ADJ
fumecheng-7385	315	4			CCONJ
fumecheng-7385	315	5			ADJ
fumecheng-7385	315	6			NOUN
fumecheng-7385	315	7	+	+	CCONJ
fumecheng-7385	316	1	+	+	PUNCT
fumecheng-7385	316	2	+	+	PUNCT
fumecheng-7385	316	3	+	+	CCONJ
fumecheng-7385	316	4	(	(	PUNCT
fumecheng-7385	316	5	58	58	NUM
fumecheng-7385	316	6	)	)	PUNCT
fumecheng-7385	316	7	746	746	NUM
fumecheng-7385	316	8	j.-h	j.-h	NOUN
fumecheng-7385	316	9	.	.	PUNCT
fumecheng-7385	317	1	he	he	PRON
fumecheng-7385	317	2	,	,	PUNCT
fumecheng-7385	317	3	y.	y.	PROPN
fumecheng-7385	317	4	o.	o.	PROPN
fumecheng-7385	317	5	el	el	PROPN
fumecheng-7385	317	6	-	-	PROPN
fumecheng-7385	317	7	dib	dib	PROPN
fumecheng-7385	317	8	where	where	SCONJ
fumecheng-7385	317	9	the	the	DET
fumecheng-7385	317	10	frequency	frequency	NOUN
fumecheng-7385	317	11	equation	equation	NOUN
fumecheng-7385	317	12	is	be	AUX
fumecheng-7385	317	13	determined	determine	VERB
fumecheng-7385	317	14	[	[	X
fumecheng-7385	317	15	35	35	NUM
fumecheng-7385	317	16	]	]	PUNCT
fumecheng-7385	317	17	as	as	ADP
fumecheng-7385	317	18	.	.	PROPN
fumecheng-7385	317	19	128	128	NUM
fumecheng-7385	317	20	3	3	NUM
fumecheng-7385	317	21	4	4	NUM
fumecheng-7385	317	22	3	3	NUM
fumecheng-7385	317	23	4	4	NUM
fumecheng-7385	317	24	1	1	NUM
fumecheng-7385	317	25	2	2	NUM
fumecheng-7385	317	26	42	42	NUM
fumecheng-7385	317	27	2	2	NUM
fumecheng-7385	317	28	2	2	NUM
fumecheng-7385	317	29	2	2	NUM
fumecheng-7385	317	30	0	0	NUM
fumecheng-7385	317	31	2	2	NUM
fumecheng-7385	317	32			X
fumecheng-7385	317	33			ADP
fumecheng-7385	317	34			PROPN
fumecheng-7385	317	35	ar	ar	PROPN
fumecheng-7385	317	36	era	era	PROPN
fumecheng-7385	317	37	p	p	X
fumecheng-7385	317	38	p	p	PROPN
fumecheng-7385	317	39	+	+	PROPN
fumecheng-7385	317	40	−−=	−−=	PROPN
fumecheng-7385	317	41	−	−	PROPN
fumecheng-7385	317	42	(	(	PUNCT
fumecheng-7385	317	43	59	59	NUM
fumecheng-7385	317	44	)	)	PUNCT
fumecheng-7385	317	45	it	it	PRON
fumecheng-7385	317	46	is	be	AUX
fumecheng-7385	317	47	worth	worth	ADJ
fumecheng-7385	317	48	observing	observe	VERB
fumecheng-7385	317	49	that	that	SCONJ
fumecheng-7385	317	50	through	through	ADP
fumecheng-7385	317	51	performing	perform	VERB
fumecheng-7385	317	52	the	the	DET
fumecheng-7385	317	53	final	final	ADJ
fumecheng-7385	317	54	solution	solution	NOUN
fumecheng-7385	317	55	(	(	PUNCT
fumecheng-7385	317	56	58	58	NUM
fumecheng-7385	317	57	)	)	PUNCT
fumecheng-7385	317	58	,	,	PUNCT
fumecheng-7385	317	59	we	we	PRON
fumecheng-7385	317	60	replace	replace	VERB
fumecheng-7385	317	61	the	the	DET
fumecheng-7385	317	62	terms	term	NOUN
fumecheng-7385	317	63	(	(	PUNCT
fumecheng-7385	317	64	1-/p+	1-/p+	NUM
fumecheng-7385	317	65	…	…	PUNCT
fumecheng-7385	317	66	)	)	PUNCT
fumecheng-7385	317	67	which	which	PRON
fumecheng-7385	317	68	refer	refer	VERB
fumecheng-7385	317	69	to	to	ADP
fumecheng-7385	317	70	the	the	DET
fumecheng-7385	317	71	first	first	ADJ
fumecheng-7385	317	72	two	two	NUM
fumecheng-7385	317	73	terms	term	NOUN
fumecheng-7385	317	74	of	of	ADP
fumecheng-7385	317	75	exponential	exponential	ADJ
fumecheng-7385	317	76	exp(-/p	exp(-/p	PROPN
fumecheng-7385	317	77	)	)	PUNCT
fumecheng-7385	317	78	;	;	PUNCT
fumecheng-7385	317	79	therefore	therefore	ADV
fumecheng-7385	317	80	,	,	PUNCT
fumecheng-7385	317	81	this	this	DET
fumecheng-7385	317	82	compact	compact	ADJ
fumecheng-7385	317	83	form	form	NOUN
fumecheng-7385	317	84	is	be	AUX
fumecheng-7385	317	85	used	use	VERB
fumecheng-7385	317	86	in	in	ADP
fumecheng-7385	317	87	eqs	eqs	PROPN
fumecheng-7385	317	88	.	.	PUNCT
fumecheng-7385	318	1	(	(	PUNCT
fumecheng-7385	318	2	58	58	NUM
fumecheng-7385	318	3	)	)	PUNCT
fumecheng-7385	318	4	and	and	CCONJ
fumecheng-7385	318	5	(	(	PUNCT
fumecheng-7385	318	6	59	59	NUM
fumecheng-7385	318	7	)	)	PUNCT
fumecheng-7385	318	8	.	.	PUNCT
fumecheng-7385	319	1	without	without	ADP
fumecheng-7385	319	2	upgrading	upgrade	VERB
fumecheng-7385	319	3	the	the	DET
fumecheng-7385	319	4	power	power	NOUN
fumecheng-7385	319	5	of	of	ADP
fumecheng-7385	319	6	frequency	frequency	NOUN
fumecheng-7385	319	7	2	2	PROPN
fumecheng-7385	319	8	,	,	PUNCT
fumecheng-7385	319	9	we	we	PRON
fumecheng-7385	319	10	proceed	proceed	VERB
fumecheng-7385	319	11	to	to	PART
fumecheng-7385	319	12	obtain	obtain	VERB
fumecheng-7385	319	13	an	an	DET
fumecheng-7385	319	14	approximate	approximate	ADJ
fumecheng-7385	319	15	solution	solution	NOUN
fumecheng-7385	319	16	of	of	ADP
fumecheng-7385	319	17	eq	eq	PROPN
fumecheng-7385	319	18	.	.	PUNCT
fumecheng-7385	320	1	(	(	PUNCT
fumecheng-7385	320	2	49	49	NUM
fumecheng-7385	320	3	)	)	PUNCT
fumecheng-7385	320	4	.	.	PUNCT
fumecheng-7385	321	1	this	this	DET
fumecheng-7385	321	2	approximate	approximate	ADJ
fumecheng-7385	321	3	solution	solution	NOUN
fumecheng-7385	321	4	is	be	AUX
fumecheng-7385	321	5	formulated	formulate	VERB
fumecheng-7385	321	6	in	in	ADP
fumecheng-7385	321	7	the	the	DET
fumecheng-7385	321	8	form	form	NOUN
fumecheng-7385	321	9	.	.	PUNCT
fumecheng-7385	322	1	4	4	NUM
fumecheng-7385	322	2	3	3	NUM
fumecheng-7385	322	3	4	4	NUM
fumecheng-7385	322	4	1	1	NUM
fumecheng-7385	322	5	128	128	NUM
fumecheng-7385	322	6	3	3	NUM
fumecheng-7385	322	7	4	4	NUM
fumecheng-7385	322	8	3	3	NUM
fumecheng-7385	322	9	4	4	NUM
fumecheng-7385	322	10	1	1	NUM
fumecheng-7385	322	11	2	2	NUM
fumecheng-7385	322	12	2	2	NUM
fumecheng-7385	322	13	2	2	NUM
fumecheng-7385	322	14	0	0	NUM
fumecheng-7385	322	15	42	42	NUM
fumecheng-7385	322	16	2	2	NUM
fumecheng-7385	322	17	2	2	NUM
fumecheng-7385	322	18	2	2	NUM
fumecheng-7385	322	19	0	0	NUM
fumecheng-7385	322	20	2	2	NUM
fumecheng-7385	322	21			PROPN
fumecheng-7385	322	22			NOUN
fumecheng-7385	322	23			PRON
fumecheng-7385	322	24			PROPN
fumecheng-7385	322	25			PROPN
fumecheng-7385	322	26			NOUN
fumecheng-7385	322	27	−−	−−	PROPN
fumecheng-7385	322	28	+	+	PROPN
fumecheng-7385	322	29	−−=	−−=	PROPN
fumecheng-7385	322	30	ra	ra	PROPN
fumecheng-7385	322	31	p	p	PROPN
fumecheng-7385	322	32	ar	ar	PROPN
fumecheng-7385	322	33	ra	ra	PROPN
fumecheng-7385	322	34	p	p	PROPN
fumecheng-7385	322	35			X
fumecheng-7385	322	36			X
fumecheng-7385	322	37	(	(	PUNCT
fumecheng-7385	322	38	60	60	NUM
fumecheng-7385	322	39	)	)	PUNCT
fumecheng-7385	322	40	the	the	DET
fumecheng-7385	322	41	necessary	necessary	ADJ
fumecheng-7385	322	42	stability	stability	NOUN
fumecheng-7385	322	43	requirements	requirement	NOUN
fumecheng-7385	322	44	need	need	VERB
fumecheng-7385	322	45	to	to	PART
fumecheng-7385	322	46	be	be	AUX
fumecheng-7385	322	47	positive	positive	ADJ
fumecheng-7385	322	48	2	2	PROPN
fumecheng-7385	322	49	.	.	PUNCT
fumecheng-7385	323	1	this	this	PRON
fumecheng-7385	323	2	requires	require	VERB
fumecheng-7385	323	3	.0	.0	NUM
fumecheng-7385	323	4	4	4	NUM
fumecheng-7385	323	5	3	3	NUM
fumecheng-7385	323	6	4	4	NUM
fumecheng-7385	323	7	1	1	NUM
fumecheng-7385	323	8	128	128	NUM
fumecheng-7385	323	9	3	3	NUM
fumecheng-7385	323	10	4	4	NUM
fumecheng-7385	323	11	3	3	NUM
fumecheng-7385	323	12	4	4	NUM
fumecheng-7385	323	13	1	1	NUM
fumecheng-7385	323	14	2	2	NUM
fumecheng-7385	323	15	2	2	NUM
fumecheng-7385	323	16	2	2	NUM
fumecheng-7385	323	17	0	0	NUM
fumecheng-7385	323	18	42	42	NUM
fumecheng-7385	323	19	2	2	NUM
fumecheng-7385	323	20	2	2	NUM
fumecheng-7385	323	21	2	2	NUM
fumecheng-7385	323	22	0	0	NUM
fumecheng-7385	323	23			INTJ
fumecheng-7385	323	24			PROPN
fumecheng-7385	323	25			PROPN
fumecheng-7385	323	26			PRON
fumecheng-7385	323	27			PROPN
fumecheng-7385	323	28			PROPN
fumecheng-7385	323	29			NOUN
fumecheng-7385	323	30	−−	−−	PROPN
fumecheng-7385	323	31	+	+	PROPN
fumecheng-7385	323	32	−−	−−	PROPN
fumecheng-7385	323	33	ra	ra	PROPN
fumecheng-7385	323	34	p	p	PROPN
fumecheng-7385	323	35	ar	ar	PROPN
fumecheng-7385	323	36	ra	ra	PROPN
fumecheng-7385	323	37	p	p	PROPN
fumecheng-7385	323	38			X
fumecheng-7385	323	39			X
fumecheng-7385	323	40	(	(	PUNCT
fumecheng-7385	323	41	61	61	NUM
fumecheng-7385	323	42	)	)	PUNCT
fumecheng-7385	323	43	the	the	DET
fumecheng-7385	323	44	above	above	ADJ
fumecheng-7385	323	45	stability	stability	NOUN
fumecheng-7385	323	46	is	be	AUX
fumecheng-7385	323	47	arranged	arrange	VERB
fumecheng-7385	323	48	in	in	ADP
fumecheng-7385	323	49	terms	term	NOUN
fumecheng-7385	323	50	of	of	ADP
fumecheng-7385	323	51	the	the	DET
fumecheng-7385	323	52	definition	definition	NOUN
fumecheng-7385	323	53	given	give	VERB
fumecheng-7385	323	54	in	in	ADP
fumecheng-7385	323	55	eq	eq	ADP
fumecheng-7385	323	56	.	.	PUNCT
fumecheng-7385	324	1	(	(	PUNCT
fumecheng-7385	324	2	48	48	NUM
fumecheng-7385	324	3	)	)	PUNCT
fumecheng-7385	324	4	,	,	PUNCT
fumecheng-7385	324	5	which	which	PRON
fumecheng-7385	324	6	leads	lead	VERB
fumecheng-7385	324	7	to	to	ADP
fumecheng-7385	324	8	the	the	DET
fumecheng-7385	324	9	same	same	ADJ
fumecheng-7385	324	10	stability	stability	NOUN
fumecheng-7385	324	11	condition	condition	NOUN
fumecheng-7385	324	12	as	as	ADP
fumecheng-7385	324	13	in	in	ADP
fumecheng-7385	324	14	eq	eq	NOUN
fumecheng-7385	324	15	.	.	PUNCT
fumecheng-7385	325	1	(	(	PUNCT
fumecheng-7385	325	2	44	44	NUM
fumecheng-7385	325	3	)	)	PUNCT
fumecheng-7385	325	4	.	.	PUNCT
fumecheng-7385	326	1	3.1	3.1	NUM
fumecheng-7385	326	2	.	.	PUNCT
fumecheng-7385	326	3	numerical	numerical	ADJ
fumecheng-7385	326	4	estimations	estimation	NOUN
fumecheng-7385	326	5	the	the	DET
fumecheng-7385	326	6	comparison	comparison	NOUN
fumecheng-7385	326	7	between	between	ADP
fumecheng-7385	326	8	the	the	DET
fumecheng-7385	326	9	numerical	numerical	ADJ
fumecheng-7385	326	10	solution	solution	NOUN
fumecheng-7385	326	11	of	of	ADP
fumecheng-7385	326	12	the	the	DET
fumecheng-7385	326	13	duffing	duffing	NOUN
fumecheng-7385	326	14	eq	eq	ADP
fumecheng-7385	326	15	.	.	PUNCT
fumecheng-7385	327	1	(	(	PUNCT
fumecheng-7385	327	2	47	47	NUM
fumecheng-7385	327	3	)	)	PUNCT
fumecheng-7385	327	4	and	and	CCONJ
fumecheng-7385	327	5	the	the	DET
fumecheng-7385	327	6	modified	modify	VERB
fumecheng-7385	327	7	hpm	hpm	NOUN
fumecheng-7385	327	8	solution	solution	NOUN
fumecheng-7385	327	9	given	give	VERB
fumecheng-7385	327	10	by	by	ADP
fumecheng-7385	327	11	(	(	PUNCT
fumecheng-7385	327	12	58	58	NUM
fumecheng-7385	327	13	)	)	PUNCT
fumecheng-7385	327	14	,	,	PUNCT
fumecheng-7385	327	15	with	with	ADP
fumecheng-7385	327	16	the	the	DET
fumecheng-7385	327	17	full	full	ADJ
fumecheng-7385	327	18	frequency	frequency	NOUN
fumecheng-7385	327	19	as	as	SCONJ
fumecheng-7385	327	20	given	give	VERB
fumecheng-7385	327	21	by	by	ADP
fumecheng-7385	327	22	(	(	PUNCT
fumecheng-7385	327	23	59	59	NUM
fumecheng-7385	327	24	)	)	PUNCT
fumecheng-7385	327	25	,	,	PUNCT
fumecheng-7385	327	26	is	be	AUX
fumecheng-7385	327	27	shown	show	VERB
fumecheng-7385	327	28	in	in	ADP
fumecheng-7385	327	29	fig	fig	NOUN
fumecheng-7385	327	30	.	.	PUNCT
fumecheng-7385	328	1	6	6	NUM
fumecheng-7385	328	2	.	.	PUNCT
fumecheng-7385	329	1	the	the	DET
fumecheng-7385	329	2	numerical	numerical	ADJ
fumecheng-7385	329	3	solution	solution	NOUN
fumecheng-7385	329	4	is	be	AUX
fumecheng-7385	329	5	made	make	VERB
fumecheng-7385	329	6	by	by	ADP
fumecheng-7385	329	7	the	the	DET
fumecheng-7385	329	8	use	use	NOUN
fumecheng-7385	329	9	of	of	ADP
fumecheng-7385	329	10	mathematical	mathematical	ADJ
fumecheng-7385	329	11	software	software	NOUN
fumecheng-7385	329	12	.	.	PUNCT
fumecheng-7385	330	1	the	the	DET
fumecheng-7385	330	2	calculation	calculation	NOUN
fumecheng-7385	330	3	is	be	AUX
fumecheng-7385	330	4	made	make	VERB
fumecheng-7385	330	5	for	for	ADP
fumecheng-7385	330	6	the	the	DET
fumecheng-7385	330	7	same	same	ADJ
fumecheng-7385	330	8	system	system	NOUN
fumecheng-7385	330	9	as	as	SCONJ
fumecheng-7385	330	10	given	give	VERB
fumecheng-7385	330	11	in	in	ADP
fumecheng-7385	330	12	fig	fig	NOUN
fumecheng-7385	330	13	.	.	PUNCT
fumecheng-7385	331	1	1	1	X
fumecheng-7385	331	2	.	.	PUNCT
fumecheng-7385	332	1	the	the	DET
fumecheng-7385	332	2	numerical	numerical	ADJ
fumecheng-7385	332	3	solution	solution	NOUN
fumecheng-7385	332	4	is	be	AUX
fumecheng-7385	332	5	located	locate	VERB
fumecheng-7385	332	6	in	in	ADP
fumecheng-7385	332	7	red	red	ADJ
fumecheng-7385	332	8	,	,	PUNCT
fumecheng-7385	332	9	while	while	SCONJ
fumecheng-7385	332	10	the	the	DET
fumecheng-7385	332	11	analytical	analytical	ADJ
fumecheng-7385	332	12	solution	solution	NOUN
fumecheng-7385	332	13	is	be	AUX
fumecheng-7385	332	14	plotted	plot	VERB
fumecheng-7385	332	15	in	in	ADP
fumecheng-7385	332	16	blue	blue	ADJ
fumecheng-7385	332	17	.	.	PUNCT
fumecheng-7385	333	1	this	this	DET
fumecheng-7385	333	2	graph	graph	NOUN
fumecheng-7385	333	3	indicates	indicate	VERB
fumecheng-7385	333	4	that	that	SCONJ
fumecheng-7385	333	5	there	there	PRON
fumecheng-7385	333	6	is	be	VERB
fumecheng-7385	333	7	an	an	DET
fumecheng-7385	333	8	excellent	excellent	ADJ
fumecheng-7385	333	9	agreement	agreement	NOUN
fumecheng-7385	333	10	between	between	ADP
fumecheng-7385	333	11	the	the	DET
fumecheng-7385	333	12	numerical	numerical	ADJ
fumecheng-7385	333	13	solution	solution	NOUN
fumecheng-7385	333	14	and	and	CCONJ
fumecheng-7385	333	15	the	the	DET
fumecheng-7385	333	16	analytical	analytical	ADJ
fumecheng-7385	333	17	modified	modify	VERB
fumecheng-7385	333	18	hpm	hpm	NOUN
fumecheng-7385	333	19	solution	solution	NOUN
fumecheng-7385	333	20	.	.	PUNCT
fumecheng-7385	334	1	fig	fig	NOUN
fumecheng-7385	334	2	.	.	PUNCT
fumecheng-7385	335	1	6	6	NUM
fumecheng-7385	335	2	the	the	DET
fumecheng-7385	335	3	comparison	comparison	NOUN
fumecheng-7385	335	4	between	between	ADP
fumecheng-7385	335	5	the	the	DET
fumecheng-7385	335	6	numerical	numerical	ADJ
fumecheng-7385	335	7	solution	solution	NOUN
fumecheng-7385	335	8	and	and	CCONJ
fumecheng-7385	335	9	the	the	DET
fumecheng-7385	335	10	analytical	analytical	ADJ
fumecheng-7385	335	11	solution	solution	NOUN
fumecheng-7385	335	12	to	to	ADP
fumecheng-7385	335	13	the	the	DET
fumecheng-7385	335	14	duffing	duffing	NOUN
fumecheng-7385	335	15	eq	eq	ADP
fumecheng-7385	335	16	.	.	PUNCT
fumecheng-7385	336	1	(	(	PUNCT
fumecheng-7385	336	2	47	47	NUM
fumecheng-7385	336	3	)	)	PUNCT
fumecheng-7385	336	4	,	,	PUNCT
fumecheng-7385	336	5	for	for	ADP
fumecheng-7385	336	6	the	the	DET
fumecheng-7385	336	7	same	same	ADJ
fumecheng-7385	336	8	system	system	NOUN
fumecheng-7385	336	9	of	of	ADP
fumecheng-7385	336	10	fig	fig	NOUN
fumecheng-7385	336	11	.	.	PUNCT
fumecheng-7385	337	1	1	1	NUM
fumecheng-7385	338	1	the	the	DET
fumecheng-7385	338	2	enhanced	enhance	VERB
fumecheng-7385	338	3	homotopy	homotopy	NOUN
fumecheng-7385	338	4	perturbation	perturbation	NOUN
fumecheng-7385	338	5	method	method	NOUN
fumecheng-7385	338	6	for	for	ADP
fumecheng-7385	338	7	axial	axial	ADJ
fumecheng-7385	338	8	vibrations	vibration	NOUN
fumecheng-7385	338	9	of	of	ADP
fumecheng-7385	338	10	strings	string	NOUN
fumecheng-7385	338	11	747	747	NUM
fumecheng-7385	338	12	fig	fig	NOUN
fumecheng-7385	338	13	.	.	PUNCT
fumecheng-7385	338	14	7	7	NUM
fumecheng-7385	338	15	the	the	DET
fumecheng-7385	338	16	modified	modify	VERB
fumecheng-7385	338	17	hpm	hpm	NOUN
fumecheng-7385	338	18	solution	solution	NOUN
fumecheng-7385	338	19	in	in	ADP
fumecheng-7385	338	20	eq	eq	ADP
fumecheng-7385	338	21	.	.	PUNCT
fumecheng-7385	339	1	(	(	PUNCT
fumecheng-7385	339	2	58	58	NUM
fumecheng-7385	339	3	)	)	PUNCT
fumecheng-7385	339	4	for	for	ADP
fumecheng-7385	339	5	the	the	DET
fumecheng-7385	339	6	same	same	ADJ
fumecheng-7385	339	7	system	system	NOUN
fumecheng-7385	339	8	as	as	SCONJ
fumecheng-7385	339	9	given	give	VERB
fumecheng-7385	339	10	in	in	ADP
fumecheng-7385	339	11	fig	fig	NOUN
fumecheng-7385	339	12	.	.	PUNCT
fumecheng-7385	340	1	2	2	NUM
fumecheng-7385	340	2	with	with	ADP
fumecheng-7385	340	3	the	the	DET
fumecheng-7385	340	4	variation	variation	NOUN
fumecheng-7385	340	5	of	of	ADP
fumecheng-7385	340	6	parameter	parameter	NOUN
fumecheng-7385	340	7			PUNCT
fumecheng-7385	340	8	in	in	ADP
fumecheng-7385	340	9	fig	fig	NOUN
fumecheng-7385	340	10	.	.	PUNCT
fumecheng-7385	341	1	7	7	NUM
fumecheng-7385	341	2	,	,	PUNCT
fumecheng-7385	341	3	we	we	PRON
fumecheng-7385	341	4	plot	plot	VERB
fumecheng-7385	341	5	the	the	DET
fumecheng-7385	341	6	modified	modify	VERB
fumecheng-7385	341	7	hpm	hpm	NOUN
fumecheng-7385	341	8	solution	solution	NOUN
fumecheng-7385	341	9	given	give	VERB
fumecheng-7385	341	10	by	by	ADP
fumecheng-7385	341	11	eq	eq	PROPN
fumecheng-7385	341	12	.	.	PUNCT
fumecheng-7385	342	1	(	(	PUNCT
fumecheng-7385	342	2	58	58	NUM
fumecheng-7385	342	3	)	)	PUNCT
fumecheng-7385	342	4	with	with	ADP
fumecheng-7385	342	5	the	the	DET
fumecheng-7385	342	6	full	full	ADJ
fumecheng-7385	342	7	frequency	frequency	NOUN
fumecheng-7385	342	8	as	as	SCONJ
fumecheng-7385	342	9	given	give	VERB
fumecheng-7385	342	10	by	by	ADP
fumecheng-7385	342	11	eq	eq	PROPN
fumecheng-7385	342	12	.	.	PUNCT
fumecheng-7385	343	1	(	(	PUNCT
fumecheng-7385	343	2	59	59	NUM
fumecheng-7385	343	3	)	)	PUNCT
fumecheng-7385	343	4	for	for	ADP
fumecheng-7385	343	5	variation	variation	NOUN
fumecheng-7385	343	6	of	of	ADP
fumecheng-7385	343	7	temporal	temporal	ADJ
fumecheng-7385	343	8	damping	damp	VERB
fumecheng-7385	343	9	coefficient	coefficient	NOUN
fumecheng-7385	343	10	=0.1	=0.1	PROPN
fumecheng-7385	343	11	,	,	PUNCT
fumecheng-7385	343	12	0.2	0.2	NUM
fumecheng-7385	343	13	,	,	PUNCT
fumecheng-7385	343	14	0.3	0.3	NUM
fumecheng-7385	343	15	,	,	PUNCT
fumecheng-7385	343	16	0.4	0.4	NUM
fumecheng-7385	343	17	.	.	PUNCT
fumecheng-7385	344	1	inspection	inspection	NOUN
fumecheng-7385	344	2	of	of	ADP
fumecheng-7385	344	3	the	the	DET
fumecheng-7385	344	4	graph	graph	NOUN
fumecheng-7385	344	5	shows	show	VERB
fumecheng-7385	344	6	that	that	SCONJ
fumecheng-7385	344	7	as	as	ADP
fumecheng-7385	344	8			NUM
fumecheng-7385	344	9	increases	increase	NOUN
fumecheng-7385	344	10	,	,	PUNCT
fumecheng-7385	344	11	the	the	DET
fumecheng-7385	344	12	amplitude	amplitude	NOUN
fumecheng-7385	344	13	of	of	ADP
fumecheng-7385	344	14	the	the	DET
fumecheng-7385	344	15	wave	wave	NOUN
fumecheng-7385	344	16	solution	solution	NOUN
fumecheng-7385	344	17	decreases	decrease	VERB
fumecheng-7385	344	18	gradually	gradually	ADV
fumecheng-7385	344	19	until	until	ADP
fumecheng-7385	344	20	vanishing	vanish	VERB
fumecheng-7385	344	21	.	.	PUNCT
fumecheng-7385	345	1	this	this	PRON
fumecheng-7385	345	2	indicates	indicate	VERB
fumecheng-7385	345	3	the	the	DET
fumecheng-7385	345	4	loss	loss	NOUN
fumecheng-7385	345	5	of	of	ADP
fumecheng-7385	345	6	energy	energy	NOUN
fumecheng-7385	345	7	as	as	ADP
fumecheng-7385	345	8			NUM
fumecheng-7385	345	9	increases	increase	NOUN
fumecheng-7385	345	10	.	.	PUNCT
fumecheng-7385	346	1	the	the	DET
fumecheng-7385	346	2	variation	variation	NOUN
fumecheng-7385	346	3	of	of	ADP
fumecheng-7385	346	4	spatial	spatial	ADJ
fumecheng-7385	346	5	damping	damp	VERB
fumecheng-7385	346	6	coefficient	coefficient	NOUN
fumecheng-7385	346	7			NOUN
fumecheng-7385	346	8	with	with	ADP
fumecheng-7385	346	9	fixation	fixation	NOUN
fumecheng-7385	346	10	of	of	ADP
fumecheng-7385	346	11	=0.1	=0.1	PUNCT
fumecheng-7385	346	12	is	be	AUX
fumecheng-7385	346	13	displayed	display	VERB
fumecheng-7385	346	14	in	in	ADP
fumecheng-7385	346	15	fig	fig	NOUN
fumecheng-7385	346	16	.	.	PUNCT
fumecheng-7385	347	1	(	(	PUNCT
fumecheng-7385	347	2	8)	8)	NUM
fumecheng-7385	347	3	.	.	PUNCT
fumecheng-7385	348	1	the	the	DET
fumecheng-7385	348	2	conclusion	conclusion	NOUN
fumecheng-7385	348	3	turns	turn	VERB
fumecheng-7385	348	4	out	out	ADP
fumecheng-7385	348	5	to	to	PART
fumecheng-7385	348	6	be	be	AUX
fumecheng-7385	348	7	similar	similar	ADJ
fumecheng-7385	348	8	to	to	ADP
fumecheng-7385	348	9	that	that	PRON
fumecheng-7385	348	10	of	of	ADP
fumecheng-7385	348	11	.	.	INTJ
fumecheng-7385	348	12	the	the	DET
fumecheng-7385	348	13	examination	examination	NOUN
fumecheng-7385	348	14	of	of	ADP
fumecheng-7385	348	15	the	the	DET
fumecheng-7385	348	16	impact	impact	NOUN
fumecheng-7385	348	17	of	of	ADP
fumecheng-7385	348	18	coefficient	coefficient	NOUN
fumecheng-7385	348	19	p	p	NOUN
fumecheng-7385	348	20	on	on	ADP
fumecheng-7385	348	21	the	the	DET
fumecheng-7385	348	22	picture	picture	NOUN
fumecheng-7385	348	23	of	of	ADP
fumecheng-7385	348	24	the	the	DET
fumecheng-7385	348	25	wave	wave	NOUN
fumecheng-7385	348	26	solution	solution	NOUN
fumecheng-7385	348	27	is	be	AUX
fumecheng-7385	348	28	indicated	indicate	VERB
fumecheng-7385	348	29	in	in	ADP
fumecheng-7385	348	30	fig	fig	NOUN
fumecheng-7385	348	31	.	.	PUNCT
fumecheng-7385	349	1	9	9	X
fumecheng-7385	349	2	.	.	X
fumecheng-7385	350	1	it	it	PRON
fumecheng-7385	350	2	is	be	AUX
fumecheng-7385	350	3	observed	observe	VERB
fumecheng-7385	350	4	that	that	SCONJ
fumecheng-7385	350	5	as	as	ADP
fumecheng-7385	350	6	p	p	ADJ
fumecheng-7385	350	7	increases	increase	NOUN
fumecheng-7385	350	8	,	,	PUNCT
fumecheng-7385	350	9	so	so	ADV
fumecheng-7385	350	10	does	do	VERB
fumecheng-7385	350	11	the	the	DET
fumecheng-7385	350	12	amplitude	amplitude	NOUN
fumecheng-7385	350	13	of	of	ADP
fumecheng-7385	350	14	the	the	DET
fumecheng-7385	350	15	wave	wave	NOUN
fumecheng-7385	350	16	solution	solution	NOUN
fumecheng-7385	350	17	.	.	PUNCT
fumecheng-7385	351	1	this	this	DET
fumecheng-7385	351	2	observation	observation	NOUN
fumecheng-7385	351	3	is	be	AUX
fumecheng-7385	351	4	expected	expect	VERB
fumecheng-7385	351	5	because	because	SCONJ
fumecheng-7385	351	6	parameter	parameter	PROPN
fumecheng-7385	351	7	p	p	NOUN
fumecheng-7385	351	8	represents	represent	VERB
fumecheng-7385	351	9	the	the	DET
fumecheng-7385	351	10	inverse	inverse	NOUN
fumecheng-7385	351	11	of	of	ADP
fumecheng-7385	351	12	the	the	DET
fumecheng-7385	351	13	damping	damp	VERB
fumecheng-7385	351	14	coefficient	coefficient	NOUN
fumecheng-7385	351	15	of	of	ADP
fumecheng-7385	351	16	the	the	DET
fumecheng-7385	351	17	duffing	duffing	NOUN
fumecheng-7385	351	18	eq	eq	ADP
fumecheng-7385	351	19	.	.	PUNCT
fumecheng-7385	352	1	(	(	PUNCT
fumecheng-7385	352	2	47	47	NUM
fumecheng-7385	352	3	)	)	PUNCT
fumecheng-7385	352	4	.	.	PUNCT
fumecheng-7385	353	1	fig	fig	NOUN
fumecheng-7385	353	2	.	.	PUNCT
fumecheng-7385	354	1	8	8	NUM
fumecheng-7385	354	2	the	the	DET
fumecheng-7385	354	3	same	same	ADJ
fumecheng-7385	354	4	system	system	NOUN
fumecheng-7385	354	5	of	of	ADP
fumecheng-7385	354	6	fig	fig	NOUN
fumecheng-7385	354	7	.	.	PUNCT
fumecheng-7385	355	1	2	2	NUM
fumecheng-7385	355	2	with	with	ADP
fumecheng-7385	355	3	the	the	DET
fumecheng-7385	355	4	variation	variation	NOUN
fumecheng-7385	355	5	of	of	ADP
fumecheng-7385	355	6			NOUN
fumecheng-7385	355	7	fig	fig	NOUN
fumecheng-7385	355	8	.	.	PUNCT
fumecheng-7385	356	1	9	9	NUM
fumecheng-7385	356	2	the	the	DET
fumecheng-7385	356	3	same	same	ADJ
fumecheng-7385	356	4	system	system	NOUN
fumecheng-7385	356	5	of	of	ADP
fumecheng-7385	356	6	fig	fig	NOUN
fumecheng-7385	356	7	.	.	PUNCT
fumecheng-7385	357	1	2	2	NUM
fumecheng-7385	357	2	with	with	ADP
fumecheng-7385	357	3	the	the	DET
fumecheng-7385	357	4	variation	variation	NOUN
fumecheng-7385	357	5	of	of	ADP
fumecheng-7385	357	6	p	p	NOUN
fumecheng-7385	357	7	748	748	NUM
fumecheng-7385	357	8	j.-h	j.-h	NOUN
fumecheng-7385	357	9	.	.	PUNCT
fumecheng-7385	358	1	he	he	PRON
fumecheng-7385	358	2	,	,	PUNCT
fumecheng-7385	358	3	y.	y.	PROPN
fumecheng-7385	358	4	o.	o.	PROPN
fumecheng-7385	358	5	el	el	PROPN
fumecheng-7385	358	6	-	-	PROPN
fumecheng-7385	358	7	dib	dib	PROPN
fumecheng-7385	358	8	4	4	NUM
fumecheng-7385	358	9	.	.	NOUN
fumecheng-7385	358	10	results	result	NOUN
fumecheng-7385	358	11	and	and	CCONJ
fumecheng-7385	358	12	discussion	discussion	NOUN
fumecheng-7385	358	13	if	if	SCONJ
fumecheng-7385	358	14	damped	damp	VERB
fumecheng-7385	358	15	parameters	parameter	NOUN
fumecheng-7385	358	16			NOUN
fumecheng-7385	358	17	and	and	CCONJ
fumecheng-7385	358	18			PRON
fumecheng-7385	358	19	tend	tend	VERB
fumecheng-7385	358	20	to	to	PART
fumecheng-7385	358	21	zero	zero	NUM
fumecheng-7385	358	22	in	in	ADP
fumecheng-7385	358	23	eq	eq	ADP
fumecheng-7385	358	24	.	.	PUNCT
fumecheng-7385	359	1	(	(	PUNCT
fumecheng-7385	359	2	11	11	NUM
fumecheng-7385	359	3	)	)	PUNCT
fumecheng-7385	359	4	,	,	PUNCT
fumecheng-7385	359	5	the	the	DET
fumecheng-7385	359	6	result	result	NOUN
fumecheng-7385	359	7	is	be	AUX
fumecheng-7385	359	8	the	the	DET
fumecheng-7385	359	9	classical	classical	ADJ
fumecheng-7385	359	10	klein	klein	PROPN
fumecheng-7385	359	11	-	-	PUNCT
fumecheng-7385	359	12	gordon	gordon	PROPN
fumecheng-7385	359	13	equation	equation	NOUN
fumecheng-7385	359	14	:	:	PUNCT
fumecheng-7385	359	15	)	)	PUNCT
fumecheng-7385	360	1	.,(;3	.,(;3	PRON
fumecheng-7385	360	2	txyyqyypyy	txyyqyypyy	NOUN
fumecheng-7385	360	3	xxtt	xxtt	NOUN
fumecheng-7385	360	4	=	=	NOUN
fumecheng-7385	360	5	=	=	SYM
fumecheng-7385	360	6	+	+	NOUN
fumecheng-7385	360	7	+	+	X
fumecheng-7385	360	8			X
fumecheng-7385	360	9	(	(	PUNCT
fumecheng-7385	360	10	62	62	NUM
fumecheng-7385	360	11	)	)	PUNCT
fumecheng-7385	360	12	further	far	ADV
fumecheng-7385	360	13	,	,	PUNCT
fumecheng-7385	360	14	let	let	VERB
fumecheng-7385	360	15	→0	→0	PROPN
fumecheng-7385	360	16	and	and	CCONJ
fumecheng-7385	360	17	→0	→0	VERB
fumecheng-7385	360	18	in	in	ADP
fumecheng-7385	360	19	the	the	DET
fumecheng-7385	360	20	frequency	frequency	NOUN
fumecheng-7385	360	21	formula	formula	NOUN
fumecheng-7385	360	22	(	(	PUNCT
fumecheng-7385	360	23	38	38	NUM
fumecheng-7385	360	24	)	)	PUNCT
fumecheng-7385	360	25	,	,	PUNCT
fumecheng-7385	360	26	it	it	PRON
fumecheng-7385	360	27	reduces	reduce	VERB
fumecheng-7385	360	28	to	to	PART
fumecheng-7385	360	29	.	.	PUNCT
fumecheng-7385	361	1	128	128	NUM
fumecheng-7385	361	2	3	3	NUM
fumecheng-7385	361	3	4	4	NUM
fumecheng-7385	361	4	3	3	NUM
fumecheng-7385	361	5	2	2	NUM
fumecheng-7385	361	6	42	42	NUM
fumecheng-7385	361	7	22	22	NUM
fumecheng-7385	361	8			PROPN
fumecheng-7385	361	9	−−=	−−=	CCONJ
fumecheng-7385	361	10	aq	aq	X
fumecheng-7385	361	11	qa	qa	NOUN
fumecheng-7385	361	12	(	(	PUNCT
fumecheng-7385	361	13	63	63	NUM
fumecheng-7385	361	14	)	)	PUNCT
fumecheng-7385	361	15	this	this	PRON
fumecheng-7385	361	16	is	be	AUX
fumecheng-7385	361	17	equivalent	equivalent	ADJ
fumecheng-7385	361	18	to	to	ADP
fumecheng-7385	361	19	those	those	PRON
fumecheng-7385	361	20	obtained	obtain	VERB
fumecheng-7385	361	21	before	before	ADV
fumecheng-7385	361	22	in	in	ADP
fumecheng-7385	361	23	[	[	X
fumecheng-7385	361	24	16	16	NUM
fumecheng-7385	361	25	]	]	PUNCT
fumecheng-7385	361	26	by	by	ADP
fumecheng-7385	361	27	using	use	VERB
fumecheng-7385	361	28	the	the	DET
fumecheng-7385	361	29	classical	classical	ADJ
fumecheng-7385	361	30	hpm	hpm	NOUN
fumecheng-7385	361	31	.	.	PUNCT
fumecheng-7385	362	1	the	the	DET
fumecheng-7385	362	2	classical	classical	ADJ
fumecheng-7385	362	3	hpm	hpm	NOUN
fumecheng-7385	362	4	has	have	AUX
fumecheng-7385	362	5	successfully	successfully	ADV
fumecheng-7385	362	6	solved	solve	VERB
fumecheng-7385	362	7	this	this	DET
fumecheng-7385	362	8	equation	equation	NOUN
fumecheng-7385	362	9	.	.	PUNCT
fumecheng-7385	363	1	el	el	PROPN
fumecheng-7385	363	2	-	-	PROPN
fumecheng-7385	363	3	dib	dib	PROPN
fumecheng-7385	363	4	[	[	X
fumecheng-7385	363	5	16	16	NUM
fumecheng-7385	363	6	]	]	PUNCT
fumecheng-7385	363	7	applied	apply	VERB
fumecheng-7385	363	8	the	the	DET
fumecheng-7385	363	9	he’s	he’s	NOUN
fumecheng-7385	363	10	-	-	PUNCT
fumecheng-7385	363	11	multiple	multiple	ADJ
fumecheng-7385	363	12	scale	scale	NOUN
fumecheng-7385	363	13	technique	technique	NOUN
fumecheng-7385	363	14	to	to	PART
fumecheng-7385	363	15	find	find	VERB
fumecheng-7385	363	16	the	the	DET
fumecheng-7385	363	17	periodic	periodic	ADJ
fumecheng-7385	363	18	solution	solution	NOUN
fumecheng-7385	363	19	and	and	CCONJ
fumecheng-7385	363	20	to	to	PART
fumecheng-7385	363	21	obtain	obtain	VERB
fumecheng-7385	363	22	the	the	DET
fumecheng-7385	363	23	stability	stability	NOUN
fumecheng-7385	363	24	conditions	condition	NOUN
fumecheng-7385	363	25	.	.	PUNCT
fumecheng-7385	364	1	further	far	ADV
fumecheng-7385	364	2	,	,	PUNCT
fumecheng-7385	364	3	el	el	PROPN
fumecheng-7385	364	4	-	-	PROPN
fumecheng-7385	364	5	dib	dib	PROPN
fumecheng-7385	364	6	[	[	X
fumecheng-7385	364	7	27	27	NUM
fumecheng-7385	364	8	]	]	PUNCT
fumecheng-7385	364	9	investigated	investigate	VERB
fumecheng-7385	364	10	eq	eq	ADP
fumecheng-7385	364	11	.	.	PUNCT
fumecheng-7385	365	1	(	(	PUNCT
fumecheng-7385	365	2	62	62	NUM
fumecheng-7385	365	3	)	)	PUNCT
fumecheng-7385	365	4	by	by	ADP
fumecheng-7385	365	5	applying	apply	VERB
fumecheng-7385	365	6	the	the	DET
fumecheng-7385	365	7	method	method	NOUN
fumecheng-7385	365	8	of	of	ADP
fumecheng-7385	365	9	variable	variable	ADJ
fumecheng-7385	365	10	separation	separation	NOUN
fumecheng-7385	365	11	to	to	ADP
fumecheng-7385	365	12	variable	variable	NOUN
fumecheng-7385	365	13	y(x	y(x	PROPN
fumecheng-7385	365	14	,	,	PUNCT
fumecheng-7385	365	15	t	t	PROPN
fumecheng-7385	365	16	)	)	PUNCT
fumecheng-7385	365	17	,	,	PUNCT
fumecheng-7385	365	18	and	and	CCONJ
fumecheng-7385	365	19	investigated	investigate	VERB
fumecheng-7385	365	20	the	the	DET
fumecheng-7385	365	21	periodic	periodic	ADJ
fumecheng-7385	365	22	solution	solution	NOUN
fumecheng-7385	365	23	using	use	VERB
fumecheng-7385	365	24	the	the	DET
fumecheng-7385	365	25	technique	technique	NOUN
fumecheng-7385	365	26	of	of	ADP
fumecheng-7385	365	27	the	the	DET
fumecheng-7385	365	28	multi	multi	ADJ
fumecheng-7385	365	29	-	-	ADJ
fumecheng-7385	365	30	homotopy	homotopy	ADJ
fumecheng-7385	365	31	perturbations	perturbation	NOUN
fumecheng-7385	365	32	.	.	PUNCT
fumecheng-7385	366	1	these	these	DET
fumecheng-7385	366	2	previous	previous	ADJ
fumecheng-7385	366	3	studies	study	NOUN
fumecheng-7385	366	4	failed	fail	VERB
fumecheng-7385	366	5	to	to	PART
fumecheng-7385	366	6	analyze	analyze	VERB
fumecheng-7385	366	7	the	the	DET
fumecheng-7385	366	8	nonlinear	nonlinear	PROPN
fumecheng-7385	366	9	damped	damped	PROPN
fumecheng-7385	366	10	klein	klein	PROPN
fumecheng-7385	366	11	-	-	PUNCT
fumecheng-7385	366	12	gordon	gordon	PROPN
fumecheng-7385	366	13	eq	eq	X
fumecheng-7385	366	14	.	.	PUNCT
fumecheng-7385	367	1	(	(	PUNCT
fumecheng-7385	367	2	11	11	NUM
fumecheng-7385	367	3	)	)	PUNCT
fumecheng-7385	367	4	.	.	PUNCT
fumecheng-7385	368	1	in	in	ADP
fumecheng-7385	368	2	ref	ref	NOUN
fumecheng-7385	368	3	.	.	PUNCT
fumecheng-7385	369	1	[	[	X
fumecheng-7385	369	2	35	35	NUM
fumecheng-7385	369	3	]	]	PUNCT
fumecheng-7385	369	4	,	,	PUNCT
fumecheng-7385	369	5	the	the	DET
fumecheng-7385	369	6	authors	author	NOUN
fumecheng-7385	369	7	tried	try	VERB
fumecheng-7385	369	8	to	to	PART
fumecheng-7385	369	9	overcome	overcome	VERB
fumecheng-7385	369	10	the	the	DET
fumecheng-7385	369	11	shortcomings	shortcoming	NOUN
fumecheng-7385	369	12	of	of	ADP
fumecheng-7385	369	13	the	the	DET
fumecheng-7385	369	14	classical	classical	ADJ
fumecheng-7385	369	15	hpm	hpm	NOUN
fumecheng-7385	369	16	.	.	PUNCT
fumecheng-7385	370	1	they	they	PRON
fumecheng-7385	370	2	converted	convert	VERB
fumecheng-7385	370	3	the	the	DET
fumecheng-7385	370	4	integer	integer	NOUN
fumecheng-7385	370	5	second	second	ADJ
fumecheng-7385	370	6	-	-	PUNCT
fumecheng-7385	370	7	time	time	NOUN
fumecheng-7385	370	8	partial	partial	ADJ
fumecheng-7385	370	9	derivative	derivative	NOUN
fumecheng-7385	370	10	to	to	ADP
fumecheng-7385	370	11	the	the	DET
fumecheng-7385	370	12	fractional	fractional	ADJ
fumecheng-7385	370	13	nonlinear	nonlinear	ADJ
fumecheng-7385	370	14	partial	partial	ADJ
fumecheng-7385	370	15	differential	differential	NOUN
fumecheng-7385	370	16	of	of	ADP
fumecheng-7385	370	17	order	order	NOUN
fumecheng-7385	370	18	(	(	PUNCT
fumecheng-7385	370	19	+1	+1	NOUN
fumecheng-7385	370	20	;	;	PUNCT
fumecheng-7385	370	21	0<1	0<1	NOUN
fumecheng-7385	370	22	)	)	PUNCT
fumecheng-7385	370	23	,	,	PUNCT
fumecheng-7385	370	24	and	and	CCONJ
fumecheng-7385	370	25	applied	apply	VERB
fumecheng-7385	370	26	the	the	DET
fumecheng-7385	370	27	properties	property	NOUN
fumecheng-7385	370	28	of	of	ADP
fumecheng-7385	370	29	the	the	DET
fumecheng-7385	370	30	riemann	riemann	PROPN
fumecheng-7385	370	31	–	–	PUNCT
fumecheng-7385	370	32	liouville	liouville	VERB
fumecheng-7385	370	33	fraction	fraction	NOUN
fumecheng-7385	370	34	derivatives	derivative	NOUN
fumecheng-7385	370	35	,	,	PUNCT
fumecheng-7385	370	36	through	through	ADP
fumecheng-7385	370	37	the	the	DET
fumecheng-7385	370	38	hpm	hpm	NOUN
fumecheng-7385	370	39	.	.	PUNCT
fumecheng-7385	371	1	this	this	DET
fumecheng-7385	371	2	technique	technique	NOUN
fumecheng-7385	371	3	allowed	allow	VERB
fumecheng-7385	371	4	the	the	DET
fumecheng-7385	371	5	authors	author	NOUN
fumecheng-7385	371	6	to	to	PART
fumecheng-7385	371	7	obtain	obtain	VERB
fumecheng-7385	371	8	the	the	DET
fumecheng-7385	371	9	periodic	periodic	ADJ
fumecheng-7385	371	10	solution	solution	NOUN
fumecheng-7385	371	11	of	of	ADP
fumecheng-7385	371	12	eq	eq	PROPN
fumecheng-7385	371	13	.	.	PUNCT
fumecheng-7385	372	1	(	(	PUNCT
fumecheng-7385	372	2	11	11	NUM
fumecheng-7385	372	3	)	)	PUNCT
fumecheng-7385	372	4	and	and	CCONJ
fumecheng-7385	372	5	the	the	DET
fumecheng-7385	372	6	stability	stability	NOUN
fumecheng-7385	372	7	conditions	condition	NOUN
fumecheng-7385	372	8	in	in	ADP
fumecheng-7385	372	9	terms	term	NOUN
fumecheng-7385	372	10	of	of	ADP
fumecheng-7385	372	11	parameter	parameter	NOUN
fumecheng-7385	372	12			X
fumecheng-7385	372	13	and	and	CCONJ
fumecheng-7385	372	14	letting	let	VERB
fumecheng-7385	372	15	→1	→1	NOUN
fumecheng-7385	372	16	in	in	ADP
fumecheng-7385	372	17	the	the	DET
fumecheng-7385	372	18	final	final	ADJ
fumecheng-7385	372	19	results	result	NOUN
fumecheng-7385	372	20	.	.	PUNCT
fumecheng-7385	373	1	the	the	DET
fumecheng-7385	373	2	new	new	ADJ
fumecheng-7385	373	3	modification	modification	NOUN
fumecheng-7385	373	4	to	to	PART
fumecheng-7385	373	5	hpm	hpm	NOUN
fumecheng-7385	373	6	discussed	discuss	VERB
fumecheng-7385	373	7	in	in	ADP
fumecheng-7385	373	8	the	the	DET
fumecheng-7385	373	9	present	present	ADJ
fumecheng-7385	373	10	study	study	NOUN
fumecheng-7385	373	11	depends	depend	VERB
fumecheng-7385	373	12	on	on	ADP
fumecheng-7385	373	13	the	the	DET
fumecheng-7385	373	14	idea	idea	NOUN
fumecheng-7385	373	15	of	of	ADP
fumecheng-7385	373	16	the	the	DET
fumecheng-7385	373	17	normal	normal	ADJ
fumecheng-7385	373	18	form	form	NOUN
fumecheng-7385	373	19	technique	technique	NOUN
fumecheng-7385	373	20	.	.	PUNCT
fumecheng-7385	374	1	it	it	PRON
fumecheng-7385	374	2	is	be	AUX
fumecheng-7385	374	3	known	know	VERB
fumecheng-7385	374	4	that	that	SCONJ
fumecheng-7385	374	5	this	this	DET
fumecheng-7385	374	6	technique	technique	NOUN
fumecheng-7385	374	7	is	be	AUX
fumecheng-7385	374	8	successfully	successfully	ADV
fumecheng-7385	374	9	used	use	VERB
fumecheng-7385	374	10	in	in	ADP
fumecheng-7385	374	11	the	the	DET
fumecheng-7385	374	12	linear	linear	ADJ
fumecheng-7385	374	13	damped	damped	NOUN
fumecheng-7385	374	14	equation	equation	NOUN
fumecheng-7385	374	15	.	.	PUNCT
fumecheng-7385	375	1	in	in	ADP
fumecheng-7385	375	2	the	the	DET
fumecheng-7385	375	3	current	current	ADJ
fumecheng-7385	375	4	work	work	NOUN
fumecheng-7385	375	5	,	,	PUNCT
fumecheng-7385	375	6	we	we	PRON
fumecheng-7385	375	7	succeeded	succeed	VERB
fumecheng-7385	375	8	to	to	PART
fumecheng-7385	375	9	adapt	adapt	VERB
fumecheng-7385	375	10	the	the	DET
fumecheng-7385	375	11	technique	technique	NOUN
fumecheng-7385	375	12	of	of	ADP
fumecheng-7385	375	13	the	the	DET
fumecheng-7385	375	14	normal	normal	ADJ
fumecheng-7385	375	15	form	form	NOUN
fumecheng-7385	375	16	when	when	SCONJ
fumecheng-7385	375	17	coupled	couple	VERB
fumecheng-7385	375	18	with	with	ADP
fumecheng-7385	375	19	the	the	DET
fumecheng-7385	375	20	hpm	hpm	NOUN
fumecheng-7385	375	21	,	,	PUNCT
fumecheng-7385	375	22	in	in	ADP
fumecheng-7385	375	23	which	which	PRON
fumecheng-7385	375	24	the	the	DET
fumecheng-7385	375	25	exponential	exponential	ADJ
fumecheng-7385	375	26	decay	decay	NOUN
fumecheng-7385	375	27	parameters	parameter	NOUN
fumecheng-7385	375	28	are	be	AUX
fumecheng-7385	375	29	established	establish	VERB
fumecheng-7385	375	30	.	.	PUNCT
fumecheng-7385	376	1	the	the	DET
fumecheng-7385	376	2	analysis	analysis	NOUN
fumecheng-7385	376	3	shows	show	VERB
fumecheng-7385	376	4	that	that	SCONJ
fumecheng-7385	376	5	the	the	DET
fumecheng-7385	376	6	amplitude	amplitude	NOUN
fumecheng-7385	376	7	behaves	behave	VERB
fumecheng-7385	376	8	as	as	ADP
fumecheng-7385	376	9	an	an	DET
fumecheng-7385	376	10	exponential	exponential	ADJ
fumecheng-7385	376	11	decay	decay	NOUN
fumecheng-7385	376	12	by	by	ADP
fumecheng-7385	376	13	the	the	DET
fumecheng-7385	376	14	damping	damp	VERB
fumecheng-7385	376	15	parameter	parameter	NOUN
fumecheng-7385	376	16	.	.	PUNCT
fumecheng-7385	377	1	an	an	DET
fumecheng-7385	377	2	excellent	excellent	ADJ
fumecheng-7385	377	3	agreement	agreement	NOUN
fumecheng-7385	377	4	with	with	ADP
fumecheng-7385	377	5	the	the	DET
fumecheng-7385	377	6	numerical	numerical	ADJ
fumecheng-7385	377	7	solution	solution	NOUN
fumecheng-7385	377	8	is	be	AUX
fumecheng-7385	377	9	observed	observe	VERB
fumecheng-7385	377	10	in	in	ADP
fumecheng-7385	377	11	these	these	DET
fumecheng-7385	377	12	calculations	calculation	NOUN
fumecheng-7385	377	13	.	.	PUNCT
fumecheng-7385	378	1	this	this	DET
fumecheng-7385	378	2	scheme	scheme	NOUN
fumecheng-7385	378	3	yielded	yield	VERB
fumecheng-7385	378	4	a	a	DET
fumecheng-7385	378	5	more	more	ADV
fumecheng-7385	378	6	effective	effective	ADJ
fumecheng-7385	378	7	result	result	NOUN
fumecheng-7385	378	8	for	for	ADP
fumecheng-7385	378	9	the	the	DET
fumecheng-7385	378	10	nonlinear	nonlinear	ADJ
fumecheng-7385	378	11	oscillators	oscillator	NOUN
fumecheng-7385	378	12	and	and	CCONJ
fumecheng-7385	378	13	helped	help	VERB
fumecheng-7385	378	14	to	to	PART
fumecheng-7385	378	15	overcome	overcome	VERB
fumecheng-7385	378	16	the	the	DET
fumecheng-7385	378	17	shortcoming	shortcoming	NOUN
fumecheng-7385	378	18	of	of	ADP
fumecheng-7385	378	19	the	the	DET
fumecheng-7385	378	20	classical	classical	ADJ
fumecheng-7385	378	21	approach	approach	NOUN
fumecheng-7385	378	22	.	.	PUNCT
fumecheng-7385	379	1	5	5	X
fumecheng-7385	379	2	.	.	X
fumecheng-7385	379	3	conclusion	conclusion	NOUN
fumecheng-7385	379	4	the	the	DET
fumecheng-7385	379	5	periodic	periodic	ADJ
fumecheng-7385	379	6	solution	solution	NOUN
fumecheng-7385	379	7	of	of	ADP
fumecheng-7385	379	8	nonlinear	nonlinear	ADJ
fumecheng-7385	379	9	models	model	NOUN
fumecheng-7385	379	10	has	have	VERB
fumecheng-7385	379	11	much	much	ADJ
fumecheng-7385	379	12	significance	significance	NOUN
fumecheng-7385	379	13	and	and	CCONJ
fumecheng-7385	379	14	has	have	AUX
fumecheng-7385	379	15	drawn	draw	VERB
fumecheng-7385	379	16	a	a	DET
fumecheng-7385	379	17	great	great	ADJ
fumecheng-7385	379	18	deal	deal	NOUN
fumecheng-7385	379	19	of	of	ADP
fumecheng-7385	379	20	interest	interest	NOUN
fumecheng-7385	379	21	.	.	PUNCT
fumecheng-7385	380	1	in	in	ADP
fumecheng-7385	380	2	the	the	DET
fumecheng-7385	380	3	current	current	ADJ
fumecheng-7385	380	4	work	work	NOUN
fumecheng-7385	380	5	,	,	PUNCT
fumecheng-7385	380	6	we	we	PRON
fumecheng-7385	380	7	have	have	AUX
fumecheng-7385	380	8	investigated	investigate	VERB
fumecheng-7385	380	9	the	the	DET
fumecheng-7385	380	10	solution	solution	NOUN
fumecheng-7385	380	11	of	of	ADP
fumecheng-7385	380	12	the	the	DET
fumecheng-7385	380	13	damping	damp	VERB
fumecheng-7385	380	14	nonlinear	nonlinear	ADJ
fumecheng-7385	380	15	wave	wave	NOUN
fumecheng-7385	380	16	equation	equation	NOUN
fumecheng-7385	380	17	.	.	PUNCT
fumecheng-7385	381	1	the	the	DET
fumecheng-7385	381	2	normal	normal	ADJ
fumecheng-7385	381	3	form	form	NOUN
fumecheng-7385	381	4	transformation	transformation	NOUN
fumecheng-7385	381	5	is	be	AUX
fumecheng-7385	381	6	used	use	VERB
fumecheng-7385	381	7	to	to	PART
fumecheng-7385	381	8	solve	solve	VERB
fumecheng-7385	381	9	the	the	DET
fumecheng-7385	381	10	damping	damp	VERB
fumecheng-7385	381	11	linear	linear	PROPN
fumecheng-7385	381	12	klein	klein	PROPN
fumecheng-7385	381	13	-	-	PUNCT
fumecheng-7385	381	14	gordon	gordon	PROPN
fumecheng-7385	381	15	equation	equation	NOUN
fumecheng-7385	381	16	.	.	PUNCT
fumecheng-7385	382	1	further	far	ADV
fumecheng-7385	382	2	,	,	PUNCT
fumecheng-7385	382	3	the	the	DET
fumecheng-7385	382	4	frequency	frequency	NOUN
fumecheng-7385	382	5	equation	equation	NOUN
fumecheng-7385	382	6	is	be	AUX
fumecheng-7385	382	7	estimated	estimate	VERB
fumecheng-7385	382	8	as	as	SCONJ
fumecheng-7385	382	9	displayed	display	VERB
fumecheng-7385	382	10	in	in	ADP
fumecheng-7385	382	11	eqs	eqs	PROPN
fumecheng-7385	382	12	.	.	PUNCT
fumecheng-7385	383	1	(	(	PUNCT
fumecheng-7385	383	2	12	12	NUM
fumecheng-7385	383	3	)	)	PUNCT
fumecheng-7385	383	4	and	and	CCONJ
fumecheng-7385	383	5	(	(	PUNCT
fumecheng-7385	383	6	13	13	NUM
fumecheng-7385	383	7	)	)	PUNCT
fumecheng-7385	383	8	.	.	PUNCT
fumecheng-7385	384	1	although	although	SCONJ
fumecheng-7385	384	2	the	the	DET
fumecheng-7385	384	3	classical	classical	ADJ
fumecheng-7385	384	4	hpm	hpm	NOUN
fumecheng-7385	384	5	is	be	AUX
fumecheng-7385	384	6	not	not	PART
fumecheng-7385	384	7	successful	successful	ADJ
fumecheng-7385	384	8	in	in	ADP
fumecheng-7385	384	9	analyzing	analyze	VERB
fumecheng-7385	384	10	the	the	DET
fumecheng-7385	384	11	damping	damp	VERB
fumecheng-7385	384	12	nonlinear	nonlinear	ADJ
fumecheng-7385	384	13	oscillator	oscillator	NOUN
fumecheng-7385	384	14	when	when	SCONJ
fumecheng-7385	384	15	it	it	PRON
fumecheng-7385	384	16	is	be	AUX
fumecheng-7385	384	17	associated	associate	VERB
fumecheng-7385	384	18	with	with	ADP
fumecheng-7385	384	19	the	the	DET
fumecheng-7385	384	20	exponential	exponential	ADJ
fumecheng-7385	384	21	decay	decay	NOUN
fumecheng-7385	384	22	parameter	parameter	NOUN
fumecheng-7385	384	23	as	as	SCONJ
fumecheng-7385	384	24	defined	define	VERB
fumecheng-7385	384	25	in	in	ADP
fumecheng-7385	384	26	eq	eq	ADP
fumecheng-7385	384	27	.	.	PUNCT
fumecheng-7385	385	1	(	(	PUNCT
fumecheng-7385	385	2	18	18	NUM
fumecheng-7385	385	3	)	)	PUNCT
fumecheng-7385	385	4	,	,	PUNCT
fumecheng-7385	385	5	the	the	DET
fumecheng-7385	385	6	solution	solution	NOUN
fumecheng-7385	385	7	is	be	AUX
fumecheng-7385	385	8	obtained	obtain	VERB
fumecheng-7385	385	9	.	.	PUNCT
fumecheng-7385	386	1	this	this	DET
fumecheng-7385	386	2	modification	modification	NOUN
fumecheng-7385	386	3	has	have	AUX
fumecheng-7385	386	4	been	be	AUX
fumecheng-7385	386	5	successful	successful	ADJ
fumecheng-7385	386	6	in	in	ADP
fumecheng-7385	386	7	suppressing	suppress	VERB
fumecheng-7385	386	8	the	the	DET
fumecheng-7385	386	9	shortcoming	shortcoming	NOUN
fumecheng-7385	386	10	of	of	ADP
fumecheng-7385	386	11	the	the	DET
fumecheng-7385	386	12	classical	classical	ADJ
fumecheng-7385	386	13	hpm	hpm	NOUN
fumecheng-7385	386	14	.	.	PUNCT
fumecheng-7385	387	1	the	the	DET
fumecheng-7385	387	2	first	first	ADJ
fumecheng-7385	387	3	-	-	PUNCT
fumecheng-7385	387	4	order	order	NOUN
fumecheng-7385	387	5	approximate	approximate	ADJ
fumecheng-7385	387	6	solution	solution	NOUN
fumecheng-7385	387	7	is	be	AUX
fumecheng-7385	387	8	derived	derive	VERB
fumecheng-7385	387	9	in	in	ADP
fumecheng-7385	387	10	eq	eq	ADP
fumecheng-7385	387	11	.	.	PUNCT
fumecheng-7385	388	1	(	(	PUNCT
fumecheng-7385	388	2	37	37	NUM
fumecheng-7385	388	3	)	)	PUNCT
fumecheng-7385	388	4	,	,	PUNCT
fumecheng-7385	388	5	the	the	DET
fumecheng-7385	388	6	frequency	frequency	NOUN
fumecheng-7385	388	7	-	-	PUNCT
fumecheng-7385	388	8	amplitude	amplitude	NOUN
fumecheng-7385	388	9	equation	equation	NOUN
fumecheng-7385	388	10	is	be	AUX
fumecheng-7385	388	11	established	establish	VERB
fumecheng-7385	388	12	in	in	ADP
fumecheng-7385	388	13	eq	eq	ADP
fumecheng-7385	388	14	.	.	PUNCT
fumecheng-7385	389	1	(	(	PUNCT
fumecheng-7385	389	2	42	42	NUM
fumecheng-7385	389	3	)	)	PUNCT
fumecheng-7385	389	4	and	and	CCONJ
fumecheng-7385	389	5	the	the	DET
fumecheng-7385	389	6	stability	stability	NOUN
fumecheng-7385	389	7	condition	condition	NOUN
fumecheng-7385	389	8	is	be	AUX
fumecheng-7385	389	9	performed	perform	VERB
fumecheng-7385	389	10	in	in	ADP
fumecheng-7385	389	11	eq	eq	ADP
fumecheng-7385	389	12	.	.	PUNCT
fumecheng-7385	390	1	(	(	PUNCT
fumecheng-7385	390	2	44	44	NUM
fumecheng-7385	390	3	)	)	PUNCT
fumecheng-7385	390	4	.	.	PUNCT
fumecheng-7385	391	1	furthermore	furthermore	ADV
fumecheng-7385	391	2	,	,	PUNCT
fumecheng-7385	391	3	the	the	DET
fumecheng-7385	391	4	traveling	travel	VERB
fumecheng-7385	391	5	-	-	PUNCT
fumecheng-7385	391	6	wave	wave	NOUN
fumecheng-7385	391	7	description	description	NOUN
fumecheng-7385	391	8	is	be	AUX
fumecheng-7385	391	9	used	use	VERB
fumecheng-7385	391	10	to	to	PART
fumecheng-7385	391	11	transform	transform	VERB
fumecheng-7385	391	12	the	the	DET
fumecheng-7385	391	13	klein	klein	PROPN
fumecheng-7385	391	14	-	-	PUNCT
fumecheng-7385	391	15	gordon	gordon	PROPN
fumecheng-7385	391	16	equation	equation	NOUN
fumecheng-7385	391	17	in	in	ADP
fumecheng-7385	391	18	the	the	DET
fumecheng-7385	391	19	damping	damp	VERB
fumecheng-7385	391	20	duffing	duffing	NOUN
fumecheng-7385	391	21	equation	equation	NOUN
fumecheng-7385	391	22	into	into	ADP
fumecheng-7385	391	23	a	a	DET
fumecheng-7385	391	24	new	new	ADJ
fumecheng-7385	391	25	dependent	dependent	ADJ
fumecheng-7385	391	26	variable	variable	NOUN
fumecheng-7385	391	27	.	.	PUNCT
fumecheng-7385	392	1	the	the	DET
fumecheng-7385	392	2	same	same	ADJ
fumecheng-7385	392	3	procedure	procedure	NOUN
fumecheng-7385	392	4	of	of	ADP
fumecheng-7385	392	5	homotopy	homotopy	NOUN
fumecheng-7385	392	6	perturbation	perturbation	NOUN
fumecheng-7385	392	7	with	with	ADP
fumecheng-7385	392	8	the	the	DET
fumecheng-7385	392	9	exponential	exponential	NOUN
fumecheng-7385	392	10	the	the	DET
fumecheng-7385	392	11	enhanced	enhanced	ADJ
fumecheng-7385	392	12	homotopy	homotopy	NOUN
fumecheng-7385	392	13	perturbation	perturbation	NOUN
fumecheng-7385	392	14	method	method	NOUN
fumecheng-7385	392	15	for	for	ADP
fumecheng-7385	392	16	axial	axial	ADJ
fumecheng-7385	392	17	vibrations	vibration	NOUN
fumecheng-7385	392	18	of	of	ADP
fumecheng-7385	392	19	strings	string	NOUN
fumecheng-7385	392	20	749	749	NUM
fumecheng-7385	392	21	decay	decay	NOUN
fumecheng-7385	392	22	parameter	parameter	NOUN
fumecheng-7385	392	23	is	be	AUX
fumecheng-7385	392	24	used	use	VERB
fumecheng-7385	392	25	,	,	PUNCT
fumecheng-7385	392	26	and	and	CCONJ
fumecheng-7385	392	27	the	the	DET
fumecheng-7385	392	28	solution	solution	NOUN
fumecheng-7385	392	29	and	and	CCONJ
fumecheng-7385	392	30	the	the	DET
fumecheng-7385	392	31	frequency	frequency	NOUN
fumecheng-7385	392	32	formula	formula	NOUN
fumecheng-7385	392	33	are	be	AUX
fumecheng-7385	392	34	obtained	obtain	VERB
fumecheng-7385	392	35	.	.	PUNCT
fumecheng-7385	393	1	numerical	numerical	PROPN
fumecheng-7385	393	2	calculations	calculation	NOUN
fumecheng-7385	393	3	are	be	AUX
fumecheng-7385	393	4	done	do	VERB
fumecheng-7385	393	5	and	and	CCONJ
fumecheng-7385	393	6	some	some	DET
fumecheng-7385	393	7	graphs	graph	NOUN
fumecheng-7385	393	8	are	be	AUX
fumecheng-7385	393	9	displayed	display	VERB
fumecheng-7385	393	10	.	.	PUNCT
fumecheng-7385	394	1	the	the	DET
fumecheng-7385	394	2	periodic	periodic	ADJ
fumecheng-7385	394	3	damping	damp	VERB
fumecheng-7385	394	4	analytical	analytical	ADJ
fumecheng-7385	394	5	solution	solution	NOUN
fumecheng-7385	394	6	is	be	AUX
fumecheng-7385	394	7	found	find	VERB
fumecheng-7385	394	8	to	to	PART
fumecheng-7385	394	9	have	have	VERB
fumecheng-7385	394	10	an	an	DET
fumecheng-7385	394	11	excellent	excellent	ADJ
fumecheng-7385	394	12	agreement	agreement	NOUN
fumecheng-7385	394	13	with	with	ADP
fumecheng-7385	394	14	the	the	DET
fumecheng-7385	394	15	numerical	numerical	ADJ
fumecheng-7385	394	16	solution	solution	NOUN
fumecheng-7385	394	17	.	.	PUNCT
fumecheng-7385	395	1	this	this	DET
fumecheng-7385	395	2	conclusion	conclusion	NOUN
fumecheng-7385	395	3	is	be	AUX
fumecheng-7385	395	4	reached	reach	VERB
fumecheng-7385	395	5	in	in	ADP
fumecheng-7385	395	6	the	the	DET
fumecheng-7385	395	7	case	case	NOUN
fumecheng-7385	395	8	of	of	ADP
fumecheng-7385	395	9	the	the	DET
fumecheng-7385	395	10	partial	partial	ADJ
fumecheng-7385	395	11	differential	differential	NOUN
fumecheng-7385	395	12	eq	eq	ADP
fumecheng-7385	395	13	.	.	PUNCT
fumecheng-7385	396	1	(	(	PUNCT
fumecheng-7385	396	2	11	11	NUM
fumecheng-7385	396	3	)	)	PUNCT
fumecheng-7385	396	4	,	,	PUNCT
fumecheng-7385	396	5	and	and	CCONJ
fumecheng-7385	396	6	,	,	PUNCT
fumecheng-7385	396	7	also	also	ADV
fumecheng-7385	396	8	,	,	PUNCT
fumecheng-7385	396	9	in	in	ADP
fumecheng-7385	396	10	the	the	DET
fumecheng-7385	396	11	case	case	NOUN
fumecheng-7385	396	12	of	of	ADP
fumecheng-7385	396	13	the	the	DET
fumecheng-7385	396	14	ordinary	ordinary	ADJ
fumecheng-7385	396	15	nonlinear	nonlinear	ADJ
fumecheng-7385	396	16	duffing	duffing	NOUN
fumecheng-7385	396	17	eq	eq	ADP
fumecheng-7385	396	18	.	.	PUNCT
fumecheng-7385	397	1	(	(	PUNCT
fumecheng-7385	397	2	37	37	NUM
fumecheng-7385	397	3	)	)	PUNCT
fumecheng-7385	397	4	.	.	PUNCT
fumecheng-7385	398	1	references	reference	NOUN
fumecheng-7385	398	2	1	1	NUM
fumecheng-7385	398	3	.	.	PUNCT
fumecheng-7385	399	1	he	he	PRON
fumecheng-7385	399	2	,	,	PUNCT
fumecheng-7385	399	3	j.-h	j.-h	PROPN
fumecheng-7385	399	4	.	.	PROPN
fumecheng-7385	399	5	,	,	PUNCT
fumecheng-7385	399	6	2000	2000	NUM
fumecheng-7385	399	7	,	,	PUNCT
fumecheng-7385	399	8	a	a	DET
fumecheng-7385	399	9	coupling	coupling	NOUN
fumecheng-7385	399	10	method	method	NOUN
fumecheng-7385	399	11	of	of	ADP
fumecheng-7385	399	12	homotopy	homotopy	NOUN
fumecheng-7385	399	13	technique	technique	NOUN
fumecheng-7385	399	14	and	and	CCONJ
fumecheng-7385	399	15	a	a	DET
fumecheng-7385	399	16	perturbation	perturbation	NOUN
fumecheng-7385	399	17	technique	technique	NOUN
fumecheng-7385	399	18	for	for	ADP
fumecheng-7385	399	19	non	non	ADJ
fumecheng-7385	399	20	-	-	ADJ
fumecheng-7385	399	21	linear	linear	ADJ
fumecheng-7385	399	22	problems	problem	NOUN
fumecheng-7385	399	23	,	,	PUNCT
fumecheng-7385	399	24	international	international	ADJ
fumecheng-7385	399	25	journal	journal	NOUN
fumecheng-7385	399	26	of	of	ADP
fumecheng-7385	399	27	nonlinear	nonlinear	ADJ
fumecheng-7385	399	28	mechanics	mechanic	NOUN
fumecheng-7385	399	29	,	,	PUNCT
fumecheng-7385	399	30	35	35	NUM
fumecheng-7385	399	31	,	,	PUNCT
fumecheng-7385	399	32	pp	pp	ADJ
fumecheng-7385	399	33	.	.	PUNCT
fumecheng-7385	400	1	37	37	NUM
fumecheng-7385	400	2	-	-	SYM
fumecheng-7385	400	3	43	43	NUM
fumecheng-7385	400	4	.	.	PUNCT
fumecheng-7385	401	1	2	2	X
fumecheng-7385	401	2	.	.	X
fumecheng-7385	402	1	he	he	PRON
fumecheng-7385	402	2	,	,	PUNCT
fumecheng-7385	402	3	j.h	j.h	PROPN
fumecheng-7385	402	4	.	.	PROPN
fumecheng-7385	402	5	,	,	PUNCT
fumecheng-7385	402	6	2019	2019	NUM
fumecheng-7385	402	7	,	,	PUNCT
fumecheng-7385	402	8	the	the	PRON
fumecheng-7385	402	9	simpler	simple	ADJ
fumecheng-7385	402	10	,	,	PUNCT
fumecheng-7385	402	11	the	the	PRON
fumecheng-7385	402	12	better	well	ADJ
fumecheng-7385	402	13	:	:	PUNCT
fumecheng-7385	402	14	analytical	analytical	ADJ
fumecheng-7385	402	15	methods	method	NOUN
fumecheng-7385	402	16	for	for	ADP
fumecheng-7385	402	17	nonlinear	nonlinear	ADJ
fumecheng-7385	402	18	oscillators	oscillator	NOUN
fumecheng-7385	402	19	and	and	CCONJ
fumecheng-7385	402	20	fractional	fractional	ADJ
fumecheng-7385	402	21	oscillators	oscillator	NOUN
fumecheng-7385	402	22	,	,	PUNCT
fumecheng-7385	402	23	journal	journal	NOUN
fumecheng-7385	402	24	of	of	ADP
fumecheng-7385	402	25	low	low	ADJ
fumecheng-7385	402	26	frequency	frequency	NOUN
fumecheng-7385	402	27	noise	noise	NOUN
fumecheng-7385	402	28	vibration	vibration	NOUN
fumecheng-7385	402	29	and	and	CCONJ
fumecheng-7385	402	30	active	active	ADJ
fumecheng-7385	402	31	control	control	NOUN
fumecheng-7385	402	32	,	,	PUNCT
fumecheng-7385	402	33	38	38	NUM
fumecheng-7385	402	34	,	,	PUNCT
fumecheng-7385	402	35	pp	pp	ADJ
fumecheng-7385	402	36	.	.	PUNCT
fumecheng-7385	402	37	1252	1252	NUM
fumecheng-7385	402	38	-	-	SYM
fumecheng-7385	402	39	1260	1260	NUM
fumecheng-7385	402	40	.	.	PUNCT
fumecheng-7385	403	1	3	3	X
fumecheng-7385	403	2	.	.	X
fumecheng-7385	403	3	he	he	PRON
fumecheng-7385	403	4	,	,	PUNCT
fumecheng-7385	403	5	j.h	j.h	PROPN
fumecheng-7385	403	6	.	.	PROPN
fumecheng-7385	403	7	,	,	PUNCT
fumecheng-7385	403	8	el	el	PROPN
fumecheng-7385	403	9	-	-	PUNCT
fumecheng-7385	403	10	dib	dib	PROPN
fumecheng-7385	403	11	,	,	PUNCT
fumecheng-7385	403	12	y.o	y.o	NOUN
fumecheng-7385	403	13	,	,	PUNCT
fumecheng-7385	403	14	2021	2021	NUM
fumecheng-7385	403	15	,	,	PUNCT
fumecheng-7385	403	16	homotopy	homotopy	VERB
fumecheng-7385	403	17	perturbation	perturbation	NOUN
fumecheng-7385	403	18	method	method	NOUN
fumecheng-7385	403	19	with	with	ADP
fumecheng-7385	403	20	three	three	NUM
fumecheng-7385	403	21	expansions	expansion	NOUN
fumecheng-7385	403	22	,	,	PUNCT
fumecheng-7385	403	23	journal	journal	NOUN
fumecheng-7385	403	24	of	of	ADP
fumecheng-7385	403	25	mathematical	mathematical	ADJ
fumecheng-7385	403	26	chemistry	chemistry	NOUN
fumecheng-7385	403	27	,	,	PUNCT
fumecheng-7385	403	28	53	53	NUM
fumecheng-7385	403	29	,	,	PUNCT
fumecheng-7385	403	30	pp	pp	ADJ
fumecheng-7385	403	31	.	.	PUNCT
fumecheng-7385	404	1	1139	1139	NUM
fumecheng-7385	404	2	-	-	SYM
fumecheng-7385	404	3	1150	1150	NUM
fumecheng-7385	404	4	.	.	PUNCT
fumecheng-7385	405	1	4	4	X
fumecheng-7385	405	2	.	.	X
fumecheng-7385	406	1	he	he	PRON
fumecheng-7385	406	2	,	,	PUNCT
fumecheng-7385	406	3	j.h	j.h	PROPN
fumecheng-7385	406	4	.	.	PROPN
fumecheng-7385	406	5	,	,	PUNCT
fumecheng-7385	406	6	qie	qie	PROPN
fumecheng-7385	406	7	,	,	PUNCT
fumecheng-7385	406	8	n.	n.	PROPN
fumecheng-7385	406	9	,	,	PUNCT
fumecheng-7385	406	10	he	he	PRON
fumecheng-7385	406	11	,	,	PUNCT
fumecheng-7385	406	12	c.h	c.h	PROPN
fumecheng-7385	406	13	.	.	PROPN
fumecheng-7385	406	14	,	,	PUNCT
fumecheng-7385	406	15	saeed	saeed	PROPN
fumecheng-7385	406	16	,	,	PUNCT
fumecheng-7385	406	17	t.	t.	PROPN
fumecheng-7385	406	18	,	,	PUNCT
fumecheng-7385	406	19	2021	2021	NUM
fumecheng-7385	406	20	,	,	PUNCT
fumecheng-7385	406	21	on	on	ADP
fumecheng-7385	406	22	a	a	DET
fumecheng-7385	406	23	strong	strong	ADJ
fumecheng-7385	406	24	minimum	minimum	ADJ
fumecheng-7385	406	25	condition	condition	NOUN
fumecheng-7385	406	26	of	of	ADP
fumecheng-7385	406	27	a	a	DET
fumecheng-7385	406	28	fractal	fractal	ADJ
fumecheng-7385	406	29	variational	variational	ADJ
fumecheng-7385	406	30	principle	principle	NOUN
fumecheng-7385	406	31	,	,	PUNCT
fumecheng-7385	406	32	applied	apply	VERB
fumecheng-7385	406	33	mathematics	mathematics	NOUN
fumecheng-7385	406	34	letters	letter	NOUN
fumecheng-7385	406	35	,	,	PUNCT
fumecheng-7385	406	36	107199	107199	NUM
fumecheng-7385	406	37	;	;	PUNCT
fumecheng-7385	406	38	doi	doi	NOUN
fumecheng-7385	406	39	:	:	PUNCT
fumecheng-7385	406	40	10.1016	10.1016	NUM
fumecheng-7385	406	41	/	/	SYM
fumecheng-7385	406	42	j.aml.2021.107199	j.aml.2021.107199	PROPN
fumecheng-7385	406	43	5	5	NUM
fumecheng-7385	406	44	.	.	X
fumecheng-7385	407	1	he	he	PRON
fumecheng-7385	407	2	,	,	PUNCT
fumecheng-7385	407	3	c.h	c.h	PROPN
fumecheng-7385	407	4	.	.	PROPN
fumecheng-7385	407	5	,	,	PUNCT
fumecheng-7385	407	6	liu	liu	PROPN
fumecheng-7385	407	7	,	,	PUNCT
fumecheng-7385	407	8	c.	c.	PROPN
fumecheng-7385	407	9	,	,	PUNCT
fumecheng-7385	407	10	he	he	PRON
fumecheng-7385	407	11	,	,	PUNCT
fumecheng-7385	407	12	j.h	j.h	PROPN
fumecheng-7385	407	13	.	.	PROPN
fumecheng-7385	407	14	,	,	PUNCT
fumecheng-7385	407	15	gepreel	gepreel	PROPN
fumecheng-7385	407	16	,	,	PUNCT
fumecheng-7385	407	17	k.a	k.a	PROPN
fumecheng-7385	407	18	.	.	PROPN
fumecheng-7385	407	19	,	,	PUNCT
fumecheng-7385	407	20	2021	2021	NUM
fumecheng-7385	407	21	,	,	PUNCT
fumecheng-7385	407	22	low	low	ADJ
fumecheng-7385	407	23	frequency	frequency	NOUN
fumecheng-7385	407	24	property	property	NOUN
fumecheng-7385	407	25	of	of	ADP
fumecheng-7385	407	26	a	a	DET
fumecheng-7385	407	27	fractal	fractal	ADJ
fumecheng-7385	407	28	vibration	vibration	NOUN
fumecheng-7385	407	29	model	model	NOUN
fumecheng-7385	407	30	for	for	ADP
fumecheng-7385	407	31	a	a	DET
fumecheng-7385	407	32	concrete	concrete	ADJ
fumecheng-7385	407	33	beam	beam	NOUN
fumecheng-7385	407	34	,	,	PUNCT
fumecheng-7385	407	35	fractals	fractal	NOUN
fumecheng-7385	407	36	,	,	PUNCT
fumecheng-7385	407	37	doi	doi	NOUN
fumecheng-7385	407	38	:	:	PUNCT
fumecheng-7385	407	39	10.1142	10.1142	NUM
fumecheng-7385	407	40	/	/	SYM
fumecheng-7385	407	41	s0218348x21501176	s0218348x21501176	NOUN
fumecheng-7385	407	42	.	.	PUNCT
fumecheng-7385	408	1	6	6	NUM
fumecheng-7385	408	2	.	.	X
fumecheng-7385	409	1	he	he	PRON
fumecheng-7385	409	2	,	,	PUNCT
fumecheng-7385	409	3	j.h	j.h	PROPN
fumecheng-7385	409	4	.	.	PROPN
fumecheng-7385	409	5	,	,	PUNCT
fumecheng-7385	409	6	kou	kou	PROPN
fumecheng-7385	409	7	,	,	PUNCT
fumecheng-7385	409	8	s.j	s.j	PROPN
fumecheng-7385	409	9	.	.	PROPN
fumecheng-7385	409	10	,	,	PUNCT
fumecheng-7385	409	11	he	he	PRON
fumecheng-7385	409	12	,	,	PUNCT
fumecheng-7385	409	13	c.h	c.h	PROPN
fumecheng-7385	409	14	.	.	PROPN
fumecheng-7385	409	15	,	,	PUNCT
fumecheng-7385	409	16	zhang	zhang	PROPN
fumecheng-7385	409	17	,	,	PUNCT
fumecheng-7385	409	18	z.w	z.w	PROPN
fumecheng-7385	409	19	,	,	PUNCT
fumecheng-7385	409	20	gepreel	gepreel	ADJ
fumecheng-7385	409	21	,	,	PUNCT
fumecheng-7385	409	22	k.a	k.a	PROPN
fumecheng-7385	409	23	.	.	PROPN
fumecheng-7385	409	24	,	,	PUNCT
fumecheng-7385	409	25	2021	2021	NUM
fumecheng-7385	409	26	,	,	PUNCT
fumecheng-7385	409	27	fractal	fractal	ADJ
fumecheng-7385	409	28	oscillation	oscillation	NOUN
fumecheng-7385	409	29	and	and	CCONJ
fumecheng-7385	409	30	its	its	PRON
fumecheng-7385	409	31	frequency	frequency	NOUN
fumecheng-7385	409	32	-	-	PUNCT
fumecheng-7385	409	33	amplitude	amplitude	NOUN
fumecheng-7385	409	34	property	property	NOUN
fumecheng-7385	409	35	,	,	PUNCT
fumecheng-7385	409	36	fractals	fractal	NOUN
fumecheng-7385	409	37	,	,	PUNCT
fumecheng-7385	409	38	doi	doi	NOUN
fumecheng-7385	409	39	:	:	PUNCT
fumecheng-7385	409	40	10.1142	10.1142	NUM
fumecheng-7385	409	41	/	/	SYM
fumecheng-7385	409	42	s0218348x2150105x	s0218348x2150105x	NOUN
fumecheng-7385	409	43	7	7	NUM
fumecheng-7385	409	44	.	.	X
fumecheng-7385	409	45	sedighi	sedighi	PROPN
fumecheng-7385	409	46	,	,	PUNCT
fumecheng-7385	409	47	h.m	h.m	PROPN
fumecheng-7385	409	48	.	.	PROPN
fumecheng-7385	409	49	,	,	PUNCT
fumecheng-7385	409	50	daneshmand	daneshmand	PROPN
fumecheng-7385	409	51	,	,	PUNCT
fumecheng-7385	409	52	f.	f.	PROPN
fumecheng-7385	409	53	,	,	PUNCT
fumecheng-7385	409	54	2015	2015	NUM
fumecheng-7385	409	55	,	,	PUNCT
fumecheng-7385	409	56	nonlinear	nonlinear	ADJ
fumecheng-7385	409	57	transversely	transversely	ADV
fumecheng-7385	409	58	vibrating	vibrating	NOUN
fumecheng-7385	409	59	beams	beam	NOUN
fumecheng-7385	409	60	by	by	ADP
fumecheng-7385	409	61	the	the	DET
fumecheng-7385	409	62	homotopy	homotopy	NOUN
fumecheng-7385	409	63	perturbation	perturbation	NOUN
fumecheng-7385	409	64	method	method	NOUN
fumecheng-7385	409	65	with	with	ADP
fumecheng-7385	409	66	an	an	DET
fumecheng-7385	409	67	auxiliary	auxiliary	ADJ
fumecheng-7385	409	68	term	term	NOUN
fumecheng-7385	409	69	,	,	PUNCT
fumecheng-7385	409	70	journal	journal	NOUN
fumecheng-7385	409	71	of	of	ADP
fumecheng-7385	409	72	applied	applied	ADJ
fumecheng-7385	409	73	and	and	CCONJ
fumecheng-7385	409	74	computational	computational	ADJ
fumecheng-7385	409	75	mechanics	mechanic	NOUN
fumecheng-7385	409	76	,	,	PUNCT
fumecheng-7385	409	77	1(1	1(1	NUM
fumecheng-7385	409	78	)	)	PUNCT
fumecheng-7385	409	79	,	,	PUNCT
fumecheng-7385	409	80	pp	pp	ADJ
fumecheng-7385	409	81	.	.	PUNCT
fumecheng-7385	410	1	1	1	NUM
fumecheng-7385	410	2	-	-	SYM
fumecheng-7385	410	3	9	9	NUM
fumecheng-7385	410	4	.	.	NOUN
fumecheng-7385	410	5	8	8	NUM
fumecheng-7385	410	6	.	.	X
fumecheng-7385	410	7	sedighi	sedighi	PROPN
fumecheng-7385	410	8	,	,	PUNCT
fumecheng-7385	410	9	h.m	h.m	PROPN
fumecheng-7385	410	10	.	.	PROPN
fumecheng-7385	410	11	,	,	PUNCT
fumecheng-7385	410	12	shirazi	shirazi	PROPN
fumecheng-7385	410	13	,	,	PUNCT
fumecheng-7385	410	14	k.h	k.h	PROPN
fumecheng-7385	410	15	,	,	PUNCT
fumecheng-7385	410	16	attarzadeh	attarzadeh	PROPN
fumecheng-7385	410	17	,	,	PUNCT
fumecheng-7385	410	18	m.a	m.a	PROPN
fumecheng-7385	410	19	.	.	PROPN
fumecheng-7385	410	20	,	,	PUNCT
fumecheng-7385	410	21	2013	2013	NUM
fumecheng-7385	410	22	,	,	PUNCT
fumecheng-7385	410	23	a	a	DET
fumecheng-7385	410	24	study	study	NOUN
fumecheng-7385	410	25	on	on	ADP
fumecheng-7385	410	26	the	the	DET
fumecheng-7385	410	27	quintic	quintic	ADJ
fumecheng-7385	410	28	nonlinear	nonlinear	ADJ
fumecheng-7385	410	29	beam	beam	NOUN
fumecheng-7385	410	30	vibrations	vibration	NOUN
fumecheng-7385	410	31	using	use	VERB
fumecheng-7385	410	32	asymptotic	asymptotic	ADJ
fumecheng-7385	410	33	approximate	approximate	ADJ
fumecheng-7385	410	34	approaches	approach	NOUN
fumecheng-7385	410	35	,	,	PUNCT
fumecheng-7385	410	36	acta	acta	PROPN
fumecheng-7385	410	37	astronautica	astronautica	PROPN
fumecheng-7385	410	38	,	,	PUNCT
fumecheng-7385	410	39	91	91	NUM
fumecheng-7385	410	40	,	,	PUNCT
fumecheng-7385	410	41	pp	pp	ADJ
fumecheng-7385	410	42	.	.	PUNCT
fumecheng-7385	411	1	245	245	NUM
fumecheng-7385	411	2	-	-	SYM
fumecheng-7385	411	3	250	250	NUM
fumecheng-7385	411	4	.	.	PUNCT
fumecheng-7385	412	1	9	9	NUM
fumecheng-7385	412	2	.	.	X
fumecheng-7385	412	3	sedighi	sedighi	PROPN
fumecheng-7385	412	4	,	,	PUNCT
fumecheng-7385	412	5	h.m	h.m	PROPN
fumecheng-7385	412	6	.	.	PROPN
fumecheng-7385	412	7	,	,	PUNCT
fumecheng-7385	412	8	daneshmand	daneshmand	PROPN
fumecheng-7385	412	9	,	,	PUNCT
fumecheng-7385	412	10	f.	f.	PROPN
fumecheng-7385	412	11	,	,	PUNCT
fumecheng-7385	412	12	2014	2014	NUM
fumecheng-7385	412	13	,	,	PUNCT
fumecheng-7385	412	14	static	static	ADJ
fumecheng-7385	412	15	and	and	CCONJ
fumecheng-7385	412	16	dynamic	dynamic	ADJ
fumecheng-7385	412	17	pull	pull	NOUN
fumecheng-7385	412	18	-	-	PUNCT
fumecheng-7385	412	19	in	in	ADP
fumecheng-7385	412	20	instability	instability	NOUN
fumecheng-7385	412	21	of	of	ADP
fumecheng-7385	412	22	multi	multi	ADJ
fumecheng-7385	412	23	-	-	ADJ
fumecheng-7385	412	24	walled	walled	ADJ
fumecheng-7385	412	25	carbon	carbon	NOUN
fumecheng-7385	412	26	nanotube	nanotube	NOUN
fumecheng-7385	412	27	probes	probe	NOUN
fumecheng-7385	412	28	by	by	ADP
fumecheng-7385	412	29	he	he	PRON
fumecheng-7385	412	30	’s	’	VERB
fumecheng-7385	412	31	iteration	iteration	NOUN
fumecheng-7385	412	32	perturbation	perturbation	NOUN
fumecheng-7385	412	33	method	method	NOUN
fumecheng-7385	412	34	,	,	PUNCT
fumecheng-7385	412	35	journal	journal	NOUN
fumecheng-7385	412	36	of	of	ADP
fumecheng-7385	412	37	mechanical	mechanical	ADJ
fumecheng-7385	412	38	science	science	NOUN
fumecheng-7385	412	39	and	and	CCONJ
fumecheng-7385	412	40	technology	technology	NOUN
fumecheng-7385	412	41	,	,	PUNCT
fumecheng-7385	412	42	28	28	NUM
fumecheng-7385	412	43	,	,	PUNCT
fumecheng-7385	412	44	pp	pp	ADJ
fumecheng-7385	412	45	.	.	PUNCT
fumecheng-7385	413	1	3459–3469	3459–3469	NUM
fumecheng-7385	413	2	.	.	NOUN
fumecheng-7385	413	3	10	10	NUM
fumecheng-7385	413	4	.	.	PUNCT
fumecheng-7385	414	1	yao	yao	PROPN
fumecheng-7385	414	2	,	,	PUNCT
fumecheng-7385	414	3	x.	x.	PROPN
fumecheng-7385	414	4	,	,	PUNCT
fumecheng-7385	414	5	he	he	PRON
fumecheng-7385	414	6	,	,	PUNCT
fumecheng-7385	414	7	j.-h	j.-h	PROPN
fumecheng-7385	414	8	.	.	PUNCT
fumecheng-7385	414	9	,	,	PUNCT
fumecheng-7385	414	10	2020	2020	NUM
fumecheng-7385	414	11	,	,	PUNCT
fumecheng-7385	414	12	on	on	ADP
fumecheng-7385	414	13	fabrication	fabrication	NOUN
fumecheng-7385	414	14	of	of	ADP
fumecheng-7385	414	15	nanoscale	nanoscale	ADJ
fumecheng-7385	414	16	non	non	ADJ
fumecheng-7385	414	17	-	-	ADJ
fumecheng-7385	414	18	smooth	smooth	ADJ
fumecheng-7385	414	19	fibers	fiber	NOUN
fumecheng-7385	414	20	with	with	ADP
fumecheng-7385	414	21	high	high	ADJ
fumecheng-7385	414	22	geometric	geometric	ADJ
fumecheng-7385	414	23	potential	potential	NOUN
fumecheng-7385	414	24	and	and	CCONJ
fumecheng-7385	414	25	nanoparticle	nanoparticle	NOUN
fumecheng-7385	414	26	’s	’s	PART
fumecheng-7385	414	27	non	non	ADJ
fumecheng-7385	414	28	-	-	ADJ
fumecheng-7385	414	29	linear	linear	ADJ
fumecheng-7385	414	30	vibration	vibration	NOUN
fumecheng-7385	414	31	,	,	PUNCT
fumecheng-7385	414	32	thermal	thermal	ADJ
fumecheng-7385	414	33	science	science	NOUN
fumecheng-7385	414	34	,	,	PUNCT
fumecheng-7385	414	35	24(4	24(4	NUM
fumecheng-7385	414	36	)	)	PUNCT
fumecheng-7385	414	37	,	,	PUNCT
fumecheng-7385	414	38	pp	pp	ADJ
fumecheng-7385	414	39	.	.	PUNCT
fumecheng-7385	414	40	2491	2491	NUM
fumecheng-7385	414	41	-	-	SYM
fumecheng-7385	414	42	2497	2497	NUM
fumecheng-7385	414	43	.	.	PUNCT
fumecheng-7385	415	1	11	11	NUM
fumecheng-7385	415	2	.	.	PUNCT
fumecheng-7385	416	1	he	he	PRON
fumecheng-7385	416	2	,	,	PUNCT
fumecheng-7385	416	3	c.-h	c.-h	PROPN
fumecheng-7385	416	4	.	.	PUNCT
fumecheng-7385	416	5	,	,	PUNCT
fumecheng-7385	416	6	he	he	PRON
fumecheng-7385	416	7	,	,	PUNCT
fumecheng-7385	416	8	j.-h	j.-h	PROPN
fumecheng-7385	416	9	.	.	PUNCT
fumecheng-7385	416	10	,	,	PUNCT
fumecheng-7385	416	11	sedighi	sedighi	PROPN
fumecheng-7385	416	12	,	,	PUNCT
fumecheng-7385	416	13	h.m	h.m	PROPN
fumecheng-7385	416	14	.	.	PROPN
fumecheng-7385	416	15	,	,	PUNCT
fumecheng-7385	416	16	2020	2020	NUM
fumecheng-7385	416	17	,	,	PUNCT
fumecheng-7385	416	18	fangzhu	fangzhu	PROPN
fumecheng-7385	416	19	(	(	PUNCT
fumecheng-7385	416	20	方诸	方诸	NOUN
fumecheng-7385	416	21	):	):	PUNCT
fumecheng-7385	416	22	an	an	DET
fumecheng-7385	416	23	ancient	ancient	ADJ
fumecheng-7385	416	24	chinese	chinese	ADJ
fumecheng-7385	416	25	nanotechnology	nanotechnology	NOUN
fumecheng-7385	416	26	for	for	ADP
fumecheng-7385	416	27	water	water	NOUN
fumecheng-7385	416	28	collection	collection	NOUN
fumecheng-7385	416	29	from	from	ADP
fumecheng-7385	416	30	air	air	NOUN
fumecheng-7385	416	31	:	:	PUNCT
fumecheng-7385	416	32	history	history	NOUN
fumecheng-7385	416	33	,	,	PUNCT
fumecheng-7385	416	34	mathematical	mathematical	ADJ
fumecheng-7385	416	35	insight	insight	NOUN
fumecheng-7385	416	36	,	,	PUNCT
fumecheng-7385	416	37	promises	promise	NOUN
fumecheng-7385	416	38	,	,	PUNCT
fumecheng-7385	416	39	and	and	CCONJ
fumecheng-7385	416	40	challenges	challenge	NOUN
fumecheng-7385	416	41	,	,	PUNCT
fumecheng-7385	416	42	mathematical	mathematical	ADJ
fumecheng-7385	416	43	methods	method	NOUN
fumecheng-7385	416	44	in	in	ADP
fumecheng-7385	416	45	the	the	DET
fumecheng-7385	416	46	applied	apply	VERB
fumecheng-7385	416	47	sciences	science	NOUN
fumecheng-7385	416	48	,	,	PUNCT
fumecheng-7385	416	49	doi	doi	NOUN
fumecheng-7385	416	50	:	:	PUNCT
fumecheng-7385	416	51	10.1002	10.1002	NUM
fumecheng-7385	416	52	/	/	SYM
fumecheng-7385	416	53	mma.6384	mma.6384	PROPN
fumecheng-7385	416	54	12	12	NUM
fumecheng-7385	416	55	.	.	PUNCT
fumecheng-7385	417	1	wang	wang	PROPN
fumecheng-7385	417	2	,	,	PUNCT
fumecheng-7385	417	3	k.l	k.l	PROPN
fumecheng-7385	417	4	.	.	PROPN
fumecheng-7385	417	5	,	,	PUNCT
fumecheng-7385	417	6	2020	2020	NUM
fumecheng-7385	417	7	,	,	PUNCT
fumecheng-7385	417	8	effect	effect	NOUN
fumecheng-7385	417	9	of	of	ADP
fumecheng-7385	417	10	fangzhu	fangzhu	PROPN
fumecheng-7385	417	11	’s	’s	PART
fumecheng-7385	417	12	nano	nano	NOUN
fumecheng-7385	417	13	-	-	PUNCT
fumecheng-7385	417	14	scale	scale	NOUN
fumecheng-7385	417	15	surface	surface	NOUN
fumecheng-7385	417	16	morphology	morphology	NOUN
fumecheng-7385	417	17	on	on	ADP
fumecheng-7385	417	18	water	water	NOUN
fumecheng-7385	417	19	collection	collection	NOUN
fumecheng-7385	417	20	,	,	PUNCT
fumecheng-7385	417	21	mathematical	mathematical	ADJ
fumecheng-7385	417	22	methods	method	NOUN
fumecheng-7385	417	23	in	in	ADP
fumecheng-7385	417	24	the	the	DET
fumecheng-7385	417	25	applied	apply	VERB
fumecheng-7385	417	26	sciences	science	NOUN
fumecheng-7385	417	27	,	,	PUNCT
fumecheng-7385	417	28	doi	doi	NOUN
fumecheng-7385	417	29	:	:	PUNCT
fumecheng-7385	417	30	10.1002	10.1002	NUM
fumecheng-7385	417	31	/	/	SYM
fumecheng-7385	417	32	mma.6569	mma.6569	NOUN
fumecheng-7385	417	33	.	.	NOUN
fumecheng-7385	417	34	13	13	NUM
fumecheng-7385	417	35	.	.	PUNCT
fumecheng-7385	418	1	he	he	PRON
fumecheng-7385	418	2	,	,	PUNCT
fumecheng-7385	418	3	j.-h	j.-h	PROPN
fumecheng-7385	418	4	.	.	PROPN
fumecheng-7385	418	5	,	,	PUNCT
fumecheng-7385	418	6	el	el	PROPN
fumecheng-7385	418	7	-	-	PUNCT
fumecheng-7385	418	8	dib	dib	PROPN
fumecheng-7385	418	9	,	,	PUNCT
fumecheng-7385	418	10	y.o	y.o	PROPN
fumecheng-7385	418	11	.	.	PROPN
fumecheng-7385	418	12	,	,	PUNCT
fumecheng-7385	418	13	2020	2020	NUM
fumecheng-7385	418	14	,	,	PUNCT
fumecheng-7385	418	15	homotopy	homotopy	VERB
fumecheng-7385	418	16	perturbation	perturbation	NOUN
fumecheng-7385	418	17	method	method	NOUN
fumecheng-7385	418	18	for	for	ADP
fumecheng-7385	418	19	fangzhu	fangzhu	PROPN
fumecheng-7385	418	20	oscillator	oscillator	NOUN
fumecheng-7385	418	21	,	,	PUNCT
fumecheng-7385	418	22	journal	journal	NOUN
fumecheng-7385	418	23	of	of	ADP
fumecheng-7385	418	24	mathematical	mathematical	ADJ
fumecheng-7385	418	25	chemistry	chemistry	NOUN
fumecheng-7385	418	26	,	,	PUNCT
fumecheng-7385	418	27	58(10	58(10	NUM
fumecheng-7385	418	28	)	)	PUNCT
fumecheng-7385	418	29	,	,	PUNCT
fumecheng-7385	418	30	pp	pp	ADJ
fumecheng-7385	418	31	.	.	PUNCT
fumecheng-7385	419	1	2245	2245	NUM
fumecheng-7385	419	2	-	-	SYM
fumecheng-7385	419	3	2253	2253	NUM
fumecheng-7385	419	4	.	.	PUNCT
fumecheng-7385	420	1	14	14	NUM
fumecheng-7385	420	2	.	.	PUNCT
fumecheng-7385	421	1	he	he	PRON
fumecheng-7385	421	2	,	,	PUNCT
fumecheng-7385	421	3	j.h	j.h	PROPN
fumecheng-7385	421	4	.	.	PROPN
fumecheng-7385	421	5	,	,	PUNCT
fumecheng-7385	421	6	2021	2021	NUM
fumecheng-7385	421	7	,	,	PUNCT
fumecheng-7385	421	8	on	on	ADP
fumecheng-7385	421	9	the	the	DET
fumecheng-7385	421	10	fractal	fractal	ADJ
fumecheng-7385	421	11	variational	variational	ADJ
fumecheng-7385	421	12	principle	principle	NOUN
fumecheng-7385	421	13	for	for	ADP
fumecheng-7385	421	14	the	the	DET
fumecheng-7385	421	15	telegraph	telegraph	NOUN
fumecheng-7385	421	16	equation	equation	NOUN
fumecheng-7385	421	17	,	,	PUNCT
fumecheng-7385	421	18	fractals	fractal	NOUN
fumecheng-7385	421	19	,	,	PUNCT
fumecheng-7385	421	20	doi	doi	NOUN
fumecheng-7385	421	21	:	:	PUNCT
fumecheng-7385	421	22	10.1142	10.1142	NUM
fumecheng-7385	421	23	/	/	SYM
fumecheng-7385	421	24	s0218348x21500225	s0218348x21500225	NOUN
fumecheng-7385	421	25	.	.	PUNCT
fumecheng-7385	421	26	15	15	NUM
fumecheng-7385	421	27	.	.	PUNCT
fumecheng-7385	422	1	he	he	PRON
fumecheng-7385	422	2	,	,	PUNCT
fumecheng-7385	422	3	j.h	j.h	PROPN
fumecheng-7385	422	4	.	.	PROPN
fumecheng-7385	422	5	,	,	PUNCT
fumecheng-7385	422	6	2020	2020	NUM
fumecheng-7385	422	7	,	,	PUNCT
fumecheng-7385	422	8	a	a	DET
fumecheng-7385	422	9	fractal	fractal	ADJ
fumecheng-7385	422	10	variational	variational	ADJ
fumecheng-7385	422	11	theory	theory	NOUN
fumecheng-7385	422	12	for	for	ADP
fumecheng-7385	422	13	one	one	NUM
fumecheng-7385	422	14	-	-	PUNCT
fumecheng-7385	422	15	dimensional	dimensional	ADJ
fumecheng-7385	422	16	compressible	compressible	ADJ
fumecheng-7385	422	17	flow	flow	NOUN
fumecheng-7385	422	18	in	in	ADP
fumecheng-7385	422	19	a	a	DET
fumecheng-7385	422	20	microgravity	microgravity	NOUN
fumecheng-7385	422	21	space	space	NOUN
fumecheng-7385	422	22	,	,	PUNCT
fumecheng-7385	422	23	fractals	fractal	NOUN
fumecheng-7385	422	24	,	,	PUNCT
fumecheng-7385	422	25	28(2	28(2	NUM
fumecheng-7385	422	26	)	)	PUNCT
fumecheng-7385	422	27	,	,	PUNCT
fumecheng-7385	422	28	2050024	2050024	NUM
fumecheng-7385	422	29	.	.	PUNCT
fumecheng-7385	423	1	16	16	NUM
fumecheng-7385	423	2	.	.	PUNCT
fumecheng-7385	424	1	el	el	PROPN
fumecheng-7385	424	2	-	-	PUNCT
fumecheng-7385	424	3	dib	dib	PROPN
fumecheng-7385	424	4	,	,	PUNCT
fumecheng-7385	424	5	y.o	y.o	PROPN
fumecheng-7385	424	6	.	.	PROPN
fumecheng-7385	424	7	,	,	PUNCT
fumecheng-7385	424	8	2019	2019	NUM
fumecheng-7385	424	9	,	,	PUNCT
fumecheng-7385	424	10	periodic	periodic	ADJ
fumecheng-7385	424	11	solution	solution	NOUN
fumecheng-7385	424	12	of	of	ADP
fumecheng-7385	424	13	the	the	DET
fumecheng-7385	424	14	cubic	cubic	PROPN
fumecheng-7385	424	15	nonlinear	nonlinear	PROPN
fumecheng-7385	424	16	klein	klein	PROPN
fumecheng-7385	424	17	–	–	PUNCT
fumecheng-7385	424	18	gordon	gordon	PROPN
fumecheng-7385	424	19	equation	equation	NOUN
fumecheng-7385	424	20	,	,	PUNCT
fumecheng-7385	424	21	and	and	CCONJ
fumecheng-7385	424	22	the	the	DET
fumecheng-7385	424	23	stability	stability	NOUN
fumecheng-7385	424	24	criteria	criterion	NOUN
fumecheng-7385	424	25	via	via	ADP
fumecheng-7385	424	26	the	the	DET
fumecheng-7385	424	27	he	he	PRON
fumecheng-7385	424	28	-	-	PUNCT
fumecheng-7385	424	29	multiple	multiple	ADJ
fumecheng-7385	424	30	-	-	PUNCT
fumecheng-7385	424	31	scales	scale	NOUN
fumecheng-7385	424	32	method	method	NOUN
fumecheng-7385	424	33	,	,	PUNCT
fumecheng-7385	424	34	pramana	pramana	PROPN
fumecheng-7385	424	35	–	–	PUNCT
fumecheng-7385	424	36	journal	journal	NOUN
fumecheng-7385	424	37	of	of	ADP
fumecheng-7385	424	38	physics	physics	PROPN
fumecheng-7385	424	39	,	,	PUNCT
fumecheng-7385	424	40	92	92	NUM
fumecheng-7385	424	41	,	,	PUNCT
fumecheng-7385	424	42	7	7	NUM
fumecheng-7385	424	43	.	.	NOUN
fumecheng-7385	424	44	17	17	NUM
fumecheng-7385	424	45	.	.	PUNCT
fumecheng-7385	425	1	el	el	PROPN
fumecheng-7385	425	2	-	-	PUNCT
fumecheng-7385	425	3	dib	dib	PROPN
fumecheng-7385	425	4	,	,	PUNCT
fumecheng-7385	425	5	y.o	y.o	PROPN
fumecheng-7385	425	6	.	.	PROPN
fumecheng-7385	425	7	moatimid	moatimid	PROPN
fumecheng-7385	425	8	,	,	PUNCT
fumecheng-7385	425	9	g.m	g.m	PROPN
fumecheng-7385	425	10	.	.	PROPN
fumecheng-7385	425	11	,	,	PUNCT
fumecheng-7385	425	12	mady	mady	PROPN
fumecheng-7385	425	13	,	,	PUNCT
fumecheng-7385	425	14	a.a	a.a	PROPN
fumecheng-7385	425	15	.	.	PROPN
fumecheng-7385	425	16	,	,	PUNCT
fumecheng-7385	425	17	2020	2020	NUM
fumecheng-7385	425	18	,	,	PUNCT
fumecheng-7385	425	19	a	a	DET
fumecheng-7385	425	20	nonlinear	nonlinear	ADJ
fumecheng-7385	425	21	azimuthal	azimuthal	NOUN
fumecheng-7385	425	22	instability	instability	NOUN
fumecheng-7385	425	23	of	of	ADP
fumecheng-7385	425	24	hydromgantic	hydromgantic	ADJ
fumecheng-7385	425	25	rigid	rigid	ADJ
fumecheng-7385	425	26	-	-	PUNCT
fumecheng-7385	425	27	rotating	rotate	VERB
fumecheng-7385	425	28	column	column	NOUN
fumecheng-7385	425	29	,	,	PUNCT
fumecheng-7385	425	30	chinese	chinese	ADJ
fumecheng-7385	425	31	journal	journal	PROPN
fumecheng-7385	425	32	of	of	ADP
fumecheng-7385	425	33	physics	physics	PROPN
fumecheng-7385	425	34	,	,	PUNCT
fumecheng-7385	425	35	66	66	NUM
fumecheng-7385	425	36	,	,	PUNCT
fumecheng-7385	425	37	pp	pp	ADJ
fumecheng-7385	425	38	.	.	PUNCT
fumecheng-7385	426	1	285	285	NUM
fumecheng-7385	426	2	-	-	SYM
fumecheng-7385	426	3	300	300	NUM
fumecheng-7385	426	4	.	.	PUNCT
fumecheng-7385	427	1	18	18	NUM
fumecheng-7385	427	2	.	.	X
fumecheng-7385	428	1	el	el	PROPN
fumecheng-7385	428	2	-	-	PUNCT
fumecheng-7385	428	3	dib	dib	PROPN
fumecheng-7385	428	4	,	,	PUNCT
fumecheng-7385	428	5	y.o	y.o	PROPN
fumecheng-7385	428	6	.	.	PROPN
fumecheng-7385	428	7	,	,	PUNCT
fumecheng-7385	428	8	moatimid	moatimid	PROPN
fumecheng-7385	428	9	,	,	PUNCT
fumecheng-7385	428	10	g.m	g.m	PROPN
fumecheng-7385	428	11	.	.	PROPN
fumecheng-7385	428	12	,	,	PUNCT
fumecheng-7385	428	13	mady	mady	PROPN
fumecheng-7385	428	14	,	,	PUNCT
fumecheng-7385	428	15	a.a	a.a	PROPN
fumecheng-7385	428	16	.	.	PROPN
fumecheng-7385	428	17	,	,	PUNCT
fumecheng-7385	428	18	2019	2019	NUM
fumecheng-7385	428	19	,	,	PUNCT
fumecheng-7385	428	20	a	a	DET
fumecheng-7385	428	21	novelty	novelty	NOUN
fumecheng-7385	428	22	to	to	ADP
fumecheng-7385	428	23	the	the	DET
fumecheng-7385	428	24	nonlinear	nonlinear	ADJ
fumecheng-7385	428	25	rotating	rotate	VERB
fumecheng-7385	428	26	rayleigh	rayleigh	PROPN
fumecheng-7385	428	27	–	–	PUNCT
fumecheng-7385	428	28	taylor	taylor	PROPN
fumecheng-7385	428	29	instability	instability	NOUN
fumecheng-7385	428	30	,	,	PUNCT
fumecheng-7385	428	31	pramana	pramana	PROPN
fumecheng-7385	428	32	–	–	PUNCT
fumecheng-7385	428	33	journal	journal	NOUN
fumecheng-7385	428	34	of	of	ADP
fumecheng-7385	428	35	physics	physics	PROPN
fumecheng-7385	428	36	,	,	PUNCT
fumecheng-7385	428	37	93	93	NUM
fumecheng-7385	428	38	,	,	PUNCT
fumecheng-7385	428	39	82	82	NUM
fumecheng-7385	428	40	.	.	NOUN
fumecheng-7385	428	41	19	19	NUM
fumecheng-7385	428	42	.	.	NUM
fumecheng-7385	428	43	cavalcanti	cavalcanti	PROPN
fumecheng-7385	428	44	,	,	PUNCT
fumecheng-7385	428	45	m.m	m.m	PROPN
fumecheng-7385	428	46	.	.	PROPN
fumecheng-7385	428	47	,	,	PUNCT
fumecheng-7385	428	48	cavalcanti	cavalcanti	VERB
fumecheng-7385	428	49	,	,	PUNCT
fumecheng-7385	428	50	v.n.d	v.n.d	NOUN
fumecheng-7385	428	51	.	.	PUNCT
fumecheng-7385	428	52	,	,	PUNCT
fumecheng-7385	428	53	2000	2000	NUM
fumecheng-7385	428	54	,	,	PUNCT
fumecheng-7385	428	55	global	global	ADJ
fumecheng-7385	428	56	existence	existence	NOUN
fumecheng-7385	428	57	and	and	CCONJ
fumecheng-7385	428	58	uniform	uniform	ADJ
fumecheng-7385	428	59	decay	decay	NOUN
fumecheng-7385	428	60	for	for	ADP
fumecheng-7385	428	61	the	the	DET
fumecheng-7385	428	62	coupled	couple	VERB
fumecheng-7385	428	63	klein	klein	PROPN
fumecheng-7385	428	64	-	-	PUNCT
fumecheng-7385	428	65	gordon	gordon	PROPN
fumecheng-7385	428	66	-	-	PUNCT
fumecheng-7385	428	67	schrödinger	schrödinger	NOUN
fumecheng-7385	428	68	equations	equation	NOUN
fumecheng-7385	428	69	,	,	PUNCT
fumecheng-7385	428	70	nodea	nodea	PROPN
fumecheng-7385	428	71	,	,	PUNCT
fumecheng-7385	428	72	nonlinear	nonlinear	NOUN
fumecheng-7385	428	73	differ	differ	VERB
fumecheng-7385	428	74	.	.	PUNCT
fumecheng-7385	429	1	equ	equ	PROPN
fumecheng-7385	429	2	.	.	PUNCT
fumecheng-7385	429	3	appl	appl	PROPN
fumecheng-7385	429	4	.	.	PROPN
fumecheng-7385	429	5	,	,	PUNCT
fumecheng-7385	429	6	7	7	NUM
fumecheng-7385	429	7	,	,	PUNCT
fumecheng-7385	429	8	pp	pp	ADJ
fumecheng-7385	429	9	.	.	PUNCT
fumecheng-7385	430	1	285	285	NUM
fumecheng-7385	430	2	-	-	SYM
fumecheng-7385	430	3	307	307	NUM
fumecheng-7385	430	4	.	.	PUNCT
fumecheng-7385	431	1	20	20	NUM
fumecheng-7385	431	2	.	.	PUNCT
fumecheng-7385	432	1	bisognin	bisognin	PROPN
fumecheng-7385	432	2	,	,	PUNCT
fumecheng-7385	432	3	v.	v.	PROPN
fumecheng-7385	432	4	,	,	PUNCT
fumecheng-7385	432	5	cavalcanti	cavalcanti	PROPN
fumecheng-7385	432	6	,	,	PUNCT
fumecheng-7385	432	7	m.m	m.m	PROPN
fumecheng-7385	432	8	.	.	PROPN
fumecheng-7385	432	9	,	,	PUNCT
fumecheng-7385	432	10	cavalcanti	cavalcanti	VERB
fumecheng-7385	432	11	,	,	PUNCT
fumecheng-7385	432	12	v.n.d	v.n.d	NOUN
fumecheng-7385	432	13	.	.	PUNCT
fumecheng-7385	432	14	,	,	PUNCT
fumecheng-7385	432	15	et	et	PROPN
fumecheng-7385	432	16	al	al	PROPN
fumecheng-7385	432	17	.	.	PROPN
fumecheng-7385	432	18	,	,	PUNCT
fumecheng-7385	432	19	2008	2008	NUM
fumecheng-7385	432	20	,	,	PUNCT
fumecheng-7385	432	21	uniform	uniform	ADJ
fumecheng-7385	432	22	decay	decay	NOUN
fumecheng-7385	432	23	for	for	ADP
fumecheng-7385	432	24	the	the	DET
fumecheng-7385	432	25	klein	klein	PROPN
fumecheng-7385	432	26	-	-	PUNCT
fumecheng-7385	432	27	gordon	gordon	PROPN
fumecheng-7385	432	28	schrödinger	schrödinger	ADJ
fumecheng-7385	432	29	equations	equation	NOUN
fumecheng-7385	432	30	with	with	ADP
fumecheng-7385	432	31	locally	locally	ADV
fumecheng-7385	432	32	distributed	distribute	VERB
fumecheng-7385	432	33	damping	damp	VERB
fumecheng-7385	432	34	,	,	PUNCT
fumecheng-7385	432	35	nonlinear	nonlinear	ADJ
fumecheng-7385	432	36	differential	differential	ADJ
fumecheng-7385	432	37	equations	equation	NOUN
fumecheng-7385	432	38	and	and	CCONJ
fumecheng-7385	432	39	applications	application	NOUN
fumecheng-7385	432	40	nodea	nodea	PROPN
fumecheng-7385	432	41	,	,	PUNCT
fumecheng-7385	432	42	15	15	NUM
fumecheng-7385	432	43	,	,	PUNCT
fumecheng-7385	432	44	pp	pp	ADJ
fumecheng-7385	432	45	.	.	PUNCT
fumecheng-7385	433	1	91	91	NUM
fumecheng-7385	433	2	-	-	SYM
fumecheng-7385	433	3	113	113	NUM
fumecheng-7385	433	4	.	.	PUNCT
fumecheng-7385	434	1	21	21	NUM
fumecheng-7385	434	2	.	.	X
fumecheng-7385	434	3	almeida	almeida	PROPN
fumecheng-7385	434	4	,	,	PUNCT
fumecheng-7385	434	5	a.f	a.f	PROPN
fumecheng-7385	434	6	.	.	PROPN
fumecheng-7385	434	7	,	,	PUNCT
fumecheng-7385	434	8	cavalcanti	cavalcanti	PROPN
fumecheng-7385	434	9	,	,	PUNCT
fumecheng-7385	434	10	m.	m.	NOUN
fumecheng-7385	434	11	,	,	PUNCT
fumecheng-7385	434	12	zanchetta	zanchetta	PROPN
fumecheng-7385	434	13	,	,	PUNCT
fumecheng-7385	434	14	j.p	j.p	PROPN
fumecheng-7385	434	15	.	.	PROPN
fumecheng-7385	434	16	,	,	PUNCT
fumecheng-7385	434	17	2018	2018	NUM
fumecheng-7385	434	18	,	,	PUNCT
fumecheng-7385	434	19	exponential	exponential	ADJ
fumecheng-7385	434	20	decay	decay	NOUN
fumecheng-7385	434	21	for	for	ADP
fumecheng-7385	434	22	the	the	DET
fumecheng-7385	434	23	coupled	couple	VERB
fumecheng-7385	434	24	klein	klein	PROPN
fumecheng-7385	434	25	-gordon	-gordon	PROPN
fumecheng-7385	434	26	-	-	PUNCT
fumecheng-7385	434	27	schrödinger	schrödinger	ADJ
fumecheng-7385	434	28	equation	equation	NOUN
fumecheng-7385	434	29	with	with	ADP
fumecheng-7385	434	30	locally	locally	ADV
fumecheng-7385	434	31	distributed	distribute	VERB
fumecheng-7385	434	32	damping	damp	VERB
fumecheng-7385	434	33	,	,	PUNCT
fumecheng-7385	434	34	communications	communication	NOUN
fumecheng-7385	434	35	on	on	ADP
fumecheng-7385	434	36	pure	pure	ADJ
fumecheng-7385	434	37	&	&	CCONJ
fumecheng-7385	434	38	applied	applied	ADJ
fumecheng-7385	434	39	analysis	analysis	NOUN
fumecheng-7385	434	40	,	,	PUNCT
fumecheng-7385	434	41	17(5	17(5	NUM
fumecheng-7385	434	42	)	)	PUNCT
fumecheng-7385	434	43	,	,	PUNCT
fumecheng-7385	434	44	pp	pp	PROPN
fumecheng-7385	434	45	.	.	PUNCT
fumecheng-7385	434	46	2039	2039	NUM
fumecheng-7385	434	47	-	-	SYM
fumecheng-7385	434	48	2061	2061	NUM
fumecheng-7385	434	49	.	.	PUNCT
fumecheng-7385	435	1	22	22	NUM
fumecheng-7385	435	2	.	.	PUNCT
fumecheng-7385	436	1	parka	parka	PROPN
fumecheng-7385	436	2	,	,	PUNCT
fumecheng-7385	436	3	j.y	j.y	PROPN
fumecheng-7385	436	4	.	.	PROPN
fumecheng-7385	436	5	,	,	PUNCT
fumecheng-7385	436	6	jeong	jeong	PROPN
fumecheng-7385	436	7	,	,	PUNCT
fumecheng-7385	436	8	j.u	j.u	PROPN
fumecheng-7385	436	9	.	.	PROPN
fumecheng-7385	436	10	,	,	PUNCT
fumecheng-7385	436	11	2007	2007	NUM
fumecheng-7385	436	12	,	,	PUNCT
fumecheng-7385	436	13	optimal	optimal	ADJ
fumecheng-7385	436	14	control	control	NOUN
fumecheng-7385	436	15	of	of	ADP
fumecheng-7385	436	16	damped	damped	PROPN
fumecheng-7385	436	17	klein	klein	PROPN
fumecheng-7385	436	18	–	–	PUNCT
fumecheng-7385	436	19	gordon	gordon	PROPN
fumecheng-7385	436	20	equations	equation	NOUN
fumecheng-7385	436	21	with	with	ADP
fumecheng-7385	436	22	state	state	NOUN
fumecheng-7385	436	23	constraints	constraint	NOUN
fumecheng-7385	436	24	,	,	PUNCT
fumecheng-7385	436	25	journal	journal	NOUN
fumecheng-7385	436	26	of	of	ADP
fumecheng-7385	436	27	mathematical	mathematical	ADJ
fumecheng-7385	436	28	analysis	analysis	NOUN
fumecheng-7385	436	29	and	and	CCONJ
fumecheng-7385	436	30	applications	application	NOUN
fumecheng-7385	436	31	,	,	PUNCT
fumecheng-7385	436	32	334(1	334(1	NUM
fumecheng-7385	436	33	)	)	PUNCT
fumecheng-7385	436	34	,	,	PUNCT
fumecheng-7385	436	35	pp	pp	PROPN
fumecheng-7385	436	36	.	.	PUNCT
fumecheng-7385	437	1	1–27	1–27	NUM
fumecheng-7385	437	2	.	.	PUNCT
fumecheng-7385	438	1	https://doi.org/10.1016/j.cjph.2020.03024	https://doi.org/10.1016/j.cjph.2020.03024	ADJ
fumecheng-7385	438	2	https://www.sciencedirect.com/science/journal/0022247x	https://www.sciencedirect.com/science/journal/0022247x	PROPN
fumecheng-7385	438	3	https://www.sciencedirect.com/science/journal/0022247x	https://www.sciencedirect.com/science/journal/0022247x	PROPN
fumecheng-7385	438	4	https://www.sciencedirect.com/science/journal/0022247x/334/1	https://www.sciencedirect.com/science/journal/0022247x/334/1	ADV
fumecheng-7385	438	5	750	750	NUM
fumecheng-7385	438	6	j.-h	j.-h	NOUN
fumecheng-7385	438	7	.	.	PUNCT
fumecheng-7385	439	1	he	he	PRON
fumecheng-7385	439	2	,	,	PUNCT
fumecheng-7385	439	3	y.	y.	PROPN
fumecheng-7385	439	4	o.	o.	PROPN
fumecheng-7385	439	5	el	el	PROPN
fumecheng-7385	439	6	-	-	PROPN
fumecheng-7385	439	7	dib	dib	PROPN
fumecheng-7385	439	8	23	23	NUM
fumecheng-7385	439	9	.	.	PUNCT
fumecheng-7385	440	1	lin	lin	PROPN
fumecheng-7385	440	2	,	,	PUNCT
fumecheng-7385	440	3	y.	y.	PROPN
fumecheng-7385	440	4	,	,	PUNCT
fumecheng-7385	440	5	cui	cui	PROPN
fumecheng-7385	440	6	,	,	PUNCT
fumecheng-7385	440	7	m.	m.	NOUN
fumecheng-7385	440	8	,	,	PUNCT
fumecheng-7385	440	9	2008	2008	NUM
fumecheng-7385	440	10	,	,	PUNCT
fumecheng-7385	440	11	a	a	DET
fumecheng-7385	440	12	new	new	ADJ
fumecheng-7385	440	13	method	method	NOUN
fumecheng-7385	440	14	to	to	PART
fumecheng-7385	440	15	solve	solve	VERB
fumecheng-7385	440	16	the	the	DET
fumecheng-7385	440	17	damped	damped	PROPN
fumecheng-7385	440	18	nonlinear	nonlinear	PROPN
fumecheng-7385	440	19	klein	klein	PROPN
fumecheng-7385	440	20	-	-	PUNCT
fumecheng-7385	440	21	gordon	gordon	PROPN
fumecheng-7385	440	22	equation	equation	NOUN
fumecheng-7385	440	23	,	,	PUNCT
fumecheng-7385	440	24	science	science	NOUN
fumecheng-7385	440	25	in	in	ADP
fumecheng-7385	440	26	china	china	PROPN
fumecheng-7385	440	27	series	series	PROPN
fumecheng-7385	440	28	a	a	PRON
fumecheng-7385	440	29	:	:	PUNCT
fumecheng-7385	440	30	mathematics	mathematic	NOUN
fumecheng-7385	440	31	,	,	PUNCT
fumecheng-7385	440	32	51	51	NUM
fumecheng-7385	440	33	,	,	PUNCT
fumecheng-7385	440	34	pp	pp	ADJ
fumecheng-7385	440	35	.	.	PUNCT
fumecheng-7385	441	1	304	304	NUM
fumecheng-7385	441	2	-	-	SYM
fumecheng-7385	441	3	313	313	NUM
fumecheng-7385	441	4	.	.	PUNCT
fumecheng-7385	442	1	24	24	NUM
fumecheng-7385	442	2	.	.	PUNCT
fumecheng-7385	443	1	lian	lian	PROPN
fumecheng-7385	443	2	,	,	PUNCT
fumecheng-7385	443	3	w.	w.	PROPN
fumecheng-7385	443	4	,	,	PUNCT
fumecheng-7385	443	5	rădulescu	rădulescu	PROPN
fumecheng-7385	443	6	,	,	PUNCT
fumecheng-7385	443	7	v.d	v.d	PROPN
fumecheng-7385	443	8	.	.	PROPN
fumecheng-7385	443	9	,	,	PUNCT
fumecheng-7385	443	10	xu	xu	PROPN
fumecheng-7385	443	11	,	,	PUNCT
fumecheng-7385	443	12	r.	r.	PROPN
fumecheng-7385	443	13	,	,	PUNCT
fumecheng-7385	443	14	et	et	PROPN
fumecheng-7385	443	15	al	al	PROPN
fumecheng-7385	443	16	.	.	PROPN
fumecheng-7385	443	17	,	,	PUNCT
fumecheng-7385	443	18	2019	2019	NUM
fumecheng-7385	443	19	,	,	PUNCT
fumecheng-7385	443	20	global	global	ADJ
fumecheng-7385	443	21	well	well	NOUN
fumecheng-7385	443	22	-	-	PUNCT
fumecheng-7385	443	23	posedness	posedness	NOUN
fumecheng-7385	443	24	for	for	ADP
fumecheng-7385	443	25	a	a	DET
fumecheng-7385	443	26	class	class	NOUN
fumecheng-7385	443	27	of	of	ADP
fumecheng-7385	443	28	fourth	fourth	ADJ
fumecheng-7385	443	29	-	-	PUNCT
fumecheng-7385	443	30	order	order	NOUN
fumecheng-7385	443	31	nonlinear	nonlinear	NOUN
fumecheng-7385	443	32	strongly	strongly	ADV
fumecheng-7385	443	33	damped	damp	VERB
fumecheng-7385	443	34	wave	wave	NOUN
fumecheng-7385	443	35	equations	equation	NOUN
fumecheng-7385	443	36	,	,	PUNCT
fumecheng-7385	443	37	advances	advance	NOUN
fumecheng-7385	443	38	in	in	ADP
fumecheng-7385	443	39	calculus	calculus	NOUN
fumecheng-7385	443	40	of	of	ADP
fumecheng-7385	443	41	variations	variation	NOUN
fumecheng-7385	443	42	,	,	PUNCT
fumecheng-7385	443	43	doi	doi	NOUN
fumecheng-7385	443	44	:	:	PUNCT
fumecheng-7385	443	45	10.1515	10.1515	NUM
fumecheng-7385	443	46	/	/	SYM
fumecheng-7385	443	47	acv-2019	acv-2019	NOUN
fumecheng-7385	443	48	-	-	PUNCT
fumecheng-7385	443	49	0039	0039	NUM
fumecheng-7385	443	50	.	.	PUNCT
fumecheng-7385	444	1	25	25	NUM
fumecheng-7385	444	2	.	.	PUNCT
fumecheng-7385	445	1	he	he	PRON
fumecheng-7385	445	2	,	,	PUNCT
fumecheng-7385	445	3	j.h	j.h	PROPN
fumecheng-7385	445	4	.	.	PROPN
fumecheng-7385	445	5	,	,	PUNCT
fumecheng-7385	445	6	el	el	PROPN
fumecheng-7385	445	7	-	-	PUNCT
fumecheng-7385	445	8	dib	dib	PROPN
fumecheng-7385	445	9	,	,	PUNCT
fumecheng-7385	445	10	y.o	y.o	PROPN
fumecheng-7385	445	11	.	.	PROPN
fumecheng-7385	445	12	,	,	PUNCT
fumecheng-7385	445	13	2020	2020	NUM
fumecheng-7385	445	14	,	,	PUNCT
fumecheng-7385	445	15	the	the	DET
fumecheng-7385	445	16	reducing	reduce	VERB
fumecheng-7385	445	17	rank	rank	NOUN
fumecheng-7385	445	18	method	method	NOUN
fumecheng-7385	445	19	to	to	PART
fumecheng-7385	445	20	solve	solve	VERB
fumecheng-7385	445	21	third	third	ADJ
fumecheng-7385	445	22	-	-	PUNCT
fumecheng-7385	445	23	order	order	NOUN
fumecheng-7385	445	24	duffing	duffing	NOUN
fumecheng-7385	445	25	equation	equation	NOUN
fumecheng-7385	445	26	with	with	ADP
fumecheng-7385	445	27	the	the	DET
fumecheng-7385	445	28	homotopy	homotopy	NOUN
fumecheng-7385	445	29	perturbation	perturbation	NOUN
fumecheng-7385	445	30	,	,	PUNCT
fumecheng-7385	445	31	numerical	numerical	ADJ
fumecheng-7385	445	32	methods	method	NOUN
fumecheng-7385	445	33	for	for	ADP
fumecheng-7385	445	34	partial	partial	ADJ
fumecheng-7385	445	35	differential	differential	NOUN
fumecheng-7385	445	36	equations	equation	NOUN
fumecheng-7385	445	37	,	,	PUNCT
fumecheng-7385	445	38	37(2	37(2	PRON
fumecheng-7385	445	39	)	)	PUNCT
fumecheng-7385	445	40	,	,	PUNCT
fumecheng-7385	445	41	pp	pp	PROPN
fumecheng-7385	445	42	.	.	PUNCT
fumecheng-7385	445	43	1800	1800	NUM
fumecheng-7385	445	44	-	-	SYM
fumecheng-7385	445	45	1808	1808	NUM
fumecheng-7385	445	46	.	.	PUNCT
fumecheng-7385	446	1	26	26	NUM
fumecheng-7385	446	2	.	.	PUNCT
fumecheng-7385	447	1	he	he	PRON
fumecheng-7385	447	2	,	,	PUNCT
fumecheng-7385	447	3	j.h	j.h	PROPN
fumecheng-7385	447	4	.	.	PROPN
fumecheng-7385	447	5	,	,	PUNCT
fumecheng-7385	447	6	1999	1999	NUM
fumecheng-7385	447	7	,	,	PUNCT
fumecheng-7385	447	8	homotopy	homotopy	VERB
fumecheng-7385	447	9	perturbation	perturbation	NOUN
fumecheng-7385	447	10	technique	technique	NOUN
fumecheng-7385	447	11	,	,	PUNCT
fumecheng-7385	447	12	computational	computational	ADJ
fumecheng-7385	447	13	methods	method	NOUN
fumecheng-7385	447	14	in	in	ADP
fumecheng-7385	447	15	applied	applied	ADJ
fumecheng-7385	447	16	mechanics	mechanic	NOUN
fumecheng-7385	447	17	and	and	CCONJ
fumecheng-7385	447	18	engineering	engineering	NOUN
fumecheng-7385	447	19	,	,	PUNCT
fumecheng-7385	447	20	178	178	NUM
fumecheng-7385	447	21	,	,	PUNCT
fumecheng-7385	447	22	pp	pp	ADJ
fumecheng-7385	447	23	.	.	PUNCT
fumecheng-7385	448	1	257	257	NUM
fumecheng-7385	448	2	-	-	SYM
fumecheng-7385	448	3	262	262	NUM
fumecheng-7385	448	4	.	.	PUNCT
fumecheng-7385	449	1	27	27	NUM
fumecheng-7385	449	2	.	.	PUNCT
fumecheng-7385	450	1	el	el	PROPN
fumecheng-7385	450	2	-	-	PUNCT
fumecheng-7385	450	3	dib	dib	PROPN
fumecheng-7385	450	4	,	,	PUNCT
fumecheng-7385	450	5	y.o	y.o	PROPN
fumecheng-7385	450	6	.	.	PROPN
fumecheng-7385	450	7	,	,	PUNCT
fumecheng-7385	450	8	2018	2018	NUM
fumecheng-7385	450	9	,	,	PUNCT
fumecheng-7385	450	10	multi	multi	ADJ
fumecheng-7385	450	11	-	-	ADJ
fumecheng-7385	450	12	homotopy	homotopy	ADJ
fumecheng-7385	450	13	perturbations	perturbation	NOUN
fumecheng-7385	450	14	technique	technique	NOUN
fumecheng-7385	450	15	for	for	ADP
fumecheng-7385	450	16	solving	solve	VERB
fumecheng-7385	450	17	nonlinear	nonlinear	ADJ
fumecheng-7385	450	18	partial	partial	ADJ
fumecheng-7385	450	19	differential	differential	NOUN
fumecheng-7385	450	20	equations	equation	NOUN
fumecheng-7385	450	21	with	with	ADP
fumecheng-7385	450	22	laplace	laplace	NOUN
fumecheng-7385	450	23	transforms	transform	VERB
fumecheng-7385	450	24	,	,	PUNCT
fumecheng-7385	450	25	nonlinear	nonlinear	ADJ
fumecheng-7385	450	26	science	science	NOUN
fumecheng-7385	450	27	letters	letter	NOUN
fumecheng-7385	450	28	a	a	PRON
fumecheng-7385	450	29	,	,	PUNCT
fumecheng-7385	450	30	9	9	NUM
fumecheng-7385	450	31	,	,	PUNCT
fumecheng-7385	450	32	pp	pp	ADJ
fumecheng-7385	450	33	.	.	PUNCT
fumecheng-7385	451	1	349	349	NUM
fumecheng-7385	451	2	-	-	SYM
fumecheng-7385	451	3	359	359	NUM
fumecheng-7385	451	4	.	.	PUNCT
fumecheng-7385	452	1	28	28	NUM
fumecheng-7385	452	2	.	.	PUNCT
fumecheng-7385	453	1	el	el	PROPN
fumecheng-7385	453	2	-	-	PUNCT
fumecheng-7385	453	3	dib	dib	PROPN
fumecheng-7385	453	4	,	,	PUNCT
fumecheng-7385	453	5	y.o	y.o	PROPN
fumecheng-7385	453	6	.	.	PROPN
fumecheng-7385	453	7	,	,	PUNCT
fumecheng-7385	453	8	moatimid	moatimid	PROPN
fumecheng-7385	453	9	,	,	PUNCT
fumecheng-7385	453	10	g.m	g.m	PROPN
fumecheng-7385	453	11	.	.	PROPN
fumecheng-7385	453	12	,	,	PUNCT
fumecheng-7385	453	13	2019	2019	NUM
fumecheng-7385	453	14	,	,	PUNCT
fumecheng-7385	453	15	stability	stability	NOUN
fumecheng-7385	453	16	configuration	configuration	NOUN
fumecheng-7385	453	17	of	of	ADP
fumecheng-7385	453	18	a	a	DET
fumecheng-7385	453	19	rocking	rock	VERB
fumecheng-7385	453	20	rigid	rigid	ADJ
fumecheng-7385	453	21	rod	rod	NOUN
fumecheng-7385	453	22	over	over	ADP
fumecheng-7385	453	23	a	a	DET
fumecheng-7385	453	24	circular	circular	ADJ
fumecheng-7385	453	25	surface	surface	NOUN
fumecheng-7385	453	26	using	use	VERB
fumecheng-7385	453	27	the	the	DET
fumecheng-7385	453	28	homotopy	homotopy	NOUN
fumecheng-7385	453	29	perturbation	perturbation	NOUN
fumecheng-7385	453	30	method	method	NOUN
fumecheng-7385	453	31	and	and	CCONJ
fumecheng-7385	453	32	laplace	laplace	NOUN
fumecheng-7385	453	33	transform	transform	NOUN
fumecheng-7385	453	34	,	,	PUNCT
fumecheng-7385	453	35	arabian	arabian	ADJ
fumecheng-7385	453	36	journal	journal	NOUN
fumecheng-7385	453	37	for	for	ADP
fumecheng-7385	453	38	science	science	NOUN
fumecheng-7385	453	39	and	and	CCONJ
fumecheng-7385	453	40	engineering	engineering	NOUN
fumecheng-7385	453	41	,	,	PUNCT
fumecheng-7385	453	42	44	44	NUM
fumecheng-7385	453	43	(	(	PUNCT
fumecheng-7385	453	44	7	7	NUM
fumecheng-7385	453	45	)	)	PUNCT
fumecheng-7385	453	46	,	,	PUNCT
fumecheng-7385	453	47	pp	pp	ADJ
fumecheng-7385	453	48	.	.	PUNCT
fumecheng-7385	454	1	6581–6659	6581–6659	NUM
fumecheng-7385	454	2	.	.	PUNCT
fumecheng-7385	455	1	29	29	NUM
fumecheng-7385	455	2	.	.	X
fumecheng-7385	456	1	el	el	PROPN
fumecheng-7385	456	2	-	-	PUNCT
fumecheng-7385	456	3	dib	dib	PROPN
fumecheng-7385	456	4	,	,	PUNCT
fumecheng-7385	456	5	y.o	y.o	PROPN
fumecheng-7385	456	6	.	.	PROPN
fumecheng-7385	456	7	,	,	PUNCT
fumecheng-7385	456	8	2017	2017	NUM
fumecheng-7385	456	9	,	,	PUNCT
fumecheng-7385	456	10	multiple	multiple	ADJ
fumecheng-7385	456	11	scales	scale	NOUN
fumecheng-7385	456	12	homotopy	homotopy	VERB
fumecheng-7385	456	13	perturbation	perturbation	NOUN
fumecheng-7385	456	14	method	method	NOUN
fumecheng-7385	456	15	for	for	ADP
fumecheng-7385	456	16	nonlinear	nonlinear	ADJ
fumecheng-7385	456	17	oscillators	oscillator	NOUN
fumecheng-7385	456	18	,	,	PUNCT
fumecheng-7385	456	19	nonlinear	nonlinear	ADJ
fumecheng-7385	456	20	science	science	NOUN
fumecheng-7385	456	21	letters	letter	NOUN
fumecheng-7385	456	22	a	a	PRON
fumecheng-7385	456	23	,	,	PUNCT
fumecheng-7385	456	24	9	9	NUM
fumecheng-7385	456	25	,	,	PUNCT
fumecheng-7385	456	26	pp	pp	ADJ
fumecheng-7385	456	27	.	.	PUNCT
fumecheng-7385	457	1	352	352	NUM
fumecheng-7385	457	2	-	-	SYM
fumecheng-7385	457	3	364	364	NUM
fumecheng-7385	457	4	.	.	NUM
fumecheng-7385	457	5	30	30	NUM
fumecheng-7385	457	6	.	.	PUNCT
fumecheng-7385	458	1	ren	ren	PROPN
fumecheng-7385	458	2	,	,	PUNCT
fumecheng-7385	458	3	z	z	PROPN
fumecheng-7385	458	4	-	-	PROPN
fumecheng-7385	458	5	f.	f.	PROPN
fumecheng-7385	458	6	,	,	PUNCT
fumecheng-7385	458	7	yao	yao	PROPN
fumecheng-7385	458	8	,	,	PUNCT
fumecheng-7385	458	9	s	s	NOUN
fumecheng-7385	458	10	-	-	PUNCT
fumecheng-7385	458	11	w	w	NOUN
fumecheng-7385	458	12	,	,	PUNCT
fumecheng-7385	458	13	he	he	PRON
fumecheng-7385	458	14	,	,	PUNCT
fumecheng-7385	458	15	j.h	j.h	PROPN
fumecheng-7385	458	16	.	.	PROPN
fumecheng-7385	458	17	,	,	PUNCT
fumecheng-7385	458	18	2019	2019	NUM
fumecheng-7385	458	19	,	,	PUNCT
fumecheng-7385	458	20	he	he	PRON
fumecheng-7385	458	21	’s	’	VERB
fumecheng-7385	458	22	multiple	multiple	ADJ
fumecheng-7385	458	23	scales	scale	NOUN
fumecheng-7385	458	24	method	method	NOUN
fumecheng-7385	458	25	for	for	ADP
fumecheng-7385	458	26	nonlinear	nonlinear	ADJ
fumecheng-7385	458	27	vibrations	vibration	NOUN
fumecheng-7385	458	28	,	,	PUNCT
fumecheng-7385	458	29	journal	journal	NOUN
fumecheng-7385	458	30	of	of	ADP
fumecheng-7385	458	31	low	low	ADJ
fumecheng-7385	458	32	-	-	PUNCT
fumecheng-7385	458	33	frequency	frequency	NOUN
fumecheng-7385	458	34	noise	noise	NOUN
fumecheng-7385	458	35	,	,	PUNCT
fumecheng-7385	458	36	vibration	vibration	NOUN
fumecheng-7385	458	37	&	&	CCONJ
fumecheng-7385	458	38	active	active	ADJ
fumecheng-7385	458	39	control	control	NOUN
fumecheng-7385	458	40	,	,	PUNCT
fumecheng-7385	458	41	38	38	NUM
fumecheng-7385	458	42	,	,	PUNCT
fumecheng-7385	458	43	pp	pp	ADJ
fumecheng-7385	458	44	.	.	PUNCT
fumecheng-7385	458	45	1708	1708	NUM
fumecheng-7385	458	46	-	-	SYM
fumecheng-7385	458	47	1712	1712	NUM
fumecheng-7385	458	48	.	.	PUNCT
fumecheng-7385	459	1	31	31	NUM
fumecheng-7385	459	2	.	.	PUNCT
fumecheng-7385	460	1	shen	shen	PROPN
fumecheng-7385	460	2	,	,	PUNCT
fumecheng-7385	460	3	y.	y.	PROPN
fumecheng-7385	460	4	,	,	PUNCT
fumecheng-7385	460	5	el	el	PROPN
fumecheng-7385	460	6	-	-	PUNCT
fumecheng-7385	460	7	dib	dib	PROPN
fumecheng-7385	460	8	,	,	PUNCT
fumecheng-7385	460	9	y.o	y.o	PROPN
fumecheng-7385	460	10	.	.	PROPN
fumecheng-7385	460	11	,	,	PUNCT
fumecheng-7385	460	12	2020	2020	NUM
fumecheng-7385	460	13	,	,	PUNCT
fumecheng-7385	460	14	a	a	DET
fumecheng-7385	460	15	periodic	periodic	ADJ
fumecheng-7385	460	16	solution	solution	NOUN
fumecheng-7385	460	17	of	of	ADP
fumecheng-7385	460	18	the	the	DET
fumecheng-7385	460	19	fractional	fractional	ADJ
fumecheng-7385	460	20	sine	sine	NOUN
fumecheng-7385	460	21	-	-	PUNCT
fumecheng-7385	460	22	gordon	gordon	NOUN
fumecheng-7385	460	23	equation	equation	NOUN
fumecheng-7385	460	24	arising	arise	VERB
fumecheng-7385	460	25	in	in	ADP
fumecheng-7385	460	26	architectural	architectural	ADJ
fumecheng-7385	460	27	engineering	engineering	NOUN
fumecheng-7385	460	28	,	,	PUNCT
fumecheng-7385	460	29	j.	j.	PROPN
fumecheng-7385	460	30	low	low	ADJ
fumecheng-7385	460	31	-	-	PUNCT
fumecheng-7385	460	32	frequency	frequency	NOUN
fumecheng-7385	460	33	noise	noise	NOUN
fumecheng-7385	460	34	,	,	PUNCT
fumecheng-7385	460	35	vibration	vibration	NOUN
fumecheng-7385	460	36	and	and	CCONJ
fumecheng-7385	460	37	active	active	ADJ
fumecheng-7385	460	38	control	control	NOUN
fumecheng-7385	460	39	,	,	PUNCT
fumecheng-7385	460	40	doi	doi	PROPN
fumecheng-7385	460	41	:	:	PUNCT
fumecheng-7385	460	42	10.1177/	10.1177/	PROPN
fumecheng-7385	460	43	1461348420917565	1461348420917565	NUM
fumecheng-7385	460	44	.	.	PUNCT
fumecheng-7385	461	1	32	32	NUM
fumecheng-7385	461	2	.	.	X
fumecheng-7385	462	1	el	el	PROPN
fumecheng-7385	462	2	-	-	PUNCT
fumecheng-7385	462	3	dib	dib	PROPN
fumecheng-7385	462	4	,	,	PUNCT
fumecheng-7385	462	5	y.o	y.o	PROPN
fumecheng-7385	462	6	.	.	PROPN
fumecheng-7385	462	7	,	,	PUNCT
fumecheng-7385	462	8	elgazery	elgazery	PROPN
fumecheng-7385	462	9	,	,	PUNCT
fumecheng-7385	462	10	n.s	n.s	PROPN
fumecheng-7385	462	11	.	.	PROPN
fumecheng-7385	462	12	,	,	PUNCT
fumecheng-7385	462	13	2020	2020	NUM
fumecheng-7385	462	14	,	,	PUNCT
fumecheng-7385	462	15	effect	effect	NOUN
fumecheng-7385	462	16	of	of	ADP
fumecheng-7385	462	17	fractional	fractional	ADJ
fumecheng-7385	462	18	derivative	derivative	ADJ
fumecheng-7385	462	19	properties	property	NOUN
fumecheng-7385	462	20	on	on	ADP
fumecheng-7385	462	21	the	the	DET
fumecheng-7385	462	22	periodic	periodic	ADJ
fumecheng-7385	462	23	solution	solution	NOUN
fumecheng-7385	462	24	of	of	ADP
fumecheng-7385	462	25	the	the	DET
fumecheng-7385	462	26	nonlinear	nonlinear	ADJ
fumecheng-7385	462	27	oscillations	oscillation	NOUN
fumecheng-7385	462	28	,	,	PUNCT
fumecheng-7385	462	29	fractals	fractal	NOUN
fumecheng-7385	462	30	,	,	PUNCT
fumecheng-7385	462	31	doi	doi	NOUN
fumecheng-7385	462	32	:	:	PUNCT
fumecheng-7385	462	33	10.1142	10.1142	NUM
fumecheng-7385	462	34	/	/	SYM
fumecheng-7385	462	35	s0218348x20500954	s0218348x20500954	VERB
fumecheng-7385	462	36	.	.	PUNCT
fumecheng-7385	463	1	33	33	NUM
fumecheng-7385	463	2	.	.	PUNCT
fumecheng-7385	464	1	raphael	raphael	PROPN
fumecheng-7385	464	2	,	,	PUNCT
fumecheng-7385	464	3	c.	c.	PROPN
fumecheng-7385	464	4	,	,	PUNCT
fumecheng-7385	464	5	yvan	yvan	PROPN
fumecheng-7385	464	6	,	,	PUNCT
fumecheng-7385	464	7	m.	m.	NOUN
fumecheng-7385	464	8	,	,	PUNCT
fumecheng-7385	464	9	xu	xu	PROPN
fumecheng-7385	464	10	,	,	PUNCT
fumecheng-7385	464	11	y.	y.	PROPN
fumecheng-7385	464	12	,	,	PUNCT
fumecheng-7385	464	13	2020	2020	NUM
fumecheng-7385	464	14	,	,	PUNCT
fumecheng-7385	464	15	long	long	ADJ
fumecheng-7385	464	16	-	-	PUNCT
fumecheng-7385	464	17	time	time	NOUN
fumecheng-7385	464	18	asymptotics	asymptotic	NOUN
fumecheng-7385	464	19	of	of	ADP
fumecheng-7385	464	20	the	the	DET
fumecheng-7385	464	21	one	one	NUM
fumecheng-7385	464	22	-	-	PUNCT
fumecheng-7385	464	23	dimensional	dimensional	ADJ
fumecheng-7385	464	24	damped	damped	NOUN
fumecheng-7385	464	25	nonlinear	nonlinear	PROPN
fumecheng-7385	464	26	klein	klein	PROPN
fumecheng-7385	464	27	-	-	PUNCT
fumecheng-7385	464	28	gordon	gordon	PROPN
fumecheng-7385	464	29	equation	equation	NOUN
fumecheng-7385	464	30	,	,	PUNCT
fumecheng-7385	464	31	available	available	ADJ
fumecheng-7385	464	32	at	at	ADP
fumecheng-7385	464	33	:	:	PUNCT
fumecheng-7385	464	34	https://arxiv.org/abs/2002.01826	https://arxiv.org/abs/2002.01826	PROPN
fumecheng-7385	464	35	(	(	PUNCT
fumecheng-7385	464	36	last	last	ADJ
fumecheng-7385	464	37	access	access	NOUN
fumecheng-7385	464	38	:	:	PUNCT
fumecheng-7385	464	39	25.01.2021	25.01.2021	NUM
fumecheng-7385	464	40	)	)	PUNCT
fumecheng-7385	464	41	34	34	NUM
fumecheng-7385	464	42	.	.	PUNCT
fumecheng-7385	465	1	el	el	PROPN
fumecheng-7385	465	2	-	-	PUNCT
fumecheng-7385	465	3	dib	dib	PROPN
fumecheng-7385	465	4	,	,	PUNCT
fumecheng-7385	465	5	y.	y.	PROPN
fumecheng-7385	465	6	o.	o.	PROPN
fumecheng-7385	465	7	,	,	PUNCT
fumecheng-7385	465	8	moatimid	moatimid	PROPN
fumecheng-7385	465	9	,	,	PUNCT
fumecheng-7385	465	10	g.	g.	PROPN
fumecheng-7385	465	11	m.	m.	PROPN
fumecheng-7385	465	12	,	,	PUNCT
fumecheng-7385	465	13	elgazery	elgazery	PROPN
fumecheng-7385	465	14	,	,	PUNCT
fumecheng-7385	465	15	n.	n.	PROPN
fumecheng-7385	465	16	s.	s.	PROPN
fumecheng-7385	465	17	,	,	PUNCT
fumecheng-7385	465	18	2020	2020	NUM
fumecheng-7385	465	19	,	,	PUNCT
fumecheng-7385	465	20	stability	stability	NOUN
fumecheng-7385	465	21	analysis	analysis	NOUN
fumecheng-7385	465	22	of	of	ADP
fumecheng-7385	465	23	a	a	DET
fumecheng-7385	465	24	damped	damped	ADJ
fumecheng-7385	465	25	nonlinear	nonlinear	ADJ
fumecheng-7385	465	26	wave	wave	NOUN
fumecheng-7385	465	27	equation	equation	NOUN
fumecheng-7385	465	28	,	,	PUNCT
fumecheng-7385	465	29	j.	j.	PROPN
fumecheng-7385	465	30	appl	appl	PROPN
fumecheng-7385	465	31	.	.	PUNCT
fumecheng-7385	466	1	comput	comput	PROPN
fumecheng-7385	466	2	.	.	PUNCT
fumecheng-7385	467	1	mech	mech	PROPN
fumecheng-7385	467	2	.	.	PROPN
fumecheng-7385	467	3	,	,	PUNCT
fumecheng-7385	467	4	6(si	6(si	PROPN
fumecheng-7385	467	5	)	)	PUNCT
fumecheng-7385	467	6	,	,	PUNCT
fumecheng-7385	467	7	pp	pp	PROPN
fumecheng-7385	467	8	.	.	PUNCT
fumecheng-7385	467	9	1394	1394	NUM
fumecheng-7385	467	10	-	-	SYM
fumecheng-7385	467	11	1403	1403	NUM
fumecheng-7385	467	12	.	.	PUNCT
fumecheng-7385	468	1	35	35	NUM
fumecheng-7385	468	2	.	.	PUNCT
fumecheng-7385	469	1	he	he	PRON
fumecheng-7385	469	2	,	,	PUNCT
fumecheng-7385	469	3	j.h	j.h	PROPN
fumecheng-7385	469	4	.	.	PROPN
fumecheng-7385	469	5	,	,	PUNCT
fumecheng-7385	469	6	el	el	PROPN
fumecheng-7385	469	7	-	-	PUNCT
fumecheng-7385	469	8	dib	dib	PROPN
fumecheng-7385	469	9	,	,	PUNCT
fumecheng-7385	469	10	y.	y.	PROPN
fumecheng-7385	469	11	o.	o.	PROPN
fumecheng-7385	469	12	,	,	PUNCT
fumecheng-7385	469	13	2020	2020	NUM
fumecheng-7385	469	14	,	,	PUNCT
fumecheng-7385	469	15	periodic	periodic	ADJ
fumecheng-7385	469	16	property	property	NOUN
fumecheng-7385	469	17	of	of	ADP
fumecheng-7385	469	18	the	the	DET
fumecheng-7385	469	19	time	time	NOUN
fumecheng-7385	469	20	-	-	PUNCT
fumecheng-7385	469	21	fractional	fractional	ADJ
fumecheng-7385	469	22	kundu	kundu	NOUN
fumecheng-7385	469	23	–	–	PUNCT
fumecheng-7385	469	24	mukherjee	mukherjee	NOUN
fumecheng-7385	469	25	–	–	PUNCT
fumecheng-7385	469	26	naskar	naskar	NOUN
fumecheng-7385	469	27	equation	equation	NOUN
fumecheng-7385	469	28	,	,	PUNCT
fumecheng-7385	469	29	results	result	NOUN
fumecheng-7385	469	30	in	in	ADP
fumecheng-7385	469	31	physics	physics	NOUN
fumecheng-7385	469	32	,	,	PUNCT
fumecheng-7385	469	33	19	19	NUM
fumecheng-7385	469	34	,	,	PUNCT
fumecheng-7385	469	35	103345	103345	NUM
fumecheng-7385	469	36	.	.	PUNCT
fumecheng-7385	470	1	https://link.springer.com/journal/11425	https://link.springer.com/journal/11425	PROPN
fumecheng-7385	470	2	https://link.springer.com/journal/11425	https://link.springer.com/journal/11425	PROPN
fumecheng-7385	470	3	https://doi.org/10.1515/acv-2019-0039	https://doi.org/10.1515/acv-2019-0039	PROPN
fumecheng-7385	470	4	https://journals.sagepub.com/home/lfn	https://journals.sagepub.com/home/lfn	PRON
fumecheng-7385	470	5	https://journals.sagepub.com/home/lfn	https://journals.sagepub.com/home/lfn	NUM
fumecheng-7385	470	6	https://www.worldscientific.com/worldscinet/fractals	https://www.worldscientific.com/worldscinet/fractal	NOUN
fumecheng-7385	470	7	https://doi.org/10.1142/s0218348x20500954	https://doi.org/10.1142/s0218348x20500954	NUM
fumecheng-7385	470	8	https://arxiv.org/search/math?searchtype=author&query=c%c3%b4te%2c+r	https://arxiv.org/search/math?searchtype=author&query=c%c3%b4te%2c+r	NOUN
fumecheng-7385	470	9	https://arxiv.org/search/math?searchtype=author&query=martel%2c+y	https://arxiv.org/search/math?searchtype=author&query=martel%2c+y	X
fumecheng-7385	470	10	https://arxiv.org/search/math?searchtype=author&query=yuan%2c+x	https://arxiv.org/search/math?searchtype=author&query=yuan%2c+x	X
fumecheng-7385	470	11	https://doi.org/10.1016/j.rinp.2020.103345	https://doi.org/10.1016/j.rinp.2020.103345	PROPN