id	sid	tid	token	lemma	pos
fumecheng-10464	1	1	10464	10464	NUM
fumecheng-10464	1	2	facta	facta	PROPN
fumecheng-10464	1	3	universitatis	universitatis	PROPN
fumecheng-10464	1	4	series	series	NOUN
fumecheng-10464	1	5	:	:	PUNCT
fumecheng-10464	1	6	mechanical	mechanical	ADJ
fumecheng-10464	1	7	engineering	engineering	NOUN
fumecheng-10464	1	8	vol	vol	NOUN
fumecheng-10464	1	9	.	.	PROPN
fumecheng-10464	1	10	20	20	NUM
fumecheng-10464	1	11	,	,	PUNCT
fumecheng-10464	1	12	no	no	DET
fumecheng-10464	1	13	1	1	NUM
fumecheng-10464	1	14	,	,	PUNCT
fumecheng-10464	1	15	2022	2022	NUM
fumecheng-10464	1	16	,	,	PUNCT
fumecheng-10464	1	17	pp	pp	ADJ
fumecheng-10464	1	18	.	.	PUNCT
fumecheng-10464	1	19	1	1	NUM
fumecheng-10464	1	20	20	20	NUM
fumecheng-10464	1	21	https://doi.org/10.22190/fume220118004h	https://doi.org/10.22190/fume220118004h	PROPN
fumecheng-10464	1	22	©	©	PROPN
fumecheng-10464	1	23	2022	2022	NUM
fumecheng-10464	1	24	by	by	ADP
fumecheng-10464	1	25	university	university	PROPN
fumecheng-10464	1	26	of	of	ADP
fumecheng-10464	1	27	niš	niš	PROPN
fumecheng-10464	1	28	,	,	PUNCT
fumecheng-10464	1	29	serbia	serbia	PROPN
fumecheng-10464	1	30	|	|	ADV
fumecheng-10464	1	31	creative	creative	ADJ
fumecheng-10464	1	32	commons	common	NOUN
fumecheng-10464	1	33	license	license	NOUN
fumecheng-10464	1	34	:	:	PUNCT
fumecheng-10464	1	35	cc	cc	VERB
fumecheng-10464	1	36	by	by	ADP
fumecheng-10464	1	37	-	-	PUNCT
fumecheng-10464	1	38	nc	nc	VERB
fumecheng-10464	1	39	-	-	PUNCT
fumecheng-10464	1	40	nd	nd	ADV
fumecheng-10464	1	41	original	original	ADJ
fumecheng-10464	1	42	scientific	scientific	ADJ
fumecheng-10464	1	43	paper	paper	VERB
fumecheng-10464	1	44	forced	force	VERB
fumecheng-10464	1	45	nonlinear	nonlinear	ADJ
fumecheng-10464	1	46	oscillator	oscillator	NOUN
fumecheng-10464	1	47	in	in	ADP
fumecheng-10464	1	48	a	a	DET
fumecheng-10464	1	49	fractal	fractal	ADJ
fumecheng-10464	1	50	space	space	NOUN
fumecheng-10464	1	51	ji	ji	PROPN
fumecheng-10464	1	52	-	-	PROPN
fumecheng-10464	1	53	huan	huan	PROPN
fumecheng-10464	1	54	he1,2,3	he1,2,3	PROPN
fumecheng-10464	1	55	,	,	PUNCT
fumecheng-10464	1	56	galal	galal	PROPN
fumecheng-10464	1	57	m.	m.	PROPN
fumecheng-10464	1	58	moatimid4	moatimid4	PROPN
fumecheng-10464	1	59	,	,	PUNCT
fumecheng-10464	1	60	marwa	marwa	PROPN
fumecheng-10464	1	61	h.	h.	PROPN
fumecheng-10464	1	62	zekry5	zekry5	PROPN
fumecheng-10464	2	1	1school	1school	NUM
fumecheng-10464	2	2	of	of	ADP
fumecheng-10464	2	3	civil	civil	ADJ
fumecheng-10464	2	4	engineering	engineering	NOUN
fumecheng-10464	2	5	,	,	PUNCT
fumecheng-10464	2	6	xi’an	xi’an	PROPN
fumecheng-10464	2	7	university	university	PROPN
fumecheng-10464	2	8	of	of	ADP
fumecheng-10464	2	9	architecture	architecture	NOUN
fumecheng-10464	2	10	&	&	CCONJ
fumecheng-10464	2	11	technology	technology	NOUN
fumecheng-10464	2	12	,	,	PUNCT
fumecheng-10464	2	13	xi’an	xi’an	PROPN
fumecheng-10464	2	14	,	,	PUNCT
fumecheng-10464	2	15	china	china	PROPN
fumecheng-10464	2	16	2national	2national	NUM
fumecheng-10464	2	17	engineering	engineering	NOUN
fumecheng-10464	2	18	laboratory	laboratory	NOUN
fumecheng-10464	2	19	for	for	ADP
fumecheng-10464	2	20	modern	modern	ADJ
fumecheng-10464	2	21	silk	silk	NOUN
fumecheng-10464	2	22	,	,	PUNCT
fumecheng-10464	2	23	college	college	NOUN
fumecheng-10464	2	24	of	of	ADP
fumecheng-10464	2	25	textile	textile	NOUN
fumecheng-10464	2	26	and	and	CCONJ
fumecheng-10464	2	27	clothing	clothing	NOUN
fumecheng-10464	2	28	engineering	engineering	NOUN
fumecheng-10464	2	29	,	,	PUNCT
fumecheng-10464	2	30	soochow	soochow	PROPN
fumecheng-10464	2	31	university	university	PROPN
fumecheng-10464	2	32	,	,	PUNCT
fumecheng-10464	2	33	suzhou	suzhou	PROPN
fumecheng-10464	2	34	,	,	PUNCT
fumecheng-10464	2	35	china	china	PROPN
fumecheng-10464	2	36	3school	3school	NUM
fumecheng-10464	2	37	of	of	ADP
fumecheng-10464	2	38	science	science	PROPN
fumecheng-10464	2	39	,	,	PUNCT
fumecheng-10464	2	40	xi'an	xi'an	PROPN
fumecheng-10464	2	41	university	university	PROPN
fumecheng-10464	2	42	of	of	ADP
fumecheng-10464	2	43	architecture	architecture	NOUN
fumecheng-10464	2	44	and	and	CCONJ
fumecheng-10464	2	45	technology	technology	NOUN
fumecheng-10464	2	46	,	,	PUNCT
fumecheng-10464	2	47	xi’an	xi’an	PROPN
fumecheng-10464	2	48	,	,	PUNCT
fumecheng-10464	2	49	china	china	PROPN
fumecheng-10464	2	50	4department	4department	NUM
fumecheng-10464	2	51	of	of	ADP
fumecheng-10464	2	52	mathematics	mathematic	NOUN
fumecheng-10464	2	53	,	,	PUNCT
fumecheng-10464	2	54	faculty	faculty	NOUN
fumecheng-10464	2	55	of	of	ADP
fumecheng-10464	2	56	education	education	NOUN
fumecheng-10464	2	57	,	,	PUNCT
fumecheng-10464	2	58	ain	ain	PROPN
fumecheng-10464	2	59	shams	shams	PROPN
fumecheng-10464	2	60	university	university	PROPN
fumecheng-10464	2	61	,	,	PUNCT
fumecheng-10464	2	62	roxy	roxy	PROPN
fumecheng-10464	2	63	,	,	PUNCT
fumecheng-10464	2	64	cairo	cairo	PROPN
fumecheng-10464	2	65	,	,	PUNCT
fumecheng-10464	2	66	egypt	egypt	PROPN
fumecheng-10464	2	67	5department	5department	NUM
fumecheng-10464	2	68	of	of	ADP
fumecheng-10464	2	69	mathematics	mathematic	NOUN
fumecheng-10464	2	70	and	and	CCONJ
fumecheng-10464	2	71	computer	computer	NOUN
fumecheng-10464	2	72	science	science	NOUN
fumecheng-10464	2	73	,	,	PUNCT
fumecheng-10464	2	74	faculty	faculty	NOUN
fumecheng-10464	2	75	of	of	ADP
fumecheng-10464	2	76	science	science	NOUN
fumecheng-10464	2	77	,	,	PUNCT
fumecheng-10464	2	78	beni	beni	ADJ
fumecheng-10464	2	79	-	-	ADJ
fumecheng-10464	2	80	suef	suef	ADJ
fumecheng-10464	2	81	university	university	NOUN
fumecheng-10464	2	82	,	,	PUNCT
fumecheng-10464	2	83	beni	beni	NOUN
fumecheng-10464	2	84	-	-	ADJ
fumecheng-10464	2	85	suef	suef	NOUN
fumecheng-10464	2	86	,	,	PUNCT
fumecheng-10464	3	1	egypt	egypt	PROPN
fumecheng-10464	3	2	abstract	abstract	PROPN
fumecheng-10464	3	3	.	.	PUNCT
fumecheng-10464	4	1	a	a	DET
fumecheng-10464	4	2	critical	critical	ADJ
fumecheng-10464	4	3	hurdle	hurdle	NOUN
fumecheng-10464	4	4	of	of	ADP
fumecheng-10464	4	5	a	a	DET
fumecheng-10464	4	6	nonlinear	nonlinear	ADJ
fumecheng-10464	4	7	vibration	vibration	NOUN
fumecheng-10464	4	8	system	system	NOUN
fumecheng-10464	4	9	in	in	ADP
fumecheng-10464	4	10	a	a	DET
fumecheng-10464	4	11	fractal	fractal	ADJ
fumecheng-10464	4	12	space	space	NOUN
fumecheng-10464	4	13	is	be	AUX
fumecheng-10464	4	14	the	the	DET
fumecheng-10464	4	15	inefficiency	inefficiency	NOUN
fumecheng-10464	4	16	in	in	ADP
fumecheng-10464	4	17	modelling	model	VERB
fumecheng-10464	4	18	the	the	DET
fumecheng-10464	4	19	system	system	NOUN
fumecheng-10464	4	20	.	.	PUNCT
fumecheng-10464	5	1	specifically	specifically	ADV
fumecheng-10464	5	2	,	,	PUNCT
fumecheng-10464	5	3	the	the	DET
fumecheng-10464	5	4	differential	differential	ADJ
fumecheng-10464	5	5	equation	equation	NOUN
fumecheng-10464	5	6	models	model	NOUN
fumecheng-10464	5	7	can	can	AUX
fumecheng-10464	5	8	not	not	PART
fumecheng-10464	5	9	elucidate	elucidate	VERB
fumecheng-10464	5	10	the	the	DET
fumecheng-10464	5	11	effect	effect	NOUN
fumecheng-10464	5	12	of	of	ADP
fumecheng-10464	5	13	porosity	porosity	NOUN
fumecheng-10464	5	14	size	size	NOUN
fumecheng-10464	5	15	and	and	CCONJ
fumecheng-10464	5	16	distribution	distribution	NOUN
fumecheng-10464	5	17	of	of	ADP
fumecheng-10464	5	18	the	the	DET
fumecheng-10464	5	19	periodic	periodic	ADJ
fumecheng-10464	5	20	property	property	NOUN
fumecheng-10464	5	21	.	.	PUNCT
fumecheng-10464	6	1	this	this	DET
fumecheng-10464	6	2	paper	paper	NOUN
fumecheng-10464	6	3	establishes	establish	VERB
fumecheng-10464	6	4	a	a	DET
fumecheng-10464	6	5	fractal	fractal	ADJ
fumecheng-10464	6	6	-	-	PUNCT
fumecheng-10464	6	7	differential	differential	NOUN
fumecheng-10464	6	8	model	model	NOUN
fumecheng-10464	6	9	for	for	ADP
fumecheng-10464	6	10	this	this	DET
fumecheng-10464	6	11	purpose	purpose	NOUN
fumecheng-10464	6	12	,	,	PUNCT
fumecheng-10464	6	13	and	and	CCONJ
fumecheng-10464	6	14	a	a	DET
fumecheng-10464	6	15	fractal	fractal	ADJ
fumecheng-10464	6	16	duffing	duffing	NOUN
fumecheng-10464	6	17	-	-	PUNCT
fumecheng-10464	6	18	van	van	PROPN
fumecheng-10464	6	19	der	der	ADJ
fumecheng-10464	6	20	pol	pol	PROPN
fumecheng-10464	6	21	oscillator	oscillator	NOUN
fumecheng-10464	6	22	(	(	PUNCT
fumecheng-10464	6	23	dvdp	dvdp	ADJ
fumecheng-10464	6	24	)	)	PUNCT
fumecheng-10464	6	25	with	with	ADP
fumecheng-10464	6	26	two	two	NUM
fumecheng-10464	6	27	-	-	PUNCT
fumecheng-10464	6	28	scale	scale	NOUN
fumecheng-10464	6	29	fractal	fractal	ADJ
fumecheng-10464	6	30	derivatives	derivative	NOUN
fumecheng-10464	6	31	and	and	CCONJ
fumecheng-10464	6	32	a	a	DET
fumecheng-10464	6	33	forced	force	VERB
fumecheng-10464	6	34	term	term	NOUN
fumecheng-10464	6	35	is	be	AUX
fumecheng-10464	6	36	considered	consider	VERB
fumecheng-10464	6	37	as	as	ADP
fumecheng-10464	6	38	an	an	DET
fumecheng-10464	6	39	example	example	NOUN
fumecheng-10464	6	40	to	to	PART
fumecheng-10464	6	41	reveal	reveal	VERB
fumecheng-10464	6	42	the	the	DET
fumecheng-10464	6	43	basic	basic	ADJ
fumecheng-10464	6	44	properties	property	NOUN
fumecheng-10464	6	45	of	of	ADP
fumecheng-10464	6	46	the	the	DET
fumecheng-10464	6	47	fractal	fractal	ADJ
fumecheng-10464	6	48	oscillator	oscillator	NOUN
fumecheng-10464	6	49	.	.	PUNCT
fumecheng-10464	7	1	utilizing	utilize	VERB
fumecheng-10464	7	2	the	the	DET
fumecheng-10464	7	3	two	two	NUM
fumecheng-10464	7	4	-	-	PUNCT
fumecheng-10464	7	5	scale	scale	NOUN
fumecheng-10464	7	6	transforms	transform	NOUN
fumecheng-10464	7	7	and	and	CCONJ
fumecheng-10464	7	8	he	he	PRON
fumecheng-10464	7	9	-	-	PUNCT
fumecheng-10464	7	10	laplace	laplace	NOUN
fumecheng-10464	7	11	method	method	NOUN
fumecheng-10464	7	12	,	,	PUNCT
fumecheng-10464	7	13	an	an	DET
fumecheng-10464	7	14	analytic	analytic	ADJ
fumecheng-10464	7	15	approximate	approximate	ADJ
fumecheng-10464	7	16	solution	solution	NOUN
fumecheng-10464	7	17	may	may	AUX
fumecheng-10464	7	18	be	be	AUX
fumecheng-10464	7	19	attained	attain	VERB
fumecheng-10464	7	20	.	.	PUNCT
fumecheng-10464	8	1	unfortunately	unfortunately	ADV
fumecheng-10464	8	2	,	,	PUNCT
fumecheng-10464	8	3	this	this	DET
fumecheng-10464	8	4	solution	solution	NOUN
fumecheng-10464	8	5	is	be	AUX
fumecheng-10464	8	6	not	not	PART
fumecheng-10464	8	7	physically	physically	ADV
fumecheng-10464	8	8	preferred	prefer	VERB
fumecheng-10464	8	9	.	.	PUNCT
fumecheng-10464	9	1	it	it	PRON
fumecheng-10464	9	2	has	have	VERB
fumecheng-10464	9	3	to	to	PART
fumecheng-10464	9	4	be	be	AUX
fumecheng-10464	9	5	modified	modify	VERB
fumecheng-10464	9	6	along	along	ADP
fumecheng-10464	9	7	with	with	ADP
fumecheng-10464	9	8	the	the	DET
fumecheng-10464	9	9	nonlinear	nonlinear	ADJ
fumecheng-10464	9	10	frequency	frequency	NOUN
fumecheng-10464	9	11	analysis	analysis	NOUN
fumecheng-10464	9	12	,	,	PUNCT
fumecheng-10464	9	13	and	and	CCONJ
fumecheng-10464	9	14	the	the	DET
fumecheng-10464	9	15	stability	stability	NOUN
fumecheng-10464	9	16	criterion	criterion	NOUN
fumecheng-10464	9	17	for	for	ADP
fumecheng-10464	9	18	the	the	DET
fumecheng-10464	9	19	equation	equation	NOUN
fumecheng-10464	9	20	under	under	ADP
fumecheng-10464	9	21	consideration	consideration	NOUN
fumecheng-10464	9	22	is	be	AUX
fumecheng-10464	9	23	obtained	obtain	VERB
fumecheng-10464	9	24	.	.	PUNCT
fumecheng-10464	10	1	on	on	ADP
fumecheng-10464	10	2	the	the	DET
fumecheng-10464	10	3	other	other	ADJ
fumecheng-10464	10	4	hand	hand	NOUN
fumecheng-10464	10	5	,	,	PUNCT
fumecheng-10464	10	6	the	the	DET
fumecheng-10464	10	7	linearized	linearize	VERB
fumecheng-10464	10	8	stability	stability	NOUN
fumecheng-10464	10	9	theory	theory	NOUN
fumecheng-10464	10	10	is	be	AUX
fumecheng-10464	10	11	employed	employ	VERB
fumecheng-10464	10	12	in	in	ADP
fumecheng-10464	10	13	the	the	DET
fumecheng-10464	10	14	autonomous	autonomous	ADJ
fumecheng-10464	10	15	arrangement	arrangement	NOUN
fumecheng-10464	10	16	.	.	PUNCT
fumecheng-10464	11	1	consequently	consequently	ADV
fumecheng-10464	11	2	,	,	PUNCT
fumecheng-10464	11	3	the	the	DET
fumecheng-10464	11	4	phase	phase	NOUN
fumecheng-10464	11	5	portraits	portrait	VERB
fumecheng-10464	11	6	around	around	ADP
fumecheng-10464	11	7	the	the	DET
fumecheng-10464	11	8	equilibrium	equilibrium	NOUN
fumecheng-10464	11	9	points	point	NOUN
fumecheng-10464	11	10	are	be	AUX
fumecheng-10464	11	11	sketched	sketch	VERB
fumecheng-10464	11	12	.	.	PUNCT
fumecheng-10464	12	1	for	for	ADP
fumecheng-10464	12	2	the	the	DET
fumecheng-10464	12	3	non	non	ADJ
fumecheng-10464	12	4	-	-	ADJ
fumecheng-10464	12	5	autonomous	autonomous	ADJ
fumecheng-10464	12	6	organization	organization	NOUN
fumecheng-10464	12	7	,	,	PUNCT
fumecheng-10464	12	8	the	the	DET
fumecheng-10464	12	9	stability	stability	NOUN
fumecheng-10464	12	10	criteria	criterion	NOUN
fumecheng-10464	12	11	are	be	AUX
fumecheng-10464	12	12	analyzed	analyze	VERB
fumecheng-10464	12	13	via	via	ADP
fumecheng-10464	12	14	the	the	DET
fumecheng-10464	12	15	multiple	multiple	ADJ
fumecheng-10464	12	16	time	time	NOUN
fumecheng-10464	12	17	scales	scale	VERB
fumecheng-10464	12	18	technique	technique	NOUN
fumecheng-10464	12	19	.	.	PUNCT
fumecheng-10464	13	1	numerical	numerical	ADJ
fumecheng-10464	13	2	estimations	estimation	NOUN
fumecheng-10464	13	3	are	be	AUX
fumecheng-10464	13	4	designed	design	VERB
fumecheng-10464	13	5	to	to	PART
fumecheng-10464	13	6	confirm	confirm	VERB
fumecheng-10464	13	7	graphically	graphically	ADV
fumecheng-10464	13	8	the	the	DET
fumecheng-10464	13	9	analytical	analytical	ADJ
fumecheng-10464	13	10	approximate	approximate	ADJ
fumecheng-10464	13	11	solutions	solution	NOUN
fumecheng-10464	13	12	as	as	ADV
fumecheng-10464	13	13	well	well	ADV
fumecheng-10464	13	14	as	as	ADP
fumecheng-10464	13	15	the	the	DET
fumecheng-10464	13	16	stability	stability	NOUN
fumecheng-10464	13	17	configuration	configuration	NOUN
fumecheng-10464	13	18	.	.	PUNCT
fumecheng-10464	14	1	it	it	PRON
fumecheng-10464	14	2	is	be	AUX
fumecheng-10464	14	3	revealed	reveal	VERB
fumecheng-10464	14	4	that	that	SCONJ
fumecheng-10464	14	5	the	the	DET
fumecheng-10464	14	6	exciting	exciting	ADJ
fumecheng-10464	14	7	external	external	ADJ
fumecheng-10464	14	8	force	force	NOUN
fumecheng-10464	14	9	parameter	parameter	NOUN
fumecheng-10464	14	10	plays	play	VERB
fumecheng-10464	14	11	a	a	DET
fumecheng-10464	14	12	destabilizing	destabilizing	ADJ
fumecheng-10464	14	13	role	role	NOUN
fumecheng-10464	14	14	.	.	PUNCT
fumecheng-10464	15	1	furthermore	furthermore	ADV
fumecheng-10464	15	2	,	,	PUNCT
fumecheng-10464	15	3	both	both	PRON
fumecheng-10464	15	4	of	of	ADP
fumecheng-10464	15	5	the	the	DET
fumecheng-10464	15	6	frequency	frequency	NOUN
fumecheng-10464	15	7	of	of	ADP
fumecheng-10464	15	8	the	the	DET
fumecheng-10464	15	9	excited	excited	ADJ
fumecheng-10464	15	10	force	force	NOUN
fumecheng-10464	15	11	and	and	CCONJ
fumecheng-10464	15	12	the	the	DET
fumecheng-10464	15	13	stiffness	stiffness	ADJ
fumecheng-10464	15	14	parameter	parameter	NOUN
fumecheng-10464	15	15	,	,	PUNCT
fumecheng-10464	15	16	execute	execute	VERB
fumecheng-10464	15	17	a	a	DET
fumecheng-10464	15	18	dual	dual	ADJ
fumecheng-10464	15	19	role	role	NOUN
fumecheng-10464	15	20	in	in	ADP
fumecheng-10464	15	21	the	the	DET
fumecheng-10464	15	22	stability	stability	NOUN
fumecheng-10464	15	23	picture	picture	NOUN
fumecheng-10464	15	24	.	.	PUNCT
fumecheng-10464	16	1	key	key	ADJ
fumecheng-10464	16	2	words	word	NOUN
fumecheng-10464	16	3	:	:	PUNCT
fumecheng-10464	16	4	fractal	fractal	ADJ
fumecheng-10464	16	5	vibration	vibration	NOUN
fumecheng-10464	16	6	theory	theory	NOUN
fumecheng-10464	16	7	,	,	PUNCT
fumecheng-10464	16	8	duffing	duffing	NOUN
fumecheng-10464	16	9	-	-	PUNCT
fumecheng-10464	16	10	van	van	PROPN
fumecheng-10464	16	11	der	der	ADJ
fumecheng-10464	16	12	pol	pol	PROPN
fumecheng-10464	16	13	oscillator	oscillator	NOUN
fumecheng-10464	16	14	,	,	PUNCT
fumecheng-10464	16	15	homotopy	homotopy	VERB
fumecheng-10464	16	16	perturbation	perturbation	NOUN
fumecheng-10464	16	17	method	method	NOUN
fumecheng-10464	16	18	,	,	PUNCT
fumecheng-10464	16	19	expanded	expand	VERB
fumecheng-10464	16	20	frequency	frequency	NOUN
fumecheng-10464	16	21	analysis	analysis	NOUN
fumecheng-10464	16	22	,	,	PUNCT
fumecheng-10464	16	23	linearized	linearize	VERB
fumecheng-10464	16	24	stability	stability	NOUN
fumecheng-10464	16	25	theory	theory	NOUN
fumecheng-10464	16	26	,	,	PUNCT
fumecheng-10464	16	27	multiple	multiple	ADJ
fumecheng-10464	16	28	timescales	timescale	NOUN
fumecheng-10464	16	29	technique	technique	NOUN
fumecheng-10464	16	30	received	receive	VERB
fumecheng-10464	16	31	january	january	PROPN
fumecheng-10464	16	32	18	18	NUM
fumecheng-10464	16	33	,	,	PUNCT
fumecheng-10464	16	34	2022	2022	NUM
fumecheng-10464	16	35	/	/	SYM
fumecheng-10464	16	36	accepted	accept	VERB
fumecheng-10464	16	37	february	february	PROPN
fumecheng-10464	16	38	12	12	NUM
fumecheng-10464	16	39	,	,	PUNCT
fumecheng-10464	16	40	2022	2022	NUM
fumecheng-10464	16	41	corresponding	correspond	VERB
fumecheng-10464	16	42	author	author	NOUN
fumecheng-10464	16	43	:	:	PUNCT
fumecheng-10464	16	44	ji	ji	PROPN
fumecheng-10464	16	45	-	-	PROPN
fumecheng-10464	16	46	huan	huan	PROPN
fumecheng-10464	16	47	he	he	PRON
fumecheng-10464	16	48	school	school	NOUN
fumecheng-10464	16	49	of	of	ADP
fumecheng-10464	16	50	civil	civil	ADJ
fumecheng-10464	16	51	engineering	engineering	NOUN
fumecheng-10464	16	52	,	,	PUNCT
fumecheng-10464	16	53	xi’an	xi’an	PROPN
fumecheng-10464	16	54	university	university	PROPN
fumecheng-10464	16	55	of	of	ADP
fumecheng-10464	16	56	architecture	architecture	NOUN
fumecheng-10464	16	57	&	&	CCONJ
fumecheng-10464	16	58	technology	technology	NOUN
fumecheng-10464	16	59	,	,	PUNCT
fumecheng-10464	16	60	xi’an	xi’an	PROPN
fumecheng-10464	16	61	710055	710055	NUM
fumecheng-10464	16	62	,	,	PUNCT
fumecheng-10464	16	63	china	china	PROPN
fumecheng-10464	16	64	e	e	PROPN
fumecheng-10464	16	65	-	-	NOUN
fumecheng-10464	16	66	mail	mail	NOUN
fumecheng-10464	16	67	:	:	PUNCT
fumecheng-10464	16	68	hejihuan@suda.edu.cn	hejihuan@suda.edu.cn	NOUN
fumecheng-10464	16	69	2	2	NUM
fumecheng-10464	16	70	j.-h	j.-h	NOUN
fumecheng-10464	16	71	.	.	PUNCT
fumecheng-10464	17	1	he	he	PRON
fumecheng-10464	17	2	,	,	PUNCT
fumecheng-10464	17	3	g.	g.	PROPN
fumecheng-10464	17	4	m.	m.	PROPN
fumecheng-10464	17	5	moatimid	moatimid	PROPN
fumecheng-10464	17	6	,	,	PUNCT
fumecheng-10464	17	7	m.	m.	PROPN
fumecheng-10464	17	8	h.	h.	PROPN
fumecheng-10464	17	9	zekry	zekry	PROPN
fumecheng-10464	17	10	1	1	X
fumecheng-10464	17	11	.	.	PUNCT
fumecheng-10464	18	1	introduction	introduction	NOUN
fumecheng-10464	18	2	the	the	DET
fumecheng-10464	18	3	fractal	fractal	ADJ
fumecheng-10464	18	4	vibration	vibration	NOUN
fumecheng-10464	18	5	theory	theory	NOUN
fumecheng-10464	18	6	has	have	AUX
fumecheng-10464	18	7	become	become	VERB
fumecheng-10464	18	8	a	a	DET
fumecheng-10464	18	9	significant	significant	ADJ
fumecheng-10464	18	10	topic	topic	NOUN
fumecheng-10464	18	11	in	in	ADP
fumecheng-10464	18	12	both	both	DET
fumecheng-10464	18	13	mathematics	mathematic	NOUN
fumecheng-10464	18	14	and	and	CCONJ
fumecheng-10464	18	15	mechanical	mechanical	ADJ
fumecheng-10464	18	16	engineering	engineering	NOUN
fumecheng-10464	18	17	.	.	PUNCT
fumecheng-10464	19	1	the	the	DET
fumecheng-10464	19	2	smart	smart	ADJ
fumecheng-10464	19	3	receptor	receptor	NOUN
fumecheng-10464	19	4	system	system	NOUN
fumecheng-10464	19	5	of	of	ADP
fumecheng-10464	19	6	a	a	DET
fumecheng-10464	19	7	three	three	NUM
fumecheng-10464	19	8	-	-	PUNCT
fumecheng-10464	19	9	dimensional	dimensional	ADJ
fumecheng-10464	19	10	printing	printing	NOUN
fumecheng-10464	19	11	processing	processing	NOUN
fumecheng-10464	19	12	can	can	AUX
fumecheng-10464	19	13	be	be	AUX
fumecheng-10464	19	14	exactly	exactly	ADV
fumecheng-10464	19	15	controlled	control	VERB
fumecheng-10464	19	16	by	by	ADP
fumecheng-10464	19	17	the	the	DET
fumecheng-10464	19	18	gecko	gecko	NOUN
fumecheng-10464	19	19	-	-	PUNCT
fumecheng-10464	19	20	like	like	ADJ
fumecheng-10464	19	21	fractal	fractal	ADJ
fumecheng-10464	19	22	vibration	vibration	NOUN
fumecheng-10464	19	23	system	system	NOUN
fumecheng-10464	19	24	[	[	X
fumecheng-10464	19	25	1	1	NUM
fumecheng-10464	19	26	]	]	PUNCT
fumecheng-10464	19	27	.	.	PUNCT
fumecheng-10464	20	1	the	the	DET
fumecheng-10464	20	2	fractal	fractal	ADJ
fumecheng-10464	20	3	toda	toda	PROPN
fumecheng-10464	20	4	oscillator	oscillator	PROPN
fumecheng-10464	20	5	exhibits	exhibit	VERB
fumecheng-10464	20	6	some	some	DET
fumecheng-10464	20	7	special	special	ADJ
fumecheng-10464	20	8	properties	property	NOUN
fumecheng-10464	20	9	,	,	PUNCT
fumecheng-10464	20	10	which	which	PRON
fumecheng-10464	20	11	the	the	DET
fumecheng-10464	20	12	traditional	traditional	ADJ
fumecheng-10464	20	13	vibration	vibration	NOUN
fumecheng-10464	20	14	theory	theory	NOUN
fumecheng-10464	20	15	can	can	AUX
fumecheng-10464	20	16	not	not	PART
fumecheng-10464	20	17	account	account	VERB
fumecheng-10464	20	18	for	for	ADP
fumecheng-10464	20	19	[	[	X
fumecheng-10464	20	20	2	2	NUM
fumecheng-10464	20	21	]	]	PUNCT
fumecheng-10464	20	22	.	.	PUNCT
fumecheng-10464	21	1	the	the	DET
fumecheng-10464	21	2	pull	pull	NOUN
fumecheng-10464	21	3	-	-	PUNCT
fumecheng-10464	21	4	in	in	ADP
fumecheng-10464	21	5	instability	instability	NOUN
fumecheng-10464	21	6	can	can	AUX
fumecheng-10464	21	7	be	be	AUX
fumecheng-10464	21	8	completely	completely	ADV
fumecheng-10464	21	9	eliminated	eliminate	VERB
fumecheng-10464	21	10	for	for	ADP
fumecheng-10464	21	11	an	an	DET
fumecheng-10464	21	12	electrostatic	electrostatic	ADJ
fumecheng-10464	21	13	nano	nano	NOUN
fumecheng-10464	21	14	/	/	SYM
fumecheng-10464	21	15	micro	micro	NOUN
fumecheng-10464	21	16	-	-	NOUN
fumecheng-10464	21	17	electromechanical	electromechanical	ADJ
fumecheng-10464	21	18	(	(	PUNCT
fumecheng-10464	21	19	n	n	CCONJ
fumecheng-10464	21	20	/	/	SYM
fumecheng-10464	21	21	mems	mem	NOUN
fumecheng-10464	21	22	)	)	PUNCT
fumecheng-10464	21	23	system	system	NOUN
fumecheng-10464	21	24	by	by	ADP
fumecheng-10464	21	25	suitably	suitably	ADV
fumecheng-10464	21	26	controlling	control	VERB
fumecheng-10464	21	27	the	the	DET
fumecheng-10464	21	28	fractal	fractal	ADJ
fumecheng-10464	21	29	vibration	vibration	NOUN
fumecheng-10464	21	30	system	system	NOUN
fumecheng-10464	21	31	[	[	X
fumecheng-10464	21	32	3	3	NUM
fumecheng-10464	21	33	-	-	SYM
fumecheng-10464	21	34	5	5	NUM
fumecheng-10464	21	35	]	]	PUNCT
fumecheng-10464	21	36	.	.	PUNCT
fumecheng-10464	22	1	the	the	DET
fumecheng-10464	22	2	nonlinear	nonlinear	ADJ
fumecheng-10464	22	3	wave	wave	NOUN
fumecheng-10464	22	4	travelling	travel	VERB
fumecheng-10464	22	5	in	in	ADP
fumecheng-10464	22	6	a	a	DET
fumecheng-10464	22	7	fractal	fractal	ADJ
fumecheng-10464	22	8	space	space	NOUN
fumecheng-10464	22	9	can	can	AUX
fumecheng-10464	22	10	be	be	AUX
fumecheng-10464	22	11	converted	convert	VERB
fumecheng-10464	22	12	into	into	ADP
fumecheng-10464	22	13	a	a	DET
fumecheng-10464	22	14	fractal	fractal	ADJ
fumecheng-10464	22	15	oscillator	oscillator	NOUN
fumecheng-10464	22	16	,	,	PUNCT
fumecheng-10464	22	17	and	and	CCONJ
fumecheng-10464	22	18	some	some	DET
fumecheng-10464	22	19	fascinating	fascinating	ADJ
fumecheng-10464	22	20	properties	property	NOUN
fumecheng-10464	22	21	are	be	AUX
fumecheng-10464	22	22	revealed	reveal	VERB
fumecheng-10464	22	23	[	[	X
fumecheng-10464	22	24	6	6	NUM
fumecheng-10464	22	25	]	]	PUNCT
fumecheng-10464	22	26	.	.	PUNCT
fumecheng-10464	23	1	the	the	DET
fumecheng-10464	23	2	fractal	fractal	ADJ
fumecheng-10464	23	3	vibration	vibration	NOUN
fumecheng-10464	23	4	theory	theory	NOUN
fumecheng-10464	23	5	provides	provide	VERB
fumecheng-10464	23	6	an	an	DET
fumecheng-10464	23	7	effective	effective	ADJ
fumecheng-10464	23	8	tool	tool	NOUN
fumecheng-10464	23	9	for	for	ADP
fumecheng-10464	23	10	studying	study	VERB
fumecheng-10464	23	11	various	various	ADJ
fumecheng-10464	23	12	unusual	unusual	ADJ
fumecheng-10464	23	13	phenomena	phenomena	NOUN
fumecheng-10464	23	14	under	under	ADP
fumecheng-10464	23	15	the	the	DET
fumecheng-10464	23	16	micro	micro	NOUN
fumecheng-10464	23	17	-	-	NOUN
fumecheng-10464	23	18	gravity	gravity	ADJ
fumecheng-10464	23	19	condition	condition	NOUN
fumecheng-10464	23	20	[	[	X
fumecheng-10464	23	21	7	7	NUM
fumecheng-10464	23	22	-	-	SYM
fumecheng-10464	23	23	9	9	NUM
fumecheng-10464	23	24	]	]	PUNCT
fumecheng-10464	23	25	.	.	PUNCT
fumecheng-10464	24	1	the	the	DET
fumecheng-10464	24	2	fractal	fractal	ADJ
fumecheng-10464	24	3	vibration	vibration	NOUN
fumecheng-10464	24	4	can	can	AUX
fumecheng-10464	24	5	effectively	effectively	ADV
fumecheng-10464	24	6	model	model	VERB
fumecheng-10464	24	7	the	the	DET
fumecheng-10464	24	8	vibration	vibration	NOUN
fumecheng-10464	24	9	arising	arise	VERB
fumecheng-10464	24	10	in	in	ADP
fumecheng-10464	24	11	porous	porous	ADJ
fumecheng-10464	24	12	media	medium	NOUN
fumecheng-10464	24	13	,	,	PUNCT
fumecheng-10464	24	14	and	and	CCONJ
fumecheng-10464	24	15	the	the	DET
fumecheng-10464	24	16	low	low	ADJ
fumecheng-10464	24	17	frequency	frequency	NOUN
fumecheng-10464	24	18	property	property	NOUN
fumecheng-10464	24	19	plays	play	VERB
fumecheng-10464	24	20	an	an	DET
fumecheng-10464	24	21	important	important	ADJ
fumecheng-10464	24	22	role	role	NOUN
fumecheng-10464	24	23	in	in	ADP
fumecheng-10464	24	24	the	the	DET
fumecheng-10464	24	25	anti	anti	ADJ
fumecheng-10464	24	26	-	-	ADJ
fumecheng-10464	24	27	vibration	vibration	ADJ
fumecheng-10464	24	28	design	design	NOUN
fumecheng-10464	24	29	[	[	X
fumecheng-10464	24	30	10	10	NUM
fumecheng-10464	24	31	,	,	PUNCT
fumecheng-10464	24	32	11	11	NUM
fumecheng-10464	24	33	]	]	PUNCT
fumecheng-10464	24	34	.	.	PUNCT
fumecheng-10464	25	1	furthermore	furthermore	ADV
fumecheng-10464	25	2	,	,	PUNCT
fumecheng-10464	25	3	the	the	DET
fumecheng-10464	25	4	fractal	fractal	ADJ
fumecheng-10464	25	5	fangzhu	fangzhu	PROPN
fumecheng-10464	25	6	oscillator	oscillator	NOUN
fumecheng-10464	25	7	explores	explore	VERB
fumecheng-10464	25	8	the	the	DET
fumecheng-10464	25	9	mechanism	mechanism	NOUN
fumecheng-10464	25	10	of	of	ADP
fumecheng-10464	25	11	an	an	DET
fumecheng-10464	25	12	ancient	ancient	ADJ
fumecheng-10464	25	13	technology	technology	NOUN
fumecheng-10464	25	14	for	for	ADP
fumecheng-10464	25	15	the	the	DET
fumecheng-10464	25	16	collection	collection	NOUN
fumecheng-10464	25	17	of	of	ADP
fumecheng-10464	25	18	water	water	NOUN
fumecheng-10464	25	19	from	from	ADP
fumecheng-10464	25	20	air	air	NOUN
fumecheng-10464	25	21	[	[	X
fumecheng-10464	25	22	12	12	NUM
fumecheng-10464	25	23	]	]	PUNCT
fumecheng-10464	25	24	.	.	PUNCT
fumecheng-10464	26	1	much	much	ADJ
fumecheng-10464	26	2	literature	literature	NOUN
fumecheng-10464	26	3	focused	focus	VERB
fumecheng-10464	26	4	on	on	ADP
fumecheng-10464	26	5	simple	simple	ADJ
fumecheng-10464	26	6	fractal	fractal	ADJ
fumecheng-10464	26	7	oscillators	oscillator	NOUN
fumecheng-10464	26	8	[	[	X
fumecheng-10464	26	9	13	13	NUM
fumecheng-10464	26	10	-	-	SYM
fumecheng-10464	26	11	15	15	NUM
fumecheng-10464	26	12	]	]	PUNCT
fumecheng-10464	26	13	,	,	PUNCT
fumecheng-10464	26	14	this	this	DET
fumecheng-10464	26	15	paper	paper	NOUN
fumecheng-10464	26	16	considers	consider	VERB
fumecheng-10464	26	17	a	a	DET
fumecheng-10464	26	18	more	more	ADV
fumecheng-10464	26	19	generalized	generalized	ADJ
fumecheng-10464	26	20	fractal	fractal	ADJ
fumecheng-10464	26	21	vibration	vibration	NOUN
fumecheng-10464	26	22	system	system	NOUN
fumecheng-10464	26	23	in	in	ADP
fumecheng-10464	26	24	the	the	DET
fumecheng-10464	26	25	following	follow	VERB
fumecheng-10464	26	26	form	form	NOUN
fumecheng-10464	26	27	:	:	PUNCT
fumecheng-10464	26	28	2	2	NUM
fumecheng-10464	26	29	2	2	NUM
fumecheng-10464	26	30	3	3	NUM
fumecheng-10464	26	31	2	2	NUM
fumecheng-10464	26	32	(	(	PUNCT
fumecheng-10464	26	33	)	)	PUNCT
fumecheng-10464	26	34	cos	cos	PROPN
fumecheng-10464	26	35	,	,	PUNCT
fumecheng-10464	26	36	d	d	X
fumecheng-10464	26	37	z	z	NOUN
fumecheng-10464	26	38	dz	dz	PROPN
fumecheng-10464	26	39	b	b	PROPN
fumecheng-10464	26	40	cz	cz	PROPN
fumecheng-10464	26	41	az	az	PROPN
fumecheng-10464	26	42	dz	dz	PROPN
fumecheng-10464	26	43	f	f	PROPN
fumecheng-10464	26	44	d	d	PROPN
fumecheng-10464	26	45	d	d	PROPN
fumecheng-10464	26	46			X
fumecheng-10464	26	47			X
fumecheng-10464	26	48			X
fumecheng-10464	26	49			PUNCT
fumecheng-10464	26	50			NOUN
fumecheng-10464	26	51			VERB
fumecheng-10464	26	52	−	−	NOUN
fumecheng-10464	27	1	−	−	PROPN
fumecheng-10464	28	1	+	+	CCONJ
fumecheng-10464	28	2	+	+	CCONJ
fumecheng-10464	28	3	=	=	SYM
fumecheng-10464	28	4	(	(	PUNCT
fumecheng-10464	28	5	1	1	NUM
fumecheng-10464	28	6	)	)	PUNCT
fumecheng-10464	28	7	where	where	SCONJ
fumecheng-10464	28	8	dz	dz	PROPN
fumecheng-10464	28	9	/	/	SYM
fumecheng-10464	28	10	dτα	dτα	PROPN
fumecheng-10464	28	11	is	be	AUX
fumecheng-10464	28	12	the	the	DET
fumecheng-10464	28	13	two	two	NUM
fumecheng-10464	28	14	-	-	PUNCT
fumecheng-10464	28	15	scale	scale	NOUN
fumecheng-10464	28	16	fractal	fractal	ADJ
fumecheng-10464	28	17	derivative	derivative	NOUN
fumecheng-10464	29	1	[	[	X
fumecheng-10464	29	2	16	16	NUM
fumecheng-10464	29	3	and	and	CCONJ
fumecheng-10464	29	4	17	17	NUM
fumecheng-10464	29	5	]	]	PUNCT
fumecheng-10464	29	6	;	;	PUNCT
fumecheng-10464	29	7	z	z	X
fumecheng-10464	29	8	,	,	PUNCT
fumecheng-10464	29	9	τ	τ	PROPN
fumecheng-10464	29	10	,	,	PUNCT
fumecheng-10464	29	11	b	b	PROPN
fumecheng-10464	29	12	,	,	PUNCT
fumecheng-10464	29	13	c	c	NOUN
fumecheng-10464	29	14	,	,	PUNCT
fumecheng-10464	29	15	a	a	DET
fumecheng-10464	29	16	,	,	PUNCT
fumecheng-10464	29	17	d	d	PROPN
fumecheng-10464	29	18	,	,	PUNCT
fumecheng-10464	29	19	f	f	PROPN
fumecheng-10464	29	20	and	and	CCONJ
fumecheng-10464	29	21	ω	ω	PROPN
fumecheng-10464	29	22	are	be	AUX
fumecheng-10464	29	23	displacement	displacement	ADJ
fumecheng-10464	29	24	,	,	PUNCT
fumecheng-10464	29	25	time	time	NOUN
fumecheng-10464	29	26	,	,	PUNCT
fumecheng-10464	29	27	the	the	DET
fumecheng-10464	29	28	coefficient	coefficient	NOUN
fumecheng-10464	29	29	of	of	ADP
fumecheng-10464	29	30	the	the	DET
fumecheng-10464	29	31	damping	damp	VERB
fumecheng-10464	29	32	term	term	NOUN
fumecheng-10464	29	33	,	,	PUNCT
fumecheng-10464	29	34	the	the	DET
fumecheng-10464	29	35	coefficient	coefficient	NOUN
fumecheng-10464	29	36	of	of	ADP
fumecheng-10464	29	37	the	the	DET
fumecheng-10464	29	38	nonlinear	nonlinear	ADJ
fumecheng-10464	29	39	damping	damp	VERB
fumecheng-10464	29	40	term	term	NOUN
fumecheng-10464	29	41	,	,	PUNCT
fumecheng-10464	29	42	the	the	DET
fumecheng-10464	29	43	root	root	NOUN
fumecheng-10464	29	44	of	of	ADP
fumecheng-10464	29	45	natural	natural	ADJ
fumecheng-10464	29	46	frequencies	frequency	NOUN
fumecheng-10464	29	47	,	,	PUNCT
fumecheng-10464	29	48	the	the	DET
fumecheng-10464	29	49	cubic	cubic	ADJ
fumecheng-10464	29	50	stiffness	stiffness	NOUN
fumecheng-10464	29	51	parameter	parameter	NOUN
fumecheng-10464	29	52	,	,	PUNCT
fumecheng-10464	29	53	the	the	DET
fumecheng-10464	29	54	amplitude	amplitude	NOUN
fumecheng-10464	29	55	of	of	ADP
fumecheng-10464	29	56	the	the	DET
fumecheng-10464	29	57	excitation	excitation	NOUN
fumecheng-10464	29	58	force	force	NOUN
fumecheng-10464	29	59	,	,	PUNCT
fumecheng-10464	29	60	and	and	CCONJ
fumecheng-10464	29	61	frequency	frequency	NOUN
fumecheng-10464	29	62	of	of	ADP
fumecheng-10464	29	63	this	this	DET
fumecheng-10464	29	64	excitation	excitation	NOUN
fumecheng-10464	29	65	,	,	PUNCT
fumecheng-10464	29	66	respectively	respectively	ADV
fumecheng-10464	29	67	.	.	PUNCT
fumecheng-10464	30	1	eq	eq	X
fumecheng-10464	30	2	.	.	PUNCT
fumecheng-10464	31	1	(	(	PUNCT
fumecheng-10464	31	2	1	1	X
fumecheng-10464	31	3	)	)	PUNCT
fumecheng-10464	31	4	displays	display	VERB
fumecheng-10464	31	5	a	a	DET
fumecheng-10464	31	6	nonlinear	nonlinear	ADJ
fumecheng-10464	31	7	vibration	vibration	NOUN
fumecheng-10464	31	8	system	system	NOUN
fumecheng-10464	31	9	in	in	ADP
fumecheng-10464	31	10	a	a	DET
fumecheng-10464	31	11	fractal	fractal	ADJ
fumecheng-10464	31	12	space	space	NOUN
fumecheng-10464	31	13	as	as	SCONJ
fumecheng-10464	31	14	discussed	discuss	VERB
fumecheng-10464	31	15	by	by	ADP
fumecheng-10464	31	16	tian	tian	PROPN
fumecheng-10464	31	17	et	et	PROPN
fumecheng-10464	31	18	al	al	PROPN
fumecheng-10464	31	19	.	.	PUNCT
fumecheng-10464	32	1	[	[	X
fumecheng-10464	32	2	3	3	NUM
fumecheng-10464	32	3	-	-	SYM
fumecheng-10464	32	4	5	5	NUM
fumecheng-10464	32	5	]	]	PUNCT
fumecheng-10464	32	6	,	,	PUNCT
fumecheng-10464	32	7	where	where	SCONJ
fumecheng-10464	32	8	the	the	DET
fumecheng-10464	32	9	air	air	NOUN
fumecheng-10464	32	10	is	be	AUX
fumecheng-10464	32	11	considered	consider	VERB
fumecheng-10464	32	12	as	as	ADP
fumecheng-10464	32	13	a	a	DET
fumecheng-10464	32	14	porous	porous	ADJ
fumecheng-10464	32	15	medium	medium	NOUN
fumecheng-10464	32	16	and	and	CCONJ
fumecheng-10464	32	17	the	the	DET
fumecheng-10464	32	18	fractal	fractal	ADJ
fumecheng-10464	32	19	dimension	dimension	NOUN
fumecheng-10464	32	20	α	α	PROPN
fumecheng-10464	32	21	reflects	reflect	VERB
fumecheng-10464	32	22	the	the	DET
fumecheng-10464	32	23	air	air	NOUN
fumecheng-10464	32	24	distribution	distribution	NOUN
fumecheng-10464	32	25	.	.	PUNCT
fumecheng-10464	33	1	when	when	SCONJ
fumecheng-10464	33	2	it	it	PRON
fumecheng-10464	33	3	vibrates	vibrate	VERB
fumecheng-10464	33	4	in	in	ADP
fumecheng-10464	33	5	a	a	DET
fumecheng-10464	33	6	vacuum	vacuum	NOUN
fumecheng-10464	33	7	,	,	PUNCT
fumecheng-10464	33	8	one	one	NUM
fumecheng-10464	33	9	has	have	VERB
fumecheng-10464	33	10	α=1	α=1	X
fumecheng-10464	33	11	.	.	PUNCT
fumecheng-10464	34	1	when	when	SCONJ
fumecheng-10464	34	2	f	f	PROPN
fumecheng-10464	34	3	=	=	SYM
fumecheng-10464	34	4	b	b	NOUN
fumecheng-10464	34	5	=	=	NOUN
fumecheng-10464	34	6	c=0	c=0	NOUN
fumecheng-10464	34	7	,	,	PUNCT
fumecheng-10464	34	8	eq	eq	NOUN
fumecheng-10464	34	9	.	.	PUNCT
fumecheng-10464	34	10	(	(	PUNCT
fumecheng-10464	34	11	1	1	X
fumecheng-10464	34	12	)	)	PUNCT
fumecheng-10464	34	13	becomes	become	VERB
fumecheng-10464	34	14	the	the	DET
fumecheng-10464	34	15	fractal	fractal	ADJ
fumecheng-10464	34	16	duffing	duffing	NOUN
fumecheng-10464	34	17	oscillator	oscillator	NOUN
fumecheng-10464	34	18	[	[	X
fumecheng-10464	34	19	1	1	NUM
fumecheng-10464	34	20	and	and	CCONJ
fumecheng-10464	34	21	13	13	NUM
fumecheng-10464	34	22	-	-	SYM
fumecheng-10464	34	23	15	15	NUM
fumecheng-10464	34	24	]	]	PUNCT
fumecheng-10464	34	25	,	,	PUNCT
fumecheng-10464	34	26	which	which	PRON
fumecheng-10464	34	27	can	can	AUX
fumecheng-10464	34	28	model	model	VERB
fumecheng-10464	34	29	the	the	DET
fumecheng-10464	34	30	nonlinear	nonlinear	ADJ
fumecheng-10464	34	31	vibration	vibration	NOUN
fumecheng-10464	34	32	arising	arise	VERB
fumecheng-10464	34	33	in	in	ADP
fumecheng-10464	34	34	a	a	DET
fumecheng-10464	34	35	three	three	NUM
fumecheng-10464	34	36	-	-	PUNCT
fumecheng-10464	34	37	dimensional	dimensional	ADJ
fumecheng-10464	34	38	printing	printing	NOUN
fumecheng-10464	34	39	technology	technology	NOUN
fumecheng-10464	34	40	,	,	PUNCT
fumecheng-10464	34	41	concrete	concrete	ADJ
fumecheng-10464	34	42	vibration	vibration	NOUN
fumecheng-10464	34	43	and	and	CCONJ
fumecheng-10464	34	44	other	other	ADJ
fumecheng-10464	34	45	applications	application	NOUN
fumecheng-10464	34	46	.	.	PUNCT
fumecheng-10464	35	1	for	for	ADP
fumecheng-10464	35	2	more	more	ADJ
fumecheng-10464	35	3	convenience	convenience	NOUN
fumecheng-10464	35	4	,	,	PUNCT
fumecheng-10464	35	5	the	the	DET
fumecheng-10464	35	6	graph	graph	NOUN
fumecheng-10464	35	7	x(	x(	NOUN
fumecheng-10464	35	8	)	)	PUNCT
fumecheng-10464	36	1	=	=	PUNCT
fumecheng-10464	37	1	cos	cos	NOUN
fumecheng-10464	37	2	α	α	NOUN
fumecheng-10464	37	3	will	will	AUX
fumecheng-10464	37	4	be	be	AUX
fumecheng-10464	37	5	plotted	plot	VERB
fumecheng-10464	37	6	for	for	ADP
fumecheng-10464	37	7	various	various	ADJ
fumecheng-10464	37	8	values	value	NOUN
fumecheng-10464	37	9	of	of	ADP
fumecheng-10464	37	10	the	the	DET
fumecheng-10464	37	11	parameter	parameter	NOUN
fumecheng-10464	37	12	α	α	PROPN
fumecheng-10464	37	13	in	in	ADP
fumecheng-10464	37	14	fig	fig	NOUN
fumecheng-10464	37	15	.	.	PUNCT
fumecheng-10464	38	1	1	1	X
fumecheng-10464	38	2	.	.	X
fumecheng-10464	39	1	it	it	PRON
fumecheng-10464	39	2	is	be	AUX
fumecheng-10464	39	3	obvious	obvious	ADJ
fumecheng-10464	39	4	that	that	SCONJ
fumecheng-10464	39	5	the	the	DET
fumecheng-10464	39	6	periodic	periodic	ADJ
fumecheng-10464	39	7	solution	solution	NOUN
fumecheng-10464	39	8	becomes	become	VERB
fumecheng-10464	39	9	an	an	DET
fumecheng-10464	39	10	asymptotic	asymptotic	ADJ
fumecheng-10464	39	11	one	one	NOUN
fumecheng-10464	39	12	.	.	PUNCT
fumecheng-10464	40	1	when	when	SCONJ
fumecheng-10464	40	2	α=1	α=1	X
fumecheng-10464	40	3	,	,	PUNCT
fumecheng-10464	40	4	eq	eq	NOUN
fumecheng-10464	40	5	.	.	PUNCT
fumecheng-10464	40	6	(	(	PUNCT
fumecheng-10464	40	7	1	1	X
fumecheng-10464	40	8	)	)	PUNCT
fumecheng-10464	40	9	reflects	reflect	VERB
fumecheng-10464	40	10	the	the	DET
fumecheng-10464	40	11	forced	force	VERB
fumecheng-10464	40	12	duffing	duffing	NOUN
fumecheng-10464	40	13	-van	-van	DET
fumecheng-10464	40	14	der	der	ADJ
fumecheng-10464	40	15	pol	pol	PROPN
fumecheng-10464	40	16	driven	drive	VERB
fumecheng-10464	40	17	oscillator	oscillator	NOUN
fumecheng-10464	40	18	.	.	PUNCT
fumecheng-10464	41	1	in	in	ADP
fumecheng-10464	41	2	view	view	NOUN
fumecheng-10464	41	3	of	of	ADP
fumecheng-10464	41	4	the	the	DET
fumecheng-10464	41	5	two	two	NUM
fumecheng-10464	41	6	-	-	PUNCT
fumecheng-10464	41	7	scale	scale	NOUN
fumecheng-10464	41	8	transforms	transform	VERB
fumecheng-10464	41	9	[	[	X
fumecheng-10464	41	10	16	16	NUM
fumecheng-10464	41	11	]	]	PUNCT
fumecheng-10464	41	12	,	,	PUNCT
fumecheng-10464	41	13	one	one	PRON
fumecheng-10464	41	14	gets	get	VERB
fumecheng-10464	41	15	z	z	NOUN
fumecheng-10464	41	16	=	=	SYM
fumecheng-10464	41	17	x√b	x√b	NOUN
fumecheng-10464	41	18	/	/	SYM
fumecheng-10464	41	19	c	c	NOUN
fumecheng-10464	41	20	,	,	PUNCT
fumecheng-10464	41	21	τα	τα	NOUN
fumecheng-10464	41	22	=	=	NOUN
fumecheng-10464	41	23	t/√a	t/√a	NOUN
fumecheng-10464	41	24	,	,	PUNCT
fumecheng-10464	41	25	b=µ√a	b=µ√a	NOUN
fumecheng-10464	41	26	and	and	CCONJ
fumecheng-10464	41	27	ω	ω	NUM
fumecheng-10464	41	28	=	=	PROPN
fumecheng-10464	41	29	ω√a	ω√a	PROPN
fumecheng-10464	41	30	to	to	PART
fumecheng-10464	41	31	convert	convert	VERB
fumecheng-10464	41	32	eq	eq	ADP
fumecheng-10464	41	33	.	.	PUNCT
fumecheng-10464	42	1	(	(	PUNCT
fumecheng-10464	42	2	1	1	NUM
fumecheng-10464	42	3	)	)	PUNCT
fumecheng-10464	42	4	into	into	ADP
fumecheng-10464	42	5	the	the	DET
fumecheng-10464	42	6	following	follow	VERB
fumecheng-10464	42	7	form	form	NOUN
fumecheng-10464	42	8	:	:	PUNCT
fumecheng-10464	42	9	2	2	NUM
fumecheng-10464	42	10	3(1	3(1	NUM
fumecheng-10464	42	11	)	)	PUNCT
fumecheng-10464	43	1	cosx	cosx	NOUN
fumecheng-10464	43	2	x	x	PUNCT
fumecheng-10464	43	3	x	x	PUNCT
fumecheng-10464	43	4	x	x	PUNCT
fumecheng-10464	43	5	x	x	SYM
fumecheng-10464	43	6	f	f	NOUN
fumecheng-10464	43	7	t	t	NUM
fumecheng-10464	43	8	−	−	NOUN
fumecheng-10464	43	9	−	−	PROPN
fumecheng-10464	44	1	+	+	CCONJ
fumecheng-10464	44	2	+	+	CCONJ
fumecheng-10464	44	3	=	=	ADJ
fumecheng-10464	44	4			PROPN
fumecheng-10464	44	5	,	,	PUNCT
fumecheng-10464	44	6	(	(	PUNCT
fumecheng-10464	44	7	2	2	X
fumecheng-10464	44	8	)	)	PUNCT
fumecheng-10464	44	9	where	where	SCONJ
fumecheng-10464	44	10	β	β	X
fumecheng-10464	44	11	=	=	NOUN
fumecheng-10464	44	12	bd	bd	PROPN
fumecheng-10464	44	13	/	/	SYM
fumecheng-10464	44	14	ac	ac	PROPN
fumecheng-10464	44	15	,	,	PUNCT
fumecheng-10464	44	16	f=(f	f=(f	NOUN
fumecheng-10464	44	17	/	/	SYM
fumecheng-10464	44	18	a)√c	a)√c	NOUN
fumecheng-10464	44	19	/	/	SYM
fumecheng-10464	44	20	b	b	NOUN
fumecheng-10464	44	21	,	,	PUNCT
fumecheng-10464	44	22	,	,	PUNCT
fumecheng-10464	44	23	and	and	CCONJ
fumecheng-10464	44	24	the	the	DET
fumecheng-10464	44	25	dot	dot	NOUN
fumecheng-10464	44	26	is	be	AUX
fumecheng-10464	44	27	the	the	DET
fumecheng-10464	44	28	derivative	derivative	NOUN
fumecheng-10464	44	29	with	with	ADP
fumecheng-10464	44	30	respect	respect	NOUN
fumecheng-10464	44	31	to	to	ADP
fumecheng-10464	44	32	t.	t.	PROPN
fumecheng-10464	44	33	the	the	DET
fumecheng-10464	44	34	two	two	NUM
fumecheng-10464	44	35	-	-	PUNCT
fumecheng-10464	44	36	scale	scale	NOUN
fumecheng-10464	44	37	fractal	fractal	ADJ
fumecheng-10464	44	38	theory	theory	NOUN
fumecheng-10464	44	39	is	be	AUX
fumecheng-10464	44	40	now	now	ADV
fumecheng-10464	44	41	widely	widely	ADV
fumecheng-10464	44	42	used	use	VERB
fumecheng-10464	44	43	to	to	PART
fumecheng-10464	44	44	model	model	VERB
fumecheng-10464	44	45	various	various	ADJ
fumecheng-10464	44	46	phenomena	phenomenon	NOUN
fumecheng-10464	44	47	arising	arise	VERB
fumecheng-10464	44	48	in	in	ADP
fumecheng-10464	44	49	porous	porous	ADJ
fumecheng-10464	44	50	media	medium	NOUN
fumecheng-10464	44	51	or	or	CCONJ
fumecheng-10464	44	52	un	un	ADJ
fumecheng-10464	44	53	-	-	ADJ
fumecheng-10464	44	54	smooth	smooth	ADJ
fumecheng-10464	44	55	boundaries	boundary	NOUN
fumecheng-10464	44	56	.	.	PUNCT
fumecheng-10464	45	1	the	the	DET
fumecheng-10464	45	2	fractal	fractal	ADJ
fumecheng-10464	45	3	rheological	rheological	ADJ
fumecheng-10464	45	4	model	model	NOUN
fumecheng-10464	45	5	gives	give	VERB
fumecheng-10464	45	6	a	a	DET
fumecheng-10464	45	7	quick	quick	ADJ
fumecheng-10464	45	8	physical	physical	ADJ
fumecheng-10464	45	9	insight	insight	NOUN
fumecheng-10464	45	10	into	into	ADP
fumecheng-10464	45	11	the	the	DET
fumecheng-10464	45	12	rheological	rheological	ADJ
fumecheng-10464	45	13	property	property	NOUN
fumecheng-10464	45	14	of	of	ADP
fumecheng-10464	45	15	a	a	DET
fumecheng-10464	45	16	non	non	ADJ
fumecheng-10464	45	17	-	-	ADJ
fumecheng-10464	45	18	newtonian	newtonian	ADJ
fumecheng-10464	45	19	fluid	fluid	NOUN
fumecheng-10464	45	20	[	[	X
fumecheng-10464	45	21	18	18	NUM
fumecheng-10464	45	22	and	and	CCONJ
fumecheng-10464	45	23	19	19	NUM
fumecheng-10464	45	24	]	]	PUNCT
fumecheng-10464	45	25	.	.	PUNCT
fumecheng-10464	46	1	the	the	DET
fumecheng-10464	46	2	fractal	fractal	ADJ
fumecheng-10464	46	3	approach	approach	NOUN
fumecheng-10464	46	4	provides	provide	VERB
fumecheng-10464	46	5	a	a	DET
fumecheng-10464	46	6	simple	simple	ADJ
fumecheng-10464	46	7	and	and	CCONJ
fumecheng-10464	46	8	good	good	ADJ
fumecheng-10464	46	9	tool	tool	NOUN
fumecheng-10464	46	10	for	for	ADP
fumecheng-10464	46	11	mechanical	mechanical	ADJ
fumecheng-10464	46	12	and	and	CCONJ
fumecheng-10464	46	13	electrical	electrical	ADJ
fumecheng-10464	46	14	properties	property	NOUN
fumecheng-10464	46	15	of	of	ADP
fumecheng-10464	46	16	composite	composite	ADJ
fumecheng-10464	46	17	materials	material	NOUN
fumecheng-10464	46	18	[	[	X
fumecheng-10464	46	19	20	20	NUM
fumecheng-10464	46	20	]	]	PUNCT
fumecheng-10464	46	21	.	.	PUNCT
fumecheng-10464	47	1	the	the	DET
fumecheng-10464	47	2	fractal	fractal	ADJ
fumecheng-10464	47	3	two	two	NUM
fumecheng-10464	47	4	-	-	PUNCT
fumecheng-10464	47	5	phase	phase	NOUN
fumecheng-10464	47	6	flow	flow	NOUN
fumecheng-10464	47	7	model	model	NOUN
fumecheng-10464	47	8	can	can	AUX
fumecheng-10464	47	9	figure	figure	VERB
fumecheng-10464	47	10	out	out	ADP
fumecheng-10464	47	11	the	the	DET
fumecheng-10464	47	12	hidden	hide	VERB
fumecheng-10464	47	13	properties	property	NOUN
fumecheng-10464	47	14	in	in	ADP
fumecheng-10464	47	15	a	a	DET
fumecheng-10464	47	16	polymer	polymer	NOUN
fumecheng-10464	47	17	filling	filling	NOUN
fumecheng-10464	47	18	process	process	NOUN
fumecheng-10464	47	19	,	,	PUNCT
fumecheng-10464	47	20	which	which	PRON
fumecheng-10464	47	21	can	can	AUX
fumecheng-10464	47	22	not	not	PART
fumecheng-10464	47	23	be	be	AUX
fumecheng-10464	47	24	revealed	reveal	VERB
fumecheng-10464	47	25	by	by	ADP
fumecheng-10464	47	26	the	the	DET
fumecheng-10464	47	27	different	different	ADJ
fumecheng-10464	47	28	models	model	NOUN
fumecheng-10464	47	29	[	[	X
fumecheng-10464	47	30	21	21	NUM
fumecheng-10464	47	31	-	-	SYM
fumecheng-10464	47	32	23	23	NUM
fumecheng-10464	47	33	]	]	PUNCT
fumecheng-10464	47	34	.	.	PUNCT
fumecheng-10464	48	1	now	now	ADV
fumecheng-10464	48	2	,	,	PUNCT
fumecheng-10464	48	3	the	the	DET
fumecheng-10464	48	4	fractal	fractal	ADJ
fumecheng-10464	48	5	variational	variational	ADJ
fumecheng-10464	48	6	principle	principle	NOUN
fumecheng-10464	48	7	has	have	AUX
fumecheng-10464	48	8	become	become	VERB
fumecheng-10464	48	9	a	a	DET
fumecheng-10464	48	10	predominant	predominant	ADJ
fumecheng-10464	48	11	topic	topic	NOUN
fumecheng-10464	48	12	in	in	ADP
fumecheng-10464	48	13	the	the	DET
fumecheng-10464	48	14	forced	force	VERB
fumecheng-10464	48	15	nonlinear	nonlinear	ADJ
fumecheng-10464	48	16	oscillator	oscillator	NOUN
fumecheng-10464	48	17	in	in	ADP
fumecheng-10464	48	18	a	a	DET
fumecheng-10464	48	19	fractal	fractal	ADJ
fumecheng-10464	48	20	space	space	NOUN
fumecheng-10464	48	21	3	3	NUM
fumecheng-10464	48	22	establishment	establishment	NOUN
fumecheng-10464	48	23	of	of	ADP
fumecheng-10464	48	24	governing	govern	VERB
fumecheng-10464	48	25	equations	equation	NOUN
fumecheng-10464	48	26	in	in	ADP
fumecheng-10464	48	27	a	a	DET
fumecheng-10464	48	28	fractal	fractal	ADJ
fumecheng-10464	48	29	space	space	NOUN
fumecheng-10464	48	30	[	[	X
fumecheng-10464	48	31	24	24	NUM
fumecheng-10464	48	32	and	and	CCONJ
fumecheng-10464	48	33	25	25	NUM
fumecheng-10464	48	34	]	]	PUNCT
fumecheng-10464	48	35	.	.	PUNCT
fumecheng-10464	49	1	it	it	PRON
fumecheng-10464	49	2	is	be	AUX
fumecheng-10464	49	3	worthy	worthy	ADJ
fumecheng-10464	49	4	to	to	PART
fumecheng-10464	49	5	observe	observe	VERB
fumecheng-10464	49	6	that	that	SCONJ
fumecheng-10464	49	7	when	when	SCONJ
fumecheng-10464	49	8	µ=0	µ=0	NOUN
fumecheng-10464	49	9	,	,	PUNCT
fumecheng-10464	49	10	eq	eq	NOUN
fumecheng-10464	49	11	.	.	PUNCT
fumecheng-10464	50	1	(	(	PUNCT
fumecheng-10464	50	2	2	2	X
fumecheng-10464	50	3	)	)	PUNCT
fumecheng-10464	50	4	yields	yield	VERB
fumecheng-10464	50	5	the	the	DET
fumecheng-10464	50	6	duffing	duffing	NOUN
fumecheng-10464	50	7	equation	equation	NOUN
fumecheng-10464	50	8	.	.	PUNCT
fumecheng-10464	51	1	simultaneously	simultaneously	ADV
fumecheng-10464	51	2	,	,	PUNCT
fumecheng-10464	51	3	the	the	DET
fumecheng-10464	51	4	cancellation	cancellation	NOUN
fumecheng-10464	51	5	of	of	ADP
fumecheng-10464	51	6	the	the	DET
fumecheng-10464	51	7	parameter	parameter	NOUN
fumecheng-10464	51	8	β	β	PROPN
fumecheng-10464	51	9	results	result	NOUN
fumecheng-10464	51	10	in	in	ADP
fumecheng-10464	51	11	the	the	DET
fumecheng-10464	51	12	vdp	vdp	PROPN
fumecheng-10464	51	13	oscillator	oscillator	NOUN
fumecheng-10464	51	14	.	.	PUNCT
fumecheng-10464	52	1	in	in	ADP
fumecheng-10464	52	2	1920	1920	NUM
fumecheng-10464	52	3	,	,	PUNCT
fumecheng-10464	52	4	van	van	PROPN
fumecheng-10464	52	5	der	der	PROPN
fumecheng-10464	52	6	pol	pol	PROPN
fumecheng-10464	52	7	performed	perform	VERB
fumecheng-10464	52	8	experimental	experimental	ADJ
fumecheng-10464	52	9	studies	study	NOUN
fumecheng-10464	52	10	on	on	ADP
fumecheng-10464	52	11	the	the	DET
fumecheng-10464	52	12	dynamics	dynamic	NOUN
fumecheng-10464	52	13	of	of	ADP
fumecheng-10464	52	14	an	an	DET
fumecheng-10464	52	15	oscillator	oscillator	NOUN
fumecheng-10464	52	16	electrical	electrical	ADJ
fumecheng-10464	52	17	circuit	circuit	NOUN
fumecheng-10464	52	18	.	.	PUNCT
fumecheng-10464	53	1	it	it	PRON
fumecheng-10464	53	2	was	be	AUX
fumecheng-10464	53	3	formulated	formulate	VERB
fumecheng-10464	53	4	by	by	ADP
fumecheng-10464	53	5	a	a	DET
fumecheng-10464	53	6	second	second	ADJ
fumecheng-10464	53	7	-	-	PUNCT
fumecheng-10464	53	8	order	order	NOUN
fumecheng-10464	53	9	nonlinear	nonlinear	ADJ
fumecheng-10464	53	10	differential	differential	ADJ
fumecheng-10464	53	11	equation	equation	NOUN
fumecheng-10464	53	12	,	,	PUNCT
fumecheng-10464	53	13	which	which	PRON
fumecheng-10464	53	14	was	be	AUX
fumecheng-10464	53	15	later	later	ADV
fumecheng-10464	53	16	known	know	VERB
fumecheng-10464	53	17	as	as	ADP
fumecheng-10464	53	18	the	the	DET
fumecheng-10464	53	19	van	van	PROPN
fumecheng-10464	53	20	der	der	PROPN
fumecheng-10464	53	21	pol	pol	PROPN
fumecheng-10464	53	22	oscillator	oscillator	NOUN
fumecheng-10464	53	23	.	.	PUNCT
fumecheng-10464	54	1	alghassab	alghassab	PROPN
fumecheng-10464	54	2	et	et	PROPN
fumecheng-10464	54	3	al	al	PROPN
fumecheng-10464	54	4	.	.	PUNCT
fumecheng-10464	55	1	[	[	X
fumecheng-10464	55	2	26	26	NUM
fumecheng-10464	55	3	]	]	PUNCT
fumecheng-10464	55	4	examined	examine	VERB
fumecheng-10464	55	5	the	the	DET
fumecheng-10464	55	6	duffing	duffing	NOUN
fumecheng-10464	55	7	oscillator	oscillator	NOUN
fumecheng-10464	55	8	together	together	ADV
fumecheng-10464	55	9	with	with	ADP
fumecheng-10464	55	10	the	the	DET
fumecheng-10464	55	11	van	van	PROPN
fumecheng-10464	55	12	der	der	ADJ
fumecheng-10464	55	13	pol	pol	PROPN
fumecheng-10464	55	14	oscillator	oscillator	NOUN
fumecheng-10464	55	15	with	with	ADP
fumecheng-10464	55	16	a	a	DET
fumecheng-10464	55	17	nonlinear	nonlinear	ADJ
fumecheng-10464	55	18	damping	damp	VERB
fumecheng-10464	55	19	term	term	NOUN
fumecheng-10464	55	20	(	(	PUNCT
fumecheng-10464	55	21	dvdp	dvdp	ADJ
fumecheng-10464	55	22	)	)	PUNCT
fumecheng-10464	55	23	.	.	PUNCT
fumecheng-10464	56	1	apart	apart	ADV
fumecheng-10464	56	2	from	from	ADP
fumecheng-10464	56	3	the	the	DET
fumecheng-10464	56	4	linearized	linearize	VERB
fumecheng-10464	56	5	analysis	analysis	NOUN
fumecheng-10464	56	6	,	,	PUNCT
fumecheng-10464	56	7	they	they	PRON
fumecheng-10464	56	8	exploited	exploit	VERB
fumecheng-10464	56	9	the	the	DET
fumecheng-10464	56	10	lyapunov	lyapunov	ADJ
fumecheng-10464	56	11	theory	theory	NOUN
fumecheng-10464	56	12	in	in	ADP
fumecheng-10464	56	13	their	their	PRON
fumecheng-10464	56	14	analysis	analysis	NOUN
fumecheng-10464	56	15	.	.	PUNCT
fumecheng-10464	57	1	zhihong	zhihong	NOUN
fumecheng-10464	57	2	and	and	CCONJ
fumecheng-10464	57	3	shaopu	shaopu	ADJ
fumecheng-10464	57	4	[	[	X
fumecheng-10464	57	5	27	27	NUM
fumecheng-10464	57	6	]	]	PUNCT
fumecheng-10464	57	7	presented	present	VERB
fumecheng-10464	57	8	a	a	DET
fumecheng-10464	57	9	novel	novel	ADJ
fumecheng-10464	57	10	weak	weak	ADJ
fumecheng-10464	57	11	signal	signal	NOUN
fumecheng-10464	57	12	detection	detection	NOUN
fumecheng-10464	57	13	approach	approach	NOUN
fumecheng-10464	57	14	grounded	ground	VERB
fumecheng-10464	57	15	on	on	ADP
fumecheng-10464	57	16	the	the	DET
fumecheng-10464	57	17	dvdp	dvdp	ADJ
fumecheng-10464	57	18	oscillator	oscillator	NOUN
fumecheng-10464	57	19	.	.	PUNCT
fumecheng-10464	58	1	they	they	PRON
fumecheng-10464	58	2	found	find	VERB
fumecheng-10464	58	3	that	that	SCONJ
fumecheng-10464	58	4	the	the	DET
fumecheng-10464	58	5	planned	plan	VERB
fumecheng-10464	58	6	method	method	NOUN
fumecheng-10464	58	7	was	be	AUX
fumecheng-10464	58	8	stronger	strong	ADJ
fumecheng-10464	58	9	than	than	ADP
fumecheng-10464	58	10	the	the	DET
fumecheng-10464	58	11	duffing	duffing	NOUN
fumecheng-10464	58	12	oscillator	oscillator	NOUN
fumecheng-10464	58	13	.	.	PUNCT
fumecheng-10464	59	1	under	under	ADP
fumecheng-10464	59	2	certain	certain	ADJ
fumecheng-10464	59	3	parametric	parametric	ADJ
fumecheng-10464	59	4	conditions	condition	NOUN
fumecheng-10464	59	5	,	,	PUNCT
fumecheng-10464	59	6	gao	gao	PROPN
fumecheng-10464	59	7	and	and	CCONJ
fumecheng-10464	59	8	feng	feng	PROPN
fumecheng-10464	60	1	[	[	X
fumecheng-10464	60	2	28	28	NUM
fumecheng-10464	60	3	]	]	PUNCT
fumecheng-10464	60	4	deduced	deduce	VERB
fumecheng-10464	60	5	the	the	DET
fumecheng-10464	60	6	first	first	ADJ
fumecheng-10464	60	7	integrals	integral	NOUN
fumecheng-10464	60	8	without	without	ADP
fumecheng-10464	60	9	complicated	complicated	ADJ
fumecheng-10464	60	10	computations	computation	NOUN
fumecheng-10464	60	11	of	of	ADP
fumecheng-10464	60	12	the	the	DET
fumecheng-10464	60	13	dvdp	dvdp	NOUN
fumecheng-10464	60	14	.	.	PUNCT
fumecheng-10464	61	1	their	their	PRON
fumecheng-10464	61	2	methodology	methodology	NOUN
fumecheng-10464	61	3	was	be	AUX
fumecheng-10464	61	4	constructed	construct	VERB
fumecheng-10464	61	5	of	of	ADP
fumecheng-10464	61	6	a	a	DET
fumecheng-10464	61	7	series	series	NOUN
fumecheng-10464	61	8	of	of	ADP
fumecheng-10464	61	9	variable	variable	ADJ
fumecheng-10464	61	10	transformations	transformation	NOUN
fumecheng-10464	61	11	with	with	ADP
fumecheng-10464	61	12	the	the	DET
fumecheng-10464	61	13	preller	preller	NOUN
fumecheng-10464	61	14	-	-	PUNCT
fumecheng-10464	61	15	singer	singer	NOUN
fumecheng-10464	61	16	method	method	NOUN
fumecheng-10464	61	17	.	.	PUNCT
fumecheng-10464	62	1	motsa	motsa	NOUN
fumecheng-10464	62	2	and	and	CCONJ
fumecheng-10464	62	3	sibanda	sibanda	ADV
fumecheng-10464	63	1	[	[	X
fumecheng-10464	63	2	29	29	NUM
fumecheng-10464	63	3	]	]	PUNCT
fumecheng-10464	63	4	presented	present	VERB
fumecheng-10464	63	5	a	a	DET
fumecheng-10464	63	6	novel	novel	ADJ
fumecheng-10464	63	7	application	application	NOUN
fumecheng-10464	63	8	of	of	ADP
fumecheng-10464	63	9	the	the	DET
fumecheng-10464	63	10	successive	successive	ADJ
fumecheng-10464	63	11	linearized	linearize	VERB
fumecheng-10464	63	12	method	method	NOUN
fumecheng-10464	63	13	to	to	ADP
fumecheng-10464	63	14	the	the	DET
fumecheng-10464	63	15	classical	classical	ADJ
fumecheng-10464	63	16	dvdp	dvdp	NOUN
fumecheng-10464	63	17	.	.	PUNCT
fumecheng-10464	64	1	they	they	PRON
fumecheng-10464	64	2	obtained	obtain	VERB
fumecheng-10464	64	3	accurate	accurate	ADJ
fumecheng-10464	64	4	values	value	NOUN
fumecheng-10464	64	5	of	of	ADP
fumecheng-10464	64	6	frequency	frequency	NOUN
fumecheng-10464	64	7	and	and	CCONJ
fumecheng-10464	64	8	amplitude	amplitude	NOUN
fumecheng-10464	64	9	.	.	PUNCT
fumecheng-10464	65	1	utilizing	utilize	VERB
fumecheng-10464	65	2	the	the	DET
fumecheng-10464	65	3	homotopy	homotopy	NOUN
fumecheng-10464	65	4	analysis	analysis	NOUN
fumecheng-10464	65	5	method	method	NOUN
fumecheng-10464	65	6	,	,	PUNCT
fumecheng-10464	65	7	cui	cui	NOUN
fumecheng-10464	65	8	et	et	PROPN
fumecheng-10464	65	9	al	al	PROPN
fumecheng-10464	65	10	.	.	PUNCT
fumecheng-10464	66	1	[	[	X
fumecheng-10464	66	2	30	30	NUM
fumecheng-10464	66	3	]	]	PUNCT
fumecheng-10464	66	4	explored	explore	VERB
fumecheng-10464	66	5	a	a	DET
fumecheng-10464	66	6	high	high	ADJ
fumecheng-10464	66	7	accuracy	accuracy	NOUN
fumecheng-10464	66	8	curve	curve	NOUN
fumecheng-10464	66	9	and	and	CCONJ
fumecheng-10464	66	10	solutions	solution	NOUN
fumecheng-10464	66	11	of	of	ADP
fumecheng-10464	66	12	the	the	DET
fumecheng-10464	66	13	dvdp	dvdp	NOUN
fumecheng-10464	66	14	.	.	PUNCT
fumecheng-10464	67	1	their	their	PRON
fumecheng-10464	67	2	stability	stability	NOUN
fumecheng-10464	67	3	analysis	analysis	NOUN
fumecheng-10464	67	4	adopted	adopt	VERB
fumecheng-10464	67	5	the	the	DET
fumecheng-10464	67	6	floquet	floquet	NOUN
fumecheng-10464	67	7	theory	theory	NOUN
fumecheng-10464	67	8	.	.	PUNCT
fumecheng-10464	68	1	additionally	additionally	ADV
fumecheng-10464	68	2	,	,	PUNCT
fumecheng-10464	68	3	their	their	PRON
fumecheng-10464	68	4	results	result	NOUN
fumecheng-10464	68	5	were	be	AUX
fumecheng-10464	68	6	validated	validate	VERB
fumecheng-10464	68	7	in	in	ADP
fumecheng-10464	68	8	light	light	NOUN
fumecheng-10464	68	9	of	of	ADP
fumecheng-10464	68	10	the	the	DET
fumecheng-10464	68	11	spectra	spectra	ADJ
fumecheng-10464	68	12	analysis	analysis	NOUN
fumecheng-10464	68	13	and	and	CCONJ
fumecheng-10464	68	14	bifurcation	bifurcation	NOUN
fumecheng-10464	68	15	theory	theory	NOUN
fumecheng-10464	68	16	.	.	PUNCT
fumecheng-10464	69	1	moatimid	moatimid	PROPN
fumecheng-10464	70	1	[	[	X
fumecheng-10464	70	2	31	31	NUM
fumecheng-10464	70	3	]	]	PUNCT
fumecheng-10464	70	4	examined	examine	VERB
fumecheng-10464	70	5	the	the	DET
fumecheng-10464	70	6	stability	stability	NOUN
fumecheng-10464	70	7	criteria	criterion	NOUN
fumecheng-10464	70	8	of	of	ADP
fumecheng-10464	70	9	the	the	DET
fumecheng-10464	70	10	parametric	parametric	ADJ
fumecheng-10464	70	11	duffing	duffing	NOUN
fumecheng-10464	70	12	oscillator	oscillator	NOUN
fumecheng-10464	70	13	.	.	PUNCT
fumecheng-10464	71	1	the	the	DET
fumecheng-10464	71	2	numerical	numerical	ADJ
fumecheng-10464	71	3	calculations	calculation	NOUN
fumecheng-10464	71	4	showed	show	VERB
fumecheng-10464	71	5	that	that	SCONJ
fumecheng-10464	71	6	the	the	DET
fumecheng-10464	71	7	damper	damper	NOUN
fumecheng-10464	71	8	and	and	CCONJ
fumecheng-10464	71	9	the	the	DET
fumecheng-10464	71	10	stiffness	stiffness	NOUN
fumecheng-10464	71	11	parameters	parameter	NOUN
fumecheng-10464	71	12	have	have	VERB
fumecheng-10464	71	13	a	a	DET
fumecheng-10464	71	14	destabilizing	destabilizing	ADJ
fumecheng-10464	71	15	influence	influence	NOUN
fumecheng-10464	71	16	.	.	PUNCT
fumecheng-10464	72	1	the	the	DET
fumecheng-10464	72	2	study	study	NOUN
fumecheng-10464	72	3	of	of	ADP
fumecheng-10464	72	4	the	the	DET
fumecheng-10464	72	5	parametric	parametric	ADJ
fumecheng-10464	72	6	excited	excited	ADJ
fumecheng-10464	72	7	systems	system	NOUN
fumecheng-10464	72	8	is	be	AUX
fumecheng-10464	72	9	actually	actually	ADV
fumecheng-10464	72	10	imperative	imperative	ADJ
fumecheng-10464	72	11	in	in	ADP
fumecheng-10464	72	12	light	light	NOUN
fumecheng-10464	72	13	of	of	ADP
fumecheng-10464	72	14	external	external	ADJ
fumecheng-10464	72	15	excited	excited	ADJ
fumecheng-10464	72	16	fields	field	NOUN
fumecheng-10464	72	17	.	.	PUNCT
fumecheng-10464	73	1	wei	wei	PROPN
fumecheng-10464	73	2	et	et	PROPN
fumecheng-10464	73	3	al	al	PROPN
fumecheng-10464	73	4	.	.	PUNCT
fumecheng-10464	74	1	[	[	X
fumecheng-10464	74	2	32	32	NUM
fumecheng-10464	74	3	]	]	PUNCT
fumecheng-10464	74	4	examined	examine	VERB
fumecheng-10464	74	5	the	the	DET
fumecheng-10464	74	6	major	major	ADJ
fumecheng-10464	74	7	response	response	NOUN
fumecheng-10464	74	8	of	of	ADP
fumecheng-10464	74	9	the	the	DET
fumecheng-10464	74	10	dvdp	dvdp	ADJ
fumecheng-10464	74	11	to	to	ADP
fumecheng-10464	74	12	collective	collective	ADJ
fumecheng-10464	74	13	deterministic	deterministic	ADJ
fumecheng-10464	74	14	and	and	CCONJ
fumecheng-10464	74	15	arbitrary	arbitrary	ADJ
fumecheng-10464	74	16	parametric	parametric	ADJ
fumecheng-10464	74	17	excitations	excitation	NOUN
fumecheng-10464	74	18	.	.	PUNCT
fumecheng-10464	75	1	they	they	PRON
fumecheng-10464	75	2	employed	employ	VERB
fumecheng-10464	75	3	the	the	DET
fumecheng-10464	75	4	method	method	NOUN
fumecheng-10464	75	5	of	of	ADP
fumecheng-10464	75	6	multiple	multiple	ADJ
fumecheng-10464	75	7	time	time	NOUN
fumecheng-10464	75	8	scales	scale	NOUN
fumecheng-10464	75	9	to	to	PART
fumecheng-10464	75	10	govern	govern	VERB
fumecheng-10464	75	11	the	the	DET
fumecheng-10464	75	12	equations	equation	NOUN
fumecheng-10464	75	13	of	of	ADP
fumecheng-10464	75	14	amplitude	amplitude	NOUN
fumecheng-10464	75	15	and	and	CCONJ
fumecheng-10464	75	16	phase	phase	NOUN
fumecheng-10464	75	17	.	.	PUNCT
fumecheng-10464	76	1	dao	dao	VERB
fumecheng-10464	76	2	et	et	PROPN
fumecheng-10464	76	3	al	al	PROPN
fumecheng-10464	76	4	.	.	PUNCT
fumecheng-10464	77	1	[	[	X
fumecheng-10464	77	2	33	33	NUM
fumecheng-10464	77	3	]	]	PUNCT
fumecheng-10464	77	4	considered	consider	VERB
fumecheng-10464	77	5	the	the	DET
fumecheng-10464	77	6	dvdp	dvdp	PROPN
fumecheng-10464	77	7	under	under	ADP
fumecheng-10464	77	8	the	the	DET
fumecheng-10464	77	9	parametric	parametric	ADJ
fumecheng-10464	77	10	exciting	exciting	ADJ
fumecheng-10464	77	11	force	force	NOUN
fumecheng-10464	77	12	.	.	PUNCT
fumecheng-10464	78	1	they	they	PRON
fumecheng-10464	78	2	evaluated	evaluate	VERB
fumecheng-10464	78	3	the	the	DET
fumecheng-10464	78	4	cases	case	NOUN
fumecheng-10464	78	5	of	of	ADP
fumecheng-10464	78	6	a	a	DET
fumecheng-10464	78	7	small	small	ADJ
fumecheng-10464	78	8	parameter	parameter	NOUN
fumecheng-10464	78	9	quasi	quasi	NOUN
fumecheng-10464	78	10	-	-	NOUN
fumecheng-10464	78	11	linear	linear	ADJ
fumecheng-10464	78	12	as	as	ADV
fumecheng-10464	78	13	well	well	ADV
fumecheng-10464	78	14	as	as	ADP
fumecheng-10464	78	15	the	the	DET
fumecheng-10464	78	16	general	general	ADJ
fumecheng-10464	78	17	case	case	NOUN
fumecheng-10464	78	18	.	.	PUNCT
fumecheng-10464	79	1	han	han	PROPN
fumecheng-10464	79	2	et	et	PROPN
fumecheng-10464	79	3	al	al	PROPN
fumecheng-10464	79	4	.	.	PUNCT
fumecheng-10464	80	1	[	[	X
fumecheng-10464	80	2	34	34	NUM
fumecheng-10464	80	3	]	]	PUNCT
fumecheng-10464	80	4	scrutinized	scrutinize	VERB
fumecheng-10464	80	5	the	the	DET
fumecheng-10464	80	6	effects	effect	NOUN
fumecheng-10464	80	7	of	of	ADP
fumecheng-10464	80	8	a	a	DET
fumecheng-10464	80	9	gradually	gradually	ADV
fumecheng-10464	80	10	changing	change	VERB
fumecheng-10464	80	11	parametric	parametric	ADJ
fumecheng-10464	80	12	excitation	excitation	NOUN
fumecheng-10464	80	13	of	of	ADP
fumecheng-10464	80	14	the	the	DET
fumecheng-10464	80	15	dvdp	dvdp	ADJ
fumecheng-10464	80	16	equation	equation	NOUN
fumecheng-10464	80	17	.	.	PUNCT
fumecheng-10464	81	1	they	they	PRON
fumecheng-10464	81	2	examined	examine	VERB
fumecheng-10464	81	3	the	the	DET
fumecheng-10464	81	4	periodic	periodic	ADJ
fumecheng-10464	81	5	bifurcation	bifurcation	NOUN
fumecheng-10464	81	6	delay	delay	NOUN
fumecheng-10464	81	7	behaviors	behavior	NOUN
fumecheng-10464	81	8	when	when	SCONJ
fumecheng-10464	81	9	there	there	PRON
fumecheng-10464	81	10	are	be	VERB
fumecheng-10464	81	11	no	no	DET
fumecheng-10464	81	12	spinning	spinning	NOUN
fumecheng-10464	81	13	points	point	NOUN
fumecheng-10464	81	14	.	.	PUNCT
fumecheng-10464	82	1	their	their	PRON
fumecheng-10464	82	2	study	study	NOUN
fumecheng-10464	82	3	showed	show	VERB
fumecheng-10464	82	4	that	that	SCONJ
fumecheng-10464	82	5	,	,	PUNCT
fumecheng-10464	82	6	at	at	ADP
fumecheng-10464	82	7	the	the	DET
fumecheng-10464	82	8	first	first	ADJ
fumecheng-10464	82	9	delay	delay	NOUN
fumecheng-10464	82	10	behavior	behavior	NOUN
fumecheng-10464	82	11	,	,	PUNCT
fumecheng-10464	82	12	the	the	DET
fumecheng-10464	82	13	delay	delay	NOUN
fumecheng-10464	82	14	time	time	NOUN
fumecheng-10464	82	15	is	be	AUX
fumecheng-10464	82	16	decided	decide	VERB
fumecheng-10464	82	17	by	by	ADP
fumecheng-10464	82	18	the	the	DET
fumecheng-10464	82	19	initial	initial	ADJ
fumecheng-10464	82	20	time	time	NOUN
fumecheng-10464	82	21	.	.	PUNCT
fumecheng-10464	83	1	the	the	DET
fumecheng-10464	83	2	phenomenon	phenomenon	NOUN
fumecheng-10464	83	3	of	of	ADP
fumecheng-10464	83	4	the	the	DET
fumecheng-10464	83	5	entertaining	entertaining	NOUN
fumecheng-10464	83	6	of	of	ADP
fumecheng-10464	83	7	a	a	DET
fumecheng-10464	83	8	generalized	generalize	VERB
fumecheng-10464	83	9	vdp	vdp	PROPN
fumecheng-10464	83	10	was	be	AUX
fumecheng-10464	83	11	considered	consider	VERB
fumecheng-10464	83	12	by	by	ADP
fumecheng-10464	83	13	kovacic	kovacic	PROPN
fumecheng-10464	83	14	[	[	X
fumecheng-10464	83	15	35	35	NUM
fumecheng-10464	83	16	]	]	PUNCT
fumecheng-10464	83	17	.	.	PUNCT
fumecheng-10464	84	1	by	by	ADP
fumecheng-10464	84	2	regulating	regulate	VERB
fumecheng-10464	84	3	the	the	DET
fumecheng-10464	84	4	method	method	NOUN
fumecheng-10464	84	5	of	of	ADP
fumecheng-10464	84	6	averaging	averaging	NOUN
fumecheng-10464	84	7	,	,	PUNCT
fumecheng-10464	84	8	the	the	DET
fumecheng-10464	84	9	approximate	approximate	ADJ
fumecheng-10464	84	10	amplitude	amplitude	NOUN
fumecheng-10464	84	11	-	-	PUNCT
fumecheng-10464	84	12	frequency	frequency	NOUN
fumecheng-10464	84	13	response	response	NOUN
fumecheng-10464	84	14	was	be	AUX
fumecheng-10464	84	15	obtained	obtain	VERB
fumecheng-10464	84	16	.	.	PUNCT
fumecheng-10464	85	1	the	the	DET
fumecheng-10464	85	2	inspiration	inspiration	NOUN
fumecheng-10464	85	3	of	of	ADP
fumecheng-10464	85	4	the	the	DET
fumecheng-10464	85	5	controls	control	NOUN
fumecheng-10464	85	6	of	of	ADP
fumecheng-10464	85	7	the	the	DET
fumecheng-10464	85	8	reinstating	reinstating	NOUN
fumecheng-10464	85	9	and	and	CCONJ
fumecheng-10464	85	10	damping	damp	VERB
fumecheng-10464	85	11	force	force	NOUN
fumecheng-10464	85	12	in	in	ADP
fumecheng-10464	85	13	the	the	DET
fumecheng-10464	85	14	fig	fig	NOUN
fumecheng-10464	85	15	.	.	PUNCT
fumecheng-10464	86	1	1	1	NUM
fumecheng-10464	86	2	basic	basic	ADJ
fumecheng-10464	86	3	property	property	NOUN
fumecheng-10464	86	4	of	of	ADP
fumecheng-10464	86	5	the	the	DET
fumecheng-10464	86	6	fractal	fractal	ADJ
fumecheng-10464	86	7	vibration	vibration	NOUN
fumecheng-10464	86	8	,	,	PUNCT
fumecheng-10464	86	9	x(	x(	PUNCT
fumecheng-10464	86	10	)	)	PUNCT
fumecheng-10464	87	1	=	=	PUNCT
fumecheng-10464	87	2	cosα	cosα	NOUN
fumecheng-10464	87	3	4	4	NUM
fumecheng-10464	87	4	j.-h	j.-h	NOUN
fumecheng-10464	87	5	.	.	PUNCT
fumecheng-10464	88	1	he	he	PRON
fumecheng-10464	88	2	,	,	PUNCT
fumecheng-10464	88	3	g.	g.	PROPN
fumecheng-10464	88	4	m.	m.	PROPN
fumecheng-10464	88	5	moatimid	moatimid	PROPN
fumecheng-10464	88	6	,	,	PUNCT
fumecheng-10464	88	7	m.	m.	PROPN
fumecheng-10464	88	8	h.	h.	PROPN
fumecheng-10464	88	9	zekry	zekry	PROPN
fumecheng-10464	88	10	existence	existence	NOUN
fumecheng-10464	88	11	of	of	ADP
fumecheng-10464	88	12	this	this	DET
fumecheng-10464	88	13	occurrence	occurrence	NOUN
fumecheng-10464	88	14	was	be	AUX
fumecheng-10464	88	15	examined	examine	VERB
fumecheng-10464	88	16	.	.	PUNCT
fumecheng-10464	89	1	shen	shen	PROPN
fumecheng-10464	89	2	et	et	PROPN
fumecheng-10464	89	3	al	al	PROPN
fumecheng-10464	89	4	.	.	PUNCT
fumecheng-10464	90	1	[	[	X
fumecheng-10464	90	2	36	36	NUM
fumecheng-10464	90	3	]	]	PUNCT
fumecheng-10464	90	4	investigated	investigate	VERB
fumecheng-10464	90	5	the	the	DET
fumecheng-10464	90	6	primary	primary	ADJ
fumecheng-10464	90	7	and	and	CCONJ
fumecheng-10464	90	8	sub	sub	ADJ
fumecheng-10464	90	9	-	-	ADJ
fumecheng-10464	90	10	harmonic	harmonic	ADJ
fumecheng-10464	90	11	simultaneous	simultaneous	ADJ
fumecheng-10464	90	12	resonance	resonance	NOUN
fumecheng-10464	90	13	of	of	ADP
fumecheng-10464	90	14	the	the	DET
fumecheng-10464	90	15	duffing	duffing	NOUN
fumecheng-10464	90	16	oscillator	oscillator	NOUN
fumecheng-10464	90	17	with	with	ADP
fumecheng-10464	90	18	a	a	DET
fumecheng-10464	90	19	fractional	fractional	ADJ
fumecheng-10464	90	20	order	order	NOUN
fumecheng-10464	90	21	derivative	derivative	NOUN
fumecheng-10464	90	22	.	.	PUNCT
fumecheng-10464	91	1	the	the	DET
fumecheng-10464	91	2	approximate	approximate	ADJ
fumecheng-10464	91	3	analytical	analytical	ADJ
fumecheng-10464	91	4	solution	solution	NOUN
fumecheng-10464	91	5	of	of	ADP
fumecheng-10464	91	6	the	the	DET
fumecheng-10464	91	7	resonance	resonance	NOUN
fumecheng-10464	91	8	was	be	AUX
fumecheng-10464	91	9	obtained	obtain	VERB
fumecheng-10464	91	10	.	.	PUNCT
fumecheng-10464	92	1	furthermore	furthermore	ADV
fumecheng-10464	92	2	,	,	PUNCT
fumecheng-10464	92	3	the	the	DET
fumecheng-10464	92	4	rightness	rightness	NOUN
fumecheng-10464	92	5	and	and	CCONJ
fumecheng-10464	92	6	acceptable	acceptable	ADJ
fumecheng-10464	92	7	exactness	exactness	NOUN
fumecheng-10464	92	8	of	of	ADP
fumecheng-10464	92	9	the	the	DET
fumecheng-10464	92	10	analytical	analytical	ADJ
fumecheng-10464	92	11	solution	solution	NOUN
fumecheng-10464	92	12	were	be	AUX
fumecheng-10464	92	13	verified	verify	VERB
fumecheng-10464	92	14	by	by	ADP
fumecheng-10464	92	15	a	a	DET
fumecheng-10464	92	16	numerical	numerical	ADJ
fumecheng-10464	92	17	simulation	simulation	NOUN
fumecheng-10464	92	18	.	.	PUNCT
fumecheng-10464	93	1	recently	recently	ADV
fumecheng-10464	93	2	,	,	PUNCT
fumecheng-10464	93	3	wu	wu	PROPN
fumecheng-10464	93	4	et	et	PROPN
fumecheng-10464	93	5	al	al	PROPN
fumecheng-10464	93	6	.	.	PUNCT
fumecheng-10464	94	1	[	[	X
fumecheng-10464	94	2	37	37	NUM
fumecheng-10464	94	3	]	]	PUNCT
fumecheng-10464	94	4	have	have	AUX
fumecheng-10464	94	5	examined	examine	VERB
fumecheng-10464	94	6	periodic	periodic	ADJ
fumecheng-10464	94	7	explanations	explanation	NOUN
fumecheng-10464	94	8	of	of	ADP
fumecheng-10464	94	9	a	a	DET
fumecheng-10464	94	10	harmonic	harmonic	ADJ
fumecheng-10464	94	11	forced	force	VERB
fumecheng-10464	94	12	duffing	duffing	NOUN
fumecheng-10464	94	13	oscillator	oscillator	NOUN
fumecheng-10464	94	14	with	with	ADP
fumecheng-10464	94	15	a	a	DET
fumecheng-10464	94	16	time	time	NOUN
fumecheng-10464	94	17	-	-	PUNCT
fumecheng-10464	94	18	delay	delay	NOUN
fumecheng-10464	94	19	state	state	NOUN
fumecheng-10464	94	20	feedback	feedback	NOUN
fumecheng-10464	94	21	by	by	ADP
fumecheng-10464	94	22	using	use	VERB
fumecheng-10464	94	23	the	the	DET
fumecheng-10464	94	24	incremental	incremental	ADJ
fumecheng-10464	94	25	harmonic	harmonic	ADJ
fumecheng-10464	94	26	balance	balance	NOUN
fumecheng-10464	94	27	method	method	NOUN
fumecheng-10464	94	28	.	.	PUNCT
fumecheng-10464	95	1	fractal	fractal	ADJ
fumecheng-10464	95	2	differential	differential	ADJ
fumecheng-10464	95	3	equations	equation	NOUN
fumecheng-10464	95	4	are	be	AUX
fumecheng-10464	95	5	convenient	convenient	ADJ
fumecheng-10464	95	6	in	in	ADP
fumecheng-10464	95	7	describing	describe	VERB
fumecheng-10464	95	8	the	the	DET
fumecheng-10464	95	9	numerous	numerous	ADJ
fumecheng-10464	95	10	occurrences	occurrence	NOUN
fumecheng-10464	95	11	in	in	ADP
fumecheng-10464	95	12	porous	porous	ADJ
fumecheng-10464	95	13	media	medium	NOUN
fumecheng-10464	95	14	or	or	CCONJ
fumecheng-10464	95	15	on	on	ADP
fumecheng-10464	95	16	un	un	ADJ
fumecheng-10464	95	17	-	-	ADJ
fumecheng-10464	95	18	smooth	smooth	ADJ
fumecheng-10464	95	19	boundaries	boundary	NOUN
fumecheng-10464	95	20	.	.	PUNCT
fumecheng-10464	96	1	it	it	PRON
fumecheng-10464	96	2	is	be	AUX
fumecheng-10464	96	3	to	to	PART
fumecheng-10464	96	4	be	be	AUX
fumecheng-10464	96	5	noted	note	VERB
fumecheng-10464	96	6	that	that	SCONJ
fumecheng-10464	96	7	the	the	DET
fumecheng-10464	96	8	exact	exact	ADJ
fumecheng-10464	96	9	solutions	solution	NOUN
fumecheng-10464	96	10	are	be	AUX
fumecheng-10464	96	11	generally	generally	ADV
fumecheng-10464	96	12	unreachable	unreachable	ADJ
fumecheng-10464	96	13	.	.	PUNCT
fumecheng-10464	97	1	therefore	therefore	ADV
fumecheng-10464	97	2	,	,	PUNCT
fumecheng-10464	97	3	these	these	DET
fumecheng-10464	97	4	nonlinear	nonlinear	ADJ
fumecheng-10464	97	5	equations	equation	NOUN
fumecheng-10464	97	6	should	should	AUX
fumecheng-10464	97	7	be	be	AUX
fumecheng-10464	97	8	solved	solve	VERB
fumecheng-10464	97	9	by	by	ADP
fumecheng-10464	97	10	expanding	expand	VERB
fumecheng-10464	97	11	approximate	approximate	ADJ
fumecheng-10464	97	12	methods	method	NOUN
fumecheng-10464	97	13	.	.	PUNCT
fumecheng-10464	98	1	many	many	ADJ
fumecheng-10464	98	2	efforts	effort	NOUN
fumecheng-10464	98	3	were	be	AUX
fumecheng-10464	98	4	exerted	exert	VERB
fumecheng-10464	98	5	to	to	PART
fumecheng-10464	98	6	analytically	analytically	ADV
fumecheng-10464	98	7	treat	treat	VERB
fumecheng-10464	98	8	these	these	DET
fumecheng-10464	98	9	phenomena	phenomenon	NOUN
fumecheng-10464	98	10	,	,	PUNCT
fumecheng-10464	98	11	ranging	range	VERB
fumecheng-10464	98	12	from	from	ADP
fumecheng-10464	98	13	the	the	DET
fumecheng-10464	98	14	traditional	traditional	ADJ
fumecheng-10464	98	15	perturbation	perturbation	NOUN
fumecheng-10464	98	16	methods	method	NOUN
fumecheng-10464	98	17	to	to	ADP
fumecheng-10464	98	18	the	the	DET
fumecheng-10464	98	19	multiple	multiple	ADJ
fumecheng-10464	98	20	time	time	NOUN
fumecheng-10464	98	21	scale	scale	NOUN
fumecheng-10464	98	22	technique	technique	NOUN
fumecheng-10464	98	23	.	.	PUNCT
fumecheng-10464	99	1	as	as	SCONJ
fumecheng-10464	99	2	known	know	VERB
fumecheng-10464	99	3	,	,	PUNCT
fumecheng-10464	99	4	the	the	DET
fumecheng-10464	99	5	straightforwardness	straightforwardness	NOUN
fumecheng-10464	99	6	of	of	ADP
fumecheng-10464	99	7	the	the	DET
fumecheng-10464	99	8	perturbation	perturbation	NOUN
fumecheng-10464	99	9	methods	method	NOUN
fumecheng-10464	99	10	renders	render	VERB
fumecheng-10464	99	11	the	the	DET
fumecheng-10464	99	12	nonlinear	nonlinear	ADJ
fumecheng-10464	99	13	equations	equation	NOUN
fumecheng-10464	99	14	into	into	ADP
fumecheng-10464	99	15	linear	linear	ADJ
fumecheng-10464	99	16	ones	one	NOUN
fumecheng-10464	99	17	.	.	PUNCT
fumecheng-10464	100	1	certainly	certainly	ADV
fumecheng-10464	100	2	,	,	PUNCT
fumecheng-10464	100	3	all	all	DET
fumecheng-10464	100	4	these	these	DET
fumecheng-10464	100	5	perturbation	perturbation	NOUN
fumecheng-10464	100	6	methods	method	NOUN
fumecheng-10464	100	7	are	be	AUX
fumecheng-10464	100	8	primarily	primarily	ADV
fumecheng-10464	100	9	contingent	contingent	ADJ
fumecheng-10464	100	10	on	on	ADP
fumecheng-10464	100	11	a	a	DET
fumecheng-10464	100	12	small	small	ADJ
fumecheng-10464	100	13	parameter	parameter	NOUN
fumecheng-10464	100	14	.	.	PUNCT
fumecheng-10464	101	1	therefore	therefore	ADV
fumecheng-10464	101	2	,	,	PUNCT
fumecheng-10464	101	3	the	the	DET
fumecheng-10464	101	4	presence	presence	NOUN
fumecheng-10464	101	5	of	of	ADP
fumecheng-10464	101	6	such	such	DET
fumecheng-10464	101	7	a	a	DET
fumecheng-10464	101	8	parameter	parameter	NOUN
fumecheng-10464	101	9	is	be	AUX
fumecheng-10464	101	10	necessary	necessary	ADJ
fumecheng-10464	101	11	to	to	PART
fumecheng-10464	101	12	attain	attain	VERB
fumecheng-10464	101	13	an	an	DET
fumecheng-10464	101	14	approximate	approximate	ADJ
fumecheng-10464	101	15	solution	solution	NOUN
fumecheng-10464	101	16	.	.	PUNCT
fumecheng-10464	102	1	frequently	frequently	ADV
fumecheng-10464	102	2	,	,	PUNCT
fumecheng-10464	102	3	the	the	DET
fumecheng-10464	102	4	solution	solution	NOUN
fumecheng-10464	102	5	of	of	ADP
fumecheng-10464	102	6	such	such	DET
fumecheng-10464	102	7	a	a	DET
fumecheng-10464	102	8	problem	problem	NOUN
fumecheng-10464	102	9	might	might	AUX
fumecheng-10464	102	10	be	be	AUX
fumecheng-10464	102	11	limited	limit	VERB
fumecheng-10464	102	12	by	by	ADP
fumecheng-10464	102	13	the	the	DET
fumecheng-10464	102	14	presence	presence	NOUN
fumecheng-10464	102	15	of	of	ADP
fumecheng-10464	102	16	this	this	DET
fumecheng-10464	102	17	parameter	parameter	NOUN
fumecheng-10464	102	18	.	.	PUNCT
fumecheng-10464	103	1	fundamentally	fundamentally	ADV
fumecheng-10464	103	2	,	,	PUNCT
fumecheng-10464	103	3	the	the	DET
fumecheng-10464	103	4	exact	exact	ADJ
fumecheng-10464	103	5	solution	solution	NOUN
fumecheng-10464	103	6	of	of	ADP
fumecheng-10464	103	7	this	this	DET
fumecheng-10464	103	8	equation	equation	NOUN
fumecheng-10464	103	9	is	be	AUX
fumecheng-10464	103	10	difficult	difficult	ADJ
fumecheng-10464	103	11	and	and	CCONJ
fumecheng-10464	103	12	a	a	DET
fumecheng-10464	103	13	perturbation	perturbation	NOUN
fumecheng-10464	103	14	technique	technique	NOUN
fumecheng-10464	103	15	is	be	AUX
fumecheng-10464	103	16	required	require	VERB
fumecheng-10464	103	17	.	.	PUNCT
fumecheng-10464	104	1	all	all	DET
fumecheng-10464	104	2	classical	classical	ADJ
fumecheng-10464	104	3	perturbation	perturbation	NOUN
fumecheng-10464	104	4	methods	method	NOUN
fumecheng-10464	104	5	ranging	range	VERB
fumecheng-10464	104	6	from	from	ADP
fumecheng-10464	104	7	the	the	DET
fumecheng-10464	104	8	traditional	traditional	ADJ
fumecheng-10464	104	9	methods	method	NOUN
fumecheng-10464	104	10	to	to	ADP
fumecheng-10464	104	11	the	the	DET
fumecheng-10464	104	12	multiple	multiple	ADJ
fumecheng-10464	104	13	-	-	PUNCT
fumecheng-10464	104	14	scales	scale	NOUN
fumecheng-10464	104	15	method	method	NOUN
fumecheng-10464	104	16	depend	depend	VERB
fumecheng-10464	104	17	mainly	mainly	ADV
fumecheng-10464	104	18	on	on	ADP
fumecheng-10464	104	19	a	a	DET
fumecheng-10464	104	20	small	small	ADJ
fumecheng-10464	104	21	parameter	parameter	NOUN
fumecheng-10464	104	22	.	.	PUNCT
fumecheng-10464	105	1	consequently	consequently	ADV
fumecheng-10464	105	2	,	,	PUNCT
fumecheng-10464	105	3	the	the	DET
fumecheng-10464	105	4	problem	problem	NOUN
fumecheng-10464	105	5	can	can	AUX
fumecheng-10464	105	6	not	not	PART
fumecheng-10464	105	7	be	be	AUX
fumecheng-10464	105	8	solved	solve	VERB
fumecheng-10464	105	9	without	without	ADP
fumecheng-10464	105	10	the	the	DET
fumecheng-10464	105	11	occurrence	occurrence	NOUN
fumecheng-10464	105	12	of	of	ADP
fumecheng-10464	105	13	such	such	DET
fumecheng-10464	105	14	a	a	DET
fumecheng-10464	105	15	parameter	parameter	NOUN
fumecheng-10464	105	16	.	.	PUNCT
fumecheng-10464	106	1	in	in	ADP
fumecheng-10464	106	2	recent	recent	ADJ
fumecheng-10464	106	3	years	year	NOUN
fumecheng-10464	106	4	,	,	PUNCT
fumecheng-10464	106	5	many	many	ADJ
fumecheng-10464	106	6	promising	promising	ADJ
fumecheng-10464	106	7	and	and	CCONJ
fumecheng-10464	106	8	powerful	powerful	ADJ
fumecheng-10464	106	9	methods	method	NOUN
fumecheng-10464	106	10	have	have	AUX
fumecheng-10464	106	11	been	be	AUX
fumecheng-10464	106	12	introduced	introduce	VERB
fumecheng-10464	106	13	to	to	PART
fumecheng-10464	106	14	construct	construct	VERB
fumecheng-10464	106	15	analytical	analytical	ADJ
fumecheng-10464	106	16	solutions	solution	NOUN
fumecheng-10464	106	17	for	for	ADP
fumecheng-10464	106	18	such	such	ADJ
fumecheng-10464	106	19	equations	equation	NOUN
fumecheng-10464	106	20	.	.	PUNCT
fumecheng-10464	107	1	one	one	NUM
fumecheng-10464	107	2	of	of	ADP
fumecheng-10464	107	3	the	the	DET
fumecheng-10464	107	4	pioneer	pioneer	NOUN
fumecheng-10464	107	5	methods	method	NOUN
fumecheng-10464	107	6	is	be	AUX
fumecheng-10464	107	7	the	the	DET
fumecheng-10464	107	8	homotopy	homotopy	NOUN
fumecheng-10464	107	9	perturbation	perturbation	NOUN
fumecheng-10464	107	10	method	method	NOUN
fumecheng-10464	107	11	(	(	PUNCT
fumecheng-10464	107	12	hpm	hpm	NOUN
fumecheng-10464	107	13	)	)	PUNCT
fumecheng-10464	107	14	.	.	PUNCT
fumecheng-10464	108	1	this	this	DET
fumecheng-10464	108	2	promising	promising	ADJ
fumecheng-10464	108	3	approach	approach	NOUN
fumecheng-10464	108	4	was	be	AUX
fumecheng-10464	108	5	first	first	ADV
fumecheng-10464	108	6	proposed	propose	VERB
fumecheng-10464	108	7	by	by	ADP
fumecheng-10464	108	8	the	the	DET
fumecheng-10464	108	9	chinese	chinese	ADJ
fumecheng-10464	108	10	mathematician	mathematician	NOUN
fumecheng-10464	108	11	he	he	PRON
fumecheng-10464	109	1	[	[	X
fumecheng-10464	109	2	38	38	NUM
fumecheng-10464	109	3	]	]	PUNCT
fumecheng-10464	109	4	.	.	PUNCT
fumecheng-10464	110	1	homotopy	homotopy	PROPN
fumecheng-10464	110	2	is	be	AUX
fumecheng-10464	110	3	constructed	construct	VERB
fumecheng-10464	110	4	in	in	ADP
fumecheng-10464	110	5	terms	term	NOUN
fumecheng-10464	110	6	of	of	ADP
fumecheng-10464	110	7	a	a	DET
fumecheng-10464	110	8	small	small	ADJ
fumecheng-10464	110	9	embedded	embed	VERB
fumecheng-10464	110	10	parameter	parameter	NOUN
fumecheng-10464	110	11	.	.	PUNCT
fumecheng-10464	111	1	the	the	DET
fumecheng-10464	111	2	hpm	hpm	NOUN
fumecheng-10464	111	3	is	be	AUX
fumecheng-10464	111	4	an	an	DET
fumecheng-10464	111	5	amalgamation	amalgamation	NOUN
fumecheng-10464	111	6	of	of	ADP
fumecheng-10464	111	7	the	the	DET
fumecheng-10464	111	8	traditional	traditional	ADJ
fumecheng-10464	111	9	perturbation	perturbation	NOUN
fumecheng-10464	111	10	performance	performance	NOUN
fumecheng-10464	111	11	and	and	CCONJ
fumecheng-10464	111	12	the	the	DET
fumecheng-10464	111	13	homotopy	homotopy	NOUN
fumecheng-10464	111	14	method	method	NOUN
fumecheng-10464	111	15	,	,	PUNCT
fumecheng-10464	111	16	which	which	PRON
fumecheng-10464	111	17	has	have	AUX
fumecheng-10464	111	18	removed	remove	VERB
fumecheng-10464	111	19	the	the	DET
fumecheng-10464	111	20	dominant	dominant	ADJ
fumecheng-10464	111	21	restrictions	restriction	NOUN
fumecheng-10464	111	22	of	of	ADP
fumecheng-10464	111	23	the	the	DET
fumecheng-10464	111	24	perturbation	perturbation	NOUN
fumecheng-10464	111	25	methods	method	NOUN
fumecheng-10464	111	26	.	.	PUNCT
fumecheng-10464	112	1	this	this	DET
fumecheng-10464	112	2	hpm	hpm	NOUN
fumecheng-10464	112	3	brings	bring	VERB
fumecheng-10464	112	4	about	about	ADP
fumecheng-10464	112	5	an	an	DET
fumecheng-10464	112	6	actual	actual	ADJ
fumecheng-10464	112	7	quick	quick	ADJ
fumecheng-10464	112	8	convergence	convergence	NOUN
fumecheng-10464	112	9	of	of	ADP
fumecheng-10464	112	10	the	the	DET
fumecheng-10464	112	11	solution	solution	NOUN
fumecheng-10464	112	12	series	series	NOUN
fumecheng-10464	112	13	in	in	ADP
fumecheng-10464	112	14	most	most	ADJ
fumecheng-10464	112	15	cases	case	NOUN
fumecheng-10464	112	16	.	.	PUNCT
fumecheng-10464	113	1	therefore	therefore	ADV
fumecheng-10464	113	2	,	,	PUNCT
fumecheng-10464	113	3	only	only	ADV
fumecheng-10464	113	4	after	after	ADP
fumecheng-10464	113	5	a	a	DET
fumecheng-10464	113	6	few	few	ADJ
fumecheng-10464	113	7	iterations	iteration	NOUN
fumecheng-10464	113	8	,	,	PUNCT
fumecheng-10464	113	9	one	one	PRON
fumecheng-10464	113	10	reaches	reach	VERB
fumecheng-10464	113	11	accurate	accurate	ADJ
fumecheng-10464	113	12	solutions	solution	NOUN
fumecheng-10464	113	13	.	.	PUNCT
fumecheng-10464	114	1	hpm	hpm	PROPN
fumecheng-10464	114	2	is	be	AUX
fumecheng-10464	114	3	a	a	DET
fumecheng-10464	114	4	universal	universal	ADJ
fumecheng-10464	114	5	technique	technique	NOUN
fumecheng-10464	114	6	which	which	PRON
fumecheng-10464	114	7	can	can	AUX
fumecheng-10464	114	8	solve	solve	VERB
fumecheng-10464	114	9	various	various	ADJ
fumecheng-10464	114	10	kinds	kind	NOUN
fumecheng-10464	114	11	of	of	ADP
fumecheng-10464	114	12	nonlinear	nonlinear	ADJ
fumecheng-10464	114	13	equations	equation	NOUN
fumecheng-10464	114	14	.	.	PUNCT
fumecheng-10464	115	1	this	this	DET
fumecheng-10464	115	2	technique	technique	NOUN
fumecheng-10464	115	3	surpasses	surpass	VERB
fumecheng-10464	115	4	the	the	DET
fumecheng-10464	115	5	traditional	traditional	ADJ
fumecheng-10464	115	6	perturbation	perturbation	NOUN
fumecheng-10464	115	7	techniques	technique	NOUN
fumecheng-10464	115	8	.	.	PUNCT
fumecheng-10464	116	1	gómez	gómez	NOUN
fumecheng-10464	116	2	-	-	PUNCT
fumecheng-10464	116	3	aguilar	aguilar	PROPN
fumecheng-10464	116	4	et	et	PROPN
fumecheng-10464	116	5	al	al	PROPN
fumecheng-10464	116	6	.	.	PUNCT
fumecheng-10464	117	1	[	[	X
fumecheng-10464	117	2	39	39	NUM
fumecheng-10464	117	3	]	]	PUNCT
fumecheng-10464	117	4	introduced	introduce	VERB
fumecheng-10464	117	5	the	the	DET
fumecheng-10464	117	6	fractional	fractional	ADJ
fumecheng-10464	117	7	equations	equation	NOUN
fumecheng-10464	117	8	of	of	ADP
fumecheng-10464	117	9	the	the	DET
fumecheng-10464	117	10	mass	mass	ADJ
fumecheng-10464	117	11	-	-	PUNCT
fumecheng-10464	117	12	spring	spring	NOUN
fumecheng-10464	117	13	-	-	PUNCT
fumecheng-10464	117	14	damper	damper	NOUN
fumecheng-10464	117	15	system	system	NOUN
fumecheng-10464	117	16	with	with	ADP
fumecheng-10464	117	17	caputo	caputo	PROPN
fumecheng-10464	117	18	and	and	CCONJ
fumecheng-10464	117	19	caputo	caputo	PROPN
fumecheng-10464	117	20	–	–	PUNCT
fumecheng-10464	117	21	fabrizio	fabrizio	NOUN
fumecheng-10464	117	22	derivatives	derivative	NOUN
fumecheng-10464	117	23	.	.	PUNCT
fumecheng-10464	118	1	their	their	PRON
fumecheng-10464	118	2	results	result	NOUN
fumecheng-10464	118	3	indicated	indicate	VERB
fumecheng-10464	118	4	that	that	SCONJ
fumecheng-10464	118	5	the	the	DET
fumecheng-10464	118	6	mechanical	mechanical	ADJ
fumecheng-10464	118	7	components	component	NOUN
fumecheng-10464	118	8	display	display	VERB
fumecheng-10464	118	9	visco	visco	ADJ
fumecheng-10464	118	10	-	-	ADJ
fumecheng-10464	118	11	elastic	elastic	ADJ
fumecheng-10464	118	12	performances	performance	NOUN
fumecheng-10464	118	13	manufacturing	manufacture	VERB
fumecheng-10464	118	14	temporal	temporal	ADJ
fumecheng-10464	118	15	fractal	fractal	ADJ
fumecheng-10464	118	16	diverse	diverse	ADJ
fumecheng-10464	118	17	scales	scale	NOUN
fumecheng-10464	118	18	.	.	PUNCT
fumecheng-10464	119	1	yang	yang	PROPN
fumecheng-10464	119	2	et	et	PROPN
fumecheng-10464	119	3	al	al	PROPN
fumecheng-10464	119	4	.	.	PUNCT
fumecheng-10464	120	1	[	[	X
fumecheng-10464	120	2	40	40	NUM
fumecheng-10464	120	3	]	]	PUNCT
fumecheng-10464	120	4	considered	consider	VERB
fumecheng-10464	120	5	boundary	boundary	ADJ
fumecheng-10464	120	6	-	-	PUNCT
fumecheng-10464	120	7	value	value	NOUN
fumecheng-10464	120	8	problems	problem	NOUN
fumecheng-10464	120	9	in	in	ADP
fumecheng-10464	120	10	a	a	DET
fumecheng-10464	120	11	fractal	fractal	ADJ
fumecheng-10464	120	12	heat	heat	NOUN
fumecheng-10464	120	13	transfer	transfer	NOUN
fumecheng-10464	120	14	.	.	PUNCT
fumecheng-10464	121	1	the	the	DET
fumecheng-10464	121	2	exact	exact	ADJ
fumecheng-10464	121	3	solutions	solution	NOUN
fumecheng-10464	121	4	of	of	ADP
fumecheng-10464	121	5	nondifferentiable	nondifferentiable	ADJ
fumecheng-10464	121	6	type	type	NOUN
fumecheng-10464	121	7	were	be	AUX
fumecheng-10464	121	8	attained	attain	VERB
fumecheng-10464	121	9	by	by	ADP
fumecheng-10464	121	10	the	the	DET
fumecheng-10464	121	11	local	local	ADJ
fumecheng-10464	121	12	fractional	fractional	ADJ
fumecheng-10464	121	13	differential	differential	NOUN
fumecheng-10464	121	14	transform	transform	NOUN
fumecheng-10464	121	15	method	method	NOUN
fumecheng-10464	121	16	.	.	PUNCT
fumecheng-10464	122	1	recently	recently	ADV
fumecheng-10464	122	2	,	,	PUNCT
fumecheng-10464	122	3	elías	elías	NOUN
fumecheng-10464	122	4	-	-	PUNCT
fumecheng-10464	122	5	zúñiga	zúñiga	PROPN
fumecheng-10464	122	6	et	et	PROPN
fumecheng-10464	122	7	al	al	PROPN
fumecheng-10464	122	8	.	.	PUNCT
fumecheng-10464	123	1	[	[	X
fumecheng-10464	123	2	41	41	NUM
fumecheng-10464	123	3	]	]	PUNCT
fumecheng-10464	123	4	introduced	introduce	VERB
fumecheng-10464	123	5	a	a	DET
fumecheng-10464	123	6	new	new	ADJ
fumecheng-10464	123	7	methodology	methodology	NOUN
fumecheng-10464	123	8	for	for	ADP
fumecheng-10464	123	9	descending	descend	VERB
fumecheng-10464	123	10	the	the	DET
fumecheng-10464	123	11	careful	careful	ADJ
fumecheng-10464	123	12	,	,	PUNCT
fumecheng-10464	123	13	steady	steady	ADJ
fumecheng-10464	123	14	-	-	PUNCT
fumecheng-10464	123	15	state	state	NOUN
fumecheng-10464	123	16	solutions	solution	NOUN
fumecheng-10464	123	17	of	of	ADP
fumecheng-10464	123	18	fractal	fractal	ADJ
fumecheng-10464	123	19	damped	damped	NOUN
fumecheng-10464	123	20	and	and	CCONJ
fumecheng-10464	123	21	forced	force	VERB
fumecheng-10464	123	22	differential	differential	ADJ
fumecheng-10464	123	23	equations	equation	NOUN
fumecheng-10464	123	24	.	.	PUNCT
fumecheng-10464	124	1	motivated	motivate	VERB
fumecheng-10464	124	2	by	by	ADP
fumecheng-10464	124	3	the	the	DET
fumecheng-10464	124	4	aforementioned	aforementioned	ADJ
fumecheng-10464	124	5	aspects	aspect	NOUN
fumecheng-10464	124	6	,	,	PUNCT
fumecheng-10464	124	7	the	the	DET
fumecheng-10464	124	8	aim	aim	NOUN
fumecheng-10464	124	9	of	of	ADP
fumecheng-10464	124	10	this	this	DET
fumecheng-10464	124	11	examination	examination	NOUN
fumecheng-10464	124	12	is	be	AUX
fumecheng-10464	124	13	to	to	PART
fumecheng-10464	124	14	investigate	investigate	VERB
fumecheng-10464	124	15	the	the	DET
fumecheng-10464	124	16	dvdp	dvdp	ADJ
fumecheng-10464	124	17	since	since	SCONJ
fumecheng-10464	124	18	it	it	PRON
fumecheng-10464	124	19	is	be	AUX
fumecheng-10464	124	20	widely	widely	ADV
fumecheng-10464	124	21	used	use	VERB
fumecheng-10464	124	22	in	in	ADP
fumecheng-10464	124	23	different	different	ADJ
fumecheng-10464	124	24	fields	field	NOUN
fumecheng-10464	124	25	.	.	PUNCT
fumecheng-10464	125	1	as	as	SCONJ
fumecheng-10464	125	2	previously	previously	ADV
fumecheng-10464	125	3	shown	show	VERB
fumecheng-10464	125	4	,	,	PUNCT
fumecheng-10464	125	5	the	the	DET
fumecheng-10464	125	6	dynamics	dynamic	NOUN
fumecheng-10464	125	7	of	of	ADP
fumecheng-10464	125	8	this	this	DET
fumecheng-10464	125	9	equation	equation	NOUN
fumecheng-10464	125	10	have	have	AUX
fumecheng-10464	125	11	been	be	AUX
fumecheng-10464	125	12	widely	widely	ADV
fumecheng-10464	125	13	investigated	investigate	VERB
fumecheng-10464	125	14	in	in	ADP
fumecheng-10464	125	15	recent	recent	ADJ
fumecheng-10464	125	16	years	year	NOUN
fumecheng-10464	125	17	.	.	PUNCT
fumecheng-10464	126	1	therefore	therefore	ADV
fumecheng-10464	126	2	,	,	PUNCT
fumecheng-10464	126	3	the	the	DET
fumecheng-10464	126	4	task	task	NOUN
fumecheng-10464	126	5	now	now	ADV
fumecheng-10464	126	6	is	be	AUX
fumecheng-10464	126	7	to	to	PART
fumecheng-10464	126	8	investigate	investigate	VERB
fumecheng-10464	126	9	an	an	DET
fumecheng-10464	126	10	analytical	analytical	ADJ
fumecheng-10464	126	11	approximate	approximate	ADJ
fumecheng-10464	126	12	solution	solution	NOUN
fumecheng-10464	126	13	together	together	ADV
fumecheng-10464	126	14	with	with	ADP
fumecheng-10464	126	15	the	the	DET
fumecheng-10464	126	16	stability	stability	NOUN
fumecheng-10464	126	17	profile	profile	NOUN
fumecheng-10464	126	18	.	.	PUNCT
fumecheng-10464	127	1	to	to	PART
fumecheng-10464	127	2	develop	develop	VERB
fumecheng-10464	127	3	the	the	DET
fumecheng-10464	127	4	existing	exist	VERB
fumecheng-10464	127	5	problem	problem	NOUN
fumecheng-10464	127	6	,	,	PUNCT
fumecheng-10464	127	7	the	the	DET
fumecheng-10464	127	8	rest	rest	NOUN
fumecheng-10464	127	9	of	of	ADP
fumecheng-10464	127	10	the	the	DET
fumecheng-10464	127	11	paper	paper	NOUN
fumecheng-10464	127	12	is	be	AUX
fumecheng-10464	127	13	organized	organize	VERB
fumecheng-10464	127	14	as	as	SCONJ
fumecheng-10464	127	15	follows	follow	VERB
fumecheng-10464	127	16	.	.	PUNCT
fumecheng-10464	128	1	a	a	DET
fumecheng-10464	128	2	periodic	periodic	ADJ
fumecheng-10464	128	3	solution	solution	NOUN
fumecheng-10464	128	4	,	,	PUNCT
fumecheng-10464	128	5	based	base	VERB
fumecheng-10464	128	6	on	on	ADP
fumecheng-10464	128	7	an	an	DET
fumecheng-10464	128	8	adaptation	adaptation	NOUN
fumecheng-10464	128	9	of	of	ADP
fumecheng-10464	128	10	the	the	DET
fumecheng-10464	128	11	expanded	expand	VERB
fumecheng-10464	128	12	natural	natural	ADJ
fumecheng-10464	128	13	frequency	frequency	NOUN
fumecheng-10464	128	14	analysis	analysis	NOUN
fumecheng-10464	128	15	,	,	PUNCT
fumecheng-10464	128	16	is	be	AUX
fumecheng-10464	128	17	given	give	VERB
fumecheng-10464	128	18	in	in	ADP
fumecheng-10464	128	19	section	section	NOUN
fumecheng-10464	128	20	2	2	NUM
fumecheng-10464	128	21	.	.	PUNCT
fumecheng-10464	129	1	the	the	DET
fumecheng-10464	129	2	stability	stability	NOUN
fumecheng-10464	129	3	analysis	analysis	NOUN
fumecheng-10464	129	4	of	of	ADP
fumecheng-10464	129	5	the	the	DET
fumecheng-10464	129	6	autonomous	autonomous	ADJ
fumecheng-10464	129	7	system	system	NOUN
fumecheng-10464	129	8	,	,	PUNCT
fumecheng-10464	129	9	based	base	VERB
fumecheng-10464	129	10	on	on	ADP
fumecheng-10464	129	11	the	the	DET
fumecheng-10464	129	12	linearized	linearize	VERB
fumecheng-10464	129	13	theory	theory	NOUN
fumecheng-10464	129	14	,	,	PUNCT
fumecheng-10464	129	15	is	be	AUX
fumecheng-10464	129	16	realized	realize	VERB
fumecheng-10464	129	17	in	in	ADP
fumecheng-10464	129	18	section	section	NOUN
fumecheng-10464	129	19	3	3	NUM
fumecheng-10464	129	20	.	.	PUNCT
fumecheng-10464	130	1	additionally	additionally	ADV
fumecheng-10464	130	2	,	,	PUNCT
fumecheng-10464	130	3	the	the	DET
fumecheng-10464	130	4	phase	phase	NOUN
fumecheng-10464	130	5	portraits	portrait	NOUN
fumecheng-10464	130	6	are	be	AUX
fumecheng-10464	130	7	drawn	draw	VERB
fumecheng-10464	130	8	in	in	ADP
fumecheng-10464	130	9	this	this	DET
fumecheng-10464	130	10	section	section	NOUN
fumecheng-10464	130	11	.	.	PUNCT
fumecheng-10464	131	1	in	in	ADP
fumecheng-10464	131	2	section	section	NOUN
fumecheng-10464	131	3	4	4	NUM
fumecheng-10464	131	4	,	,	PUNCT
fumecheng-10464	131	5	the	the	DET
fumecheng-10464	131	6	stability	stability	NOUN
fumecheng-10464	131	7	analysis	analysis	NOUN
fumecheng-10464	131	8	of	of	ADP
fumecheng-10464	131	9	the	the	DET
fumecheng-10464	131	10	resonance	resonance	NOUN
fumecheng-10464	131	11	as	as	ADV
fumecheng-10464	131	12	well	well	ADV
fumecheng-10464	131	13	as	as	ADP
fumecheng-10464	131	14	the	the	DET
fumecheng-10464	131	15	non	non	ADJ
fumecheng-10464	131	16	-	-	ADJ
fumecheng-10464	131	17	resonance	resonance	ADJ
fumecheng-10464	131	18	cases	case	NOUN
fumecheng-10464	131	19	are	be	AUX
fumecheng-10464	131	20	accomplished	accomplish	VERB
fumecheng-10464	131	21	by	by	ADP
fumecheng-10464	131	22	utilizing	utilize	VERB
fumecheng-10464	131	23	a	a	DET
fumecheng-10464	131	24	combination	combination	NOUN
fumecheng-10464	131	25	of	of	ADP
fumecheng-10464	131	26	the	the	DET
fumecheng-10464	131	27	homotopy	homotopy	NOUN
fumecheng-10464	131	28	concept	concept	NOUN
fumecheng-10464	131	29	and	and	CCONJ
fumecheng-10464	131	30	the	the	DET
fumecheng-10464	131	31	multiple	multiple	ADJ
fumecheng-10464	131	32	time	time	NOUN
fumecheng-10464	131	33	forced	force	VERB
fumecheng-10464	131	34	nonlinear	nonlinear	ADJ
fumecheng-10464	131	35	oscillator	oscillator	NOUN
fumecheng-10464	131	36	in	in	ADP
fumecheng-10464	131	37	a	a	DET
fumecheng-10464	131	38	fractal	fractal	ADJ
fumecheng-10464	131	39	space	space	NOUN
fumecheng-10464	131	40	5	5	NUM
fumecheng-10464	131	41	scale	scale	NOUN
fumecheng-10464	131	42	analysis	analysis	NOUN
fumecheng-10464	131	43	.	.	PUNCT
fumecheng-10464	132	1	finally	finally	ADV
fumecheng-10464	132	2	,	,	PUNCT
fumecheng-10464	132	3	concluding	conclude	VERB
fumecheng-10464	132	4	remarks	remark	NOUN
fumecheng-10464	132	5	grounded	ground	VERB
fumecheng-10464	132	6	on	on	ADP
fumecheng-10464	132	7	the	the	DET
fumecheng-10464	132	8	consequences	consequence	NOUN
fumecheng-10464	132	9	are	be	AUX
fumecheng-10464	132	10	summarized	summarize	VERB
fumecheng-10464	132	11	in	in	ADP
fumecheng-10464	132	12	section	section	NOUN
fumecheng-10464	132	13	5	5	NUM
fumecheng-10464	132	14	.	.	NOUN
fumecheng-10464	133	1	2	2	NUM
fumecheng-10464	133	2	.	.	X
fumecheng-10464	133	3	an	an	DET
fumecheng-10464	133	4	approximate	approximate	ADJ
fumecheng-10464	133	5	bounded	bound	VERB
fumecheng-10464	133	6	solution	solution	NOUN
fumecheng-10464	133	7	through	through	ADP
fumecheng-10464	133	8	resources	resource	NOUN
fumecheng-10464	133	9	of	of	ADP
fumecheng-10464	133	10	the	the	DET
fumecheng-10464	133	11	nonlinear	nonlinear	ADJ
fumecheng-10464	133	12	frequency	frequency	NOUN
fumecheng-10464	133	13	analysis	analysis	NOUN
fumecheng-10464	133	14	as	as	SCONJ
fumecheng-10464	133	15	known	know	VERB
fumecheng-10464	133	16	,	,	PUNCT
fumecheng-10464	133	17	the	the	DET
fumecheng-10464	133	18	classical	classical	ADJ
fumecheng-10464	133	19	hpm	hpm	NOUN
fumecheng-10464	133	20	fails	fail	VERB
fumecheng-10464	133	21	to	to	PART
fumecheng-10464	133	22	solve	solve	VERB
fumecheng-10464	133	23	the	the	DET
fumecheng-10464	133	24	damping	damp	VERB
fumecheng-10464	133	25	nonlinear	nonlinear	ADJ
fumecheng-10464	133	26	oscillator	oscillator	NOUN
fumecheng-10464	133	27	,	,	PUNCT
fumecheng-10464	133	28	especially	especially	ADV
fumecheng-10464	133	29	for	for	ADP
fumecheng-10464	133	30	the	the	DET
fumecheng-10464	133	31	van	van	PROPN
fumecheng-10464	133	32	der	der	ADJ
fumecheng-10464	133	33	pol	pol	PROPN
fumecheng-10464	133	34	oscillator	oscillator	NOUN
fumecheng-10464	133	35	because	because	SCONJ
fumecheng-10464	133	36	it	it	PRON
fumecheng-10464	133	37	contains	contain	VERB
fumecheng-10464	133	38	linear	linear	ADJ
fumecheng-10464	133	39	and	and	CCONJ
fumecheng-10464	133	40	nonlinear	nonlinear	ADJ
fumecheng-10464	133	41	damping	damp	VERB
fumecheng-10464	133	42	forces	force	NOUN
fumecheng-10464	133	43	.	.	PUNCT
fumecheng-10464	134	1	therefore	therefore	ADV
fumecheng-10464	134	2	,	,	PUNCT
fumecheng-10464	134	3	the	the	DET
fumecheng-10464	134	4	main	main	ADJ
fumecheng-10464	134	5	purpose	purpose	NOUN
fumecheng-10464	134	6	of	of	ADP
fumecheng-10464	134	7	this	this	DET
fumecheng-10464	134	8	section	section	NOUN
fumecheng-10464	134	9	is	be	AUX
fumecheng-10464	134	10	to	to	PART
fumecheng-10464	134	11	attain	attain	VERB
fumecheng-10464	134	12	an	an	DET
fumecheng-10464	134	13	analytical	analytical	ADJ
fumecheng-10464	134	14	bounded	bound	VERB
fumecheng-10464	134	15	approximate	approximate	ADJ
fumecheng-10464	134	16	solution	solution	NOUN
fumecheng-10464	134	17	for	for	ADP
fumecheng-10464	134	18	the	the	DET
fumecheng-10464	134	19	dvdp	dvdp	ADJ
fumecheng-10464	134	20	equation	equation	NOUN
fumecheng-10464	134	21	.	.	PUNCT
fumecheng-10464	135	1	the	the	DET
fumecheng-10464	135	2	the	the	DET
fumecheng-10464	135	3	classical	classical	ADJ
fumecheng-10464	135	4	hpm	hpm	NOUN
fumecheng-10464	135	5	does	do	AUX
fumecheng-10464	135	6	not	not	PART
fumecheng-10464	135	7	enable	enable	VERB
fumecheng-10464	135	8	us	we	PRON
fumecheng-10464	135	9	to	to	PART
fumecheng-10464	135	10	satisfy	satisfy	VERB
fumecheng-10464	135	11	this	this	DET
fumecheng-10464	135	12	end	end	NOUN
fumecheng-10464	135	13	properly	properly	ADV
fumecheng-10464	135	14	.	.	PUNCT
fumecheng-10464	136	1	consequently	consequently	ADV
fumecheng-10464	136	2	,	,	PUNCT
fumecheng-10464	136	3	one	one	PRON
fumecheng-10464	136	4	necessarily	necessarily	ADV
fumecheng-10464	136	5	seeks	seek	VERB
fumecheng-10464	136	6	another	another	DET
fumecheng-10464	136	7	new	new	ADJ
fumecheng-10464	136	8	technique	technique	NOUN
fumecheng-10464	136	9	to	to	PART
fumecheng-10464	136	10	realize	realize	VERB
fumecheng-10464	136	11	a	a	DET
fumecheng-10464	136	12	bounded	bounded	ADJ
fumecheng-10464	136	13	solution	solution	NOUN
fumecheng-10464	136	14	of	of	ADP
fumecheng-10464	136	15	the	the	DET
fumecheng-10464	136	16	considered	consider	VERB
fumecheng-10464	136	17	equation	equation	NOUN
fumecheng-10464	136	18	.	.	PUNCT
fumecheng-10464	137	1	to	to	ADP
fumecheng-10464	137	2	this	this	DET
fumecheng-10464	137	3	end	end	NOUN
fumecheng-10464	137	4	,	,	PUNCT
fumecheng-10464	137	5	consider	consider	VERB
fumecheng-10464	137	6	the	the	DET
fumecheng-10464	137	7	homotopy	homotopy	NOUN
fumecheng-10464	137	8	equation	equation	NOUN
fumecheng-10464	137	9	that	that	PRON
fumecheng-10464	137	10	is	be	AUX
fumecheng-10464	137	11	given	give	VERB
fumecheng-10464	137	12	by	by	ADP
fumecheng-10464	137	13	eq	eq	PROPN
fumecheng-10464	137	14	.	.	PUNCT
fumecheng-10464	138	1	(	(	PUNCT
fumecheng-10464	138	2	3	3	NUM
fumecheng-10464	138	3	)	)	PUNCT
fumecheng-10464	138	4	,	,	PUNCT
fumecheng-10464	138	5	where	where	SCONJ
fumecheng-10464	138	6	the	the	DET
fumecheng-10464	138	7	natural	natural	ADJ
fumecheng-10464	138	8	frequency	frequency	NOUN
fumecheng-10464	138	9	of	of	ADP
fumecheng-10464	138	10	the	the	DET
fumecheng-10464	138	11	current	current	ADJ
fumecheng-10464	138	12	model	model	NOUN
fumecheng-10464	138	13	is	be	AUX
fumecheng-10464	138	14	the	the	DET
fumecheng-10464	138	15	unity	unity	NOUN
fumecheng-10464	138	16	.	.	PUNCT
fumecheng-10464	139	1	2	2	NUM
fumecheng-10464	139	2	3	3	NUM
fumecheng-10464	139	3	(	(	PUNCT
fumecheng-10464	139	4	(	(	PUNCT
fumecheng-10464	139	5	1	1	X
fumecheng-10464	139	6	)	)	PUNCT
fumecheng-10464	139	7	cos	cos	NOUN
fumecheng-10464	139	8	)	)	PUNCT
fumecheng-10464	139	9	0	0	NUM
fumecheng-10464	139	10	;	;	PUNCT
fumecheng-10464	140	1	[	[	X
fumecheng-10464	140	2	0,1]x	0,1]x	NOUN
fumecheng-10464	140	3	x	x	X
fumecheng-10464	140	4	x	x	PUNCT
fumecheng-10464	140	5	x	x	PUNCT
fumecheng-10464	140	6	x	x	X
fumecheng-10464	140	7	f	f	NOUN
fumecheng-10464	140	8	t	t	NOUN
fumecheng-10464	140	9			NOUN
fumecheng-10464	140	10			NOUN
fumecheng-10464	140	11	+	+	NOUN
fumecheng-10464	140	12	+	+	CCONJ
fumecheng-10464	140	13	−	−	PROPN
fumecheng-10464	140	14	+	+	CCONJ
fumecheng-10464	140	15	−	−	PROPN
fumecheng-10464	140	16			PROPN
fumecheng-10464	140	17	=	=	NOUN
fumecheng-10464	140	18			NOUN
fumecheng-10464	140	19	(	(	PUNCT
fumecheng-10464	140	20	3	3	NUM
fumecheng-10464	140	21	)	)	PUNCT
fumecheng-10464	140	22	along	along	ADP
fumecheng-10464	140	23	with	with	ADP
fumecheng-10464	140	24	this	this	DET
fumecheng-10464	140	25	approach	approach	NOUN
fumecheng-10464	140	26	,	,	PUNCT
fumecheng-10464	140	27	the	the	DET
fumecheng-10464	140	28	time	time	NOUN
fumecheng-10464	140	29	dependent	dependent	ADJ
fumecheng-10464	140	30	function	function	NOUN
fumecheng-10464	140	31	may	may	AUX
fumecheng-10464	140	32	be	be	AUX
fumecheng-10464	140	33	determined	determine	VERB
fumecheng-10464	140	34	as	as	SCONJ
fumecheng-10464	140	35	follows	follow	VERB
fumecheng-10464	140	36	:	:	PUNCT
fumecheng-10464	140	37			X
fumecheng-10464	140	38			VERB
fumecheng-10464	140	39	=	=	PUNCT
fumecheng-10464	140	40	=	=	NOUN
fumecheng-10464	140	41	0	0	NUM
fumecheng-10464	140	42	)	)	PUNCT
fumecheng-10464	140	43	(	(	PUNCT
fumecheng-10464	140	44	)	)	PUNCT
fumecheng-10464	140	45	;	;	PUNCT
fumecheng-10464	140	46	(	(	PUNCT
fumecheng-10464	140	47	n	n	CCONJ
fumecheng-10464	140	48	n	n	CCONJ
fumecheng-10464	140	49	n	n	ADV
fumecheng-10464	140	50	txtx	txtx	ADJ
fumecheng-10464	140	51			NOUN
fumecheng-10464	140	52	(	(	PUNCT
fumecheng-10464	140	53	4	4	X
fumecheng-10464	140	54	)	)	PUNCT
fumecheng-10464	140	55	the	the	DET
fumecheng-10464	140	56	following	follow	VERB
fumecheng-10464	140	57	stability	stability	NOUN
fumecheng-10464	140	58	examination	examination	NOUN
fumecheng-10464	140	59	will	will	AUX
fumecheng-10464	140	60	be	be	AUX
fumecheng-10464	140	61	constructed	construct	VERB
fumecheng-10464	140	62	on	on	ADP
fumecheng-10464	140	63	the	the	DET
fumecheng-10464	140	64	nonlinear	nonlinear	ADJ
fumecheng-10464	140	65	frequency	frequency	NOUN
fumecheng-10464	140	66	analysis	analysis	NOUN
fumecheng-10464	140	67	given	give	VERB
fumecheng-10464	140	68	by	by	ADP
fumecheng-10464	140	69	moatimid	moatimid	NOUN
fumecheng-10464	140	70	[	[	X
fumecheng-10464	140	71	31	31	NUM
fumecheng-10464	140	72	]	]	PUNCT
fumecheng-10464	140	73	.	.	PUNCT
fumecheng-10464	141	1	in	in	ADP
fumecheng-10464	141	2	accordance	accordance	NOUN
fumecheng-10464	141	3	with	with	ADP
fumecheng-10464	141	4	this	this	DET
fumecheng-10464	141	5	approach	approach	NOUN
fumecheng-10464	141	6	,	,	PUNCT
fumecheng-10464	141	7	an	an	DET
fumecheng-10464	141	8	expanded	expand	VERB
fumecheng-10464	141	9	artificial	artificial	ADJ
fumecheng-10464	141	10	frequency	frequency	NOUN
fumecheng-10464	141	11	σ2	σ2	NOUN
fumecheng-10464	141	12	may	may	AUX
fumecheng-10464	141	13	be	be	AUX
fumecheng-10464	141	14	formulated	formulate	VERB
fumecheng-10464	141	15	as	as	SCONJ
fumecheng-10464	141	16	follows	follow	VERB
fumecheng-10464	141	17	:	:	PUNCT
fumecheng-10464	141	18			X
fumecheng-10464	141	19			VERB
fumecheng-10464	141	20	=	=	PUNCT
fumecheng-10464	142	1	+	+	SYM
fumecheng-10464	142	2	=	=	SYM
fumecheng-10464	142	3	1	1	NUM
fumecheng-10464	142	4	2	2	NUM
fumecheng-10464	142	5	1	1	NUM
fumecheng-10464	142	6	j	j	NOUN
fumecheng-10464	142	7	j	j	PROPN
fumecheng-10464	142	8	j	j	NOUN
fumecheng-10464	142	9	(	(	PUNCT
fumecheng-10464	142	10	5	5	NUM
fumecheng-10464	142	11	)	)	PUNCT
fumecheng-10464	142	12	where	where	SCONJ
fumecheng-10464	142	13	the	the	DET
fumecheng-10464	142	14	parameters	parameter	NOUN
fumecheng-10464	142	15	σj	σj	VERB
fumecheng-10464	142	16	(	(	PUNCT
fumecheng-10464	142	17	j=1,2	j=1,2	ADJ
fumecheng-10464	142	18	,	,	PUNCT
fumecheng-10464	142	19	…	…	PUNCT
fumecheng-10464	142	20	)	)	PUNCT
fumecheng-10464	142	21	will	will	AUX
fumecheng-10464	142	22	be	be	AUX
fumecheng-10464	142	23	determined	determine	VERB
fumecheng-10464	142	24	from	from	ADP
fumecheng-10464	142	25	the	the	DET
fumecheng-10464	142	26	invalidation	invalidation	NOUN
fumecheng-10464	142	27	of	of	ADP
fumecheng-10464	142	28	the	the	DET
fumecheng-10464	142	29	sources	source	NOUN
fumecheng-10464	142	30	of	of	ADP
fumecheng-10464	142	31	the	the	DET
fumecheng-10464	142	32	secular	secular	ADJ
fumecheng-10464	142	33	terms	term	NOUN
fumecheng-10464	142	34	.	.	PUNCT
fumecheng-10464	143	1	by	by	ADP
fumecheng-10464	143	2	combining	combine	VERB
fumecheng-10464	143	3	eqs	eqs	PROPN
fumecheng-10464	143	4	.	.	PUNCT
fumecheng-10464	144	1	(	(	PUNCT
fumecheng-10464	144	2	3	3	X
fumecheng-10464	144	3	)	)	PUNCT
fumecheng-10464	144	4	and	and	CCONJ
fumecheng-10464	144	5	(	(	PUNCT
fumecheng-10464	144	6	4	4	NUM
fumecheng-10464	144	7	)	)	PUNCT
fumecheng-10464	144	8	,	,	PUNCT
fumecheng-10464	144	9	the	the	DET
fumecheng-10464	144	10	homotopy	homotopy	NOUN
fumecheng-10464	144	11	equation	equation	NOUN
fumecheng-10464	144	12	may	may	AUX
fumecheng-10464	144	13	be	be	AUX
fumecheng-10464	144	14	rewritten	rewrite	VERB
fumecheng-10464	144	15	as	as	ADP
fumecheng-10464	144	16	:	:	SYM
fumecheng-10464	144	17	2	2	NUM
fumecheng-10464	144	18	2	2	NUM
fumecheng-10464	144	19	2	2	NUM
fumecheng-10464	144	20	3	3	NUM
fumecheng-10464	144	21	1	1	NUM
fumecheng-10464	144	22	2	2	NUM
fumecheng-10464	144	23	3	3	NUM
fumecheng-10464	144	24	(	(	PUNCT
fumecheng-10464	144	25	(	(	PUNCT
fumecheng-10464	144	26	1	1	X
fumecheng-10464	144	27	)	)	PUNCT
fumecheng-10464	144	28	(	(	PUNCT
fumecheng-10464	144	29	)	)	PUNCT
fumecheng-10464	144	30	cos	cos	X
fumecheng-10464	144	31	)	)	PUNCT
fumecheng-10464	144	32	0x	0x	NOUN
fumecheng-10464	144	33	x	x	SYM
fumecheng-10464	144	34	x	x	PUNCT
fumecheng-10464	144	35	x	x	PUNCT
fumecheng-10464	144	36	x	x	SYM
fumecheng-10464	144	37	x	x	SYM
fumecheng-10464	144	38	f	f	PROPN
fumecheng-10464	144	39	t	t	PROPN
fumecheng-10464	144	40			ADP
fumecheng-10464	145	1			NOUN
fumecheng-10464	145	2			NUM
fumecheng-10464	145	3			PUNCT
fumecheng-10464	145	4			X
fumecheng-10464	145	5			X
fumecheng-10464	145	6	+	+	PROPN
fumecheng-10464	145	7	+	+	CCONJ
fumecheng-10464	145	8	−	−	PROPN
fumecheng-10464	145	9	−	−	PROPN
fumecheng-10464	146	1	+	+	CCONJ
fumecheng-10464	146	2	+	+	PUNCT
fumecheng-10464	147	1	+	+	CCONJ
fumecheng-10464	147	2	−	−	NUM
fumecheng-10464	147	3			NOUN
fumecheng-10464	147	4	=	=	PUNCT
fumecheng-10464	147	5	(	(	PUNCT
fumecheng-10464	147	6	6	6	NUM
fumecheng-10464	147	7	)	)	PUNCT
fumecheng-10464	147	8	it	it	PRON
fumecheng-10464	147	9	is	be	AUX
fumecheng-10464	147	10	worth	worth	ADJ
fumecheng-10464	147	11	mentioning	mention	VERB
fumecheng-10464	147	12	that	that	SCONJ
fumecheng-10464	147	13	if	if	SCONJ
fumecheng-10464	147	14	the	the	DET
fumecheng-10464	147	15	standard	standard	ADJ
fumecheng-10464	147	16	initial	initial	ADJ
fumecheng-10464	147	17	conditions	condition	NOUN
fumecheng-10464	147	18	are	be	AUX
fumecheng-10464	147	19	considered	consider	VERB
fumecheng-10464	147	20	as	as	SCONJ
fumecheng-10464	147	21	approached	approach	VERB
fumecheng-10464	147	22	by	by	ADP
fumecheng-10464	147	23	moatimid	moatimid	PROPN
fumecheng-10464	147	24	[	[	X
fumecheng-10464	147	25	36	36	NUM
fumecheng-10464	147	26	]	]	PUNCT
fumecheng-10464	147	27	,	,	PUNCT
fumecheng-10464	147	28	the	the	DET
fumecheng-10464	147	29	stiffness	stiffness	NOUN
fumecheng-10464	147	30	parameter	parameter	NOUN
fumecheng-10464	147	31	µ	µ	PROPN
fumecheng-10464	147	32	will	will	AUX
fumecheng-10464	147	33	disappear	disappear	VERB
fumecheng-10464	147	34	.	.	PUNCT
fumecheng-10464	148	1	therefore	therefore	ADV
fumecheng-10464	148	2	,	,	PUNCT
fumecheng-10464	148	3	to	to	PART
fumecheng-10464	148	4	preserve	preserve	VERB
fumecheng-10464	148	5	the	the	DET
fumecheng-10464	148	6	presence	presence	NOUN
fumecheng-10464	148	7	of	of	ADP
fumecheng-10464	148	8	this	this	DET
fumecheng-10464	148	9	parameter	parameter	NOUN
fumecheng-10464	148	10	in	in	ADP
fumecheng-10464	148	11	the	the	DET
fumecheng-10464	148	12	following	follow	VERB
fumecheng-10464	148	13	analysis	analysis	NOUN
fumecheng-10464	148	14	,	,	PUNCT
fumecheng-10464	148	15	an	an	DET
fumecheng-10464	148	16	adjustment	adjustment	NOUN
fumecheng-10464	148	17	of	of	ADP
fumecheng-10464	148	18	the	the	DET
fumecheng-10464	148	19	initial	initial	ADJ
fumecheng-10464	148	20	conditions	condition	NOUN
fumecheng-10464	148	21	must	must	AUX
fumecheng-10464	148	22	take	take	VERB
fumecheng-10464	148	23	place	place	NOUN
fumecheng-10464	148	24	.	.	PUNCT
fumecheng-10464	149	1	consequently	consequently	ADV
fumecheng-10464	149	2	,	,	PUNCT
fumecheng-10464	149	3	a	a	DET
fumecheng-10464	149	4	modification	modification	NOUN
fumecheng-10464	149	5	of	of	ADP
fumecheng-10464	149	6	the	the	DET
fumecheng-10464	149	7	initial	initial	ADJ
fumecheng-10464	149	8	conditions	condition	NOUN
fumecheng-10464	149	9	may	may	AUX
fumecheng-10464	149	10	be	be	AUX
fumecheng-10464	149	11	written	write	VERB
fumecheng-10464	149	12	as	as	SCONJ
fumecheng-10464	149	13	follows	follow	VERB
fumecheng-10464	149	14	:	:	PUNCT
fumecheng-10464	149	15	,	,	PUNCT
fumecheng-10464	149	16	0)0	0)0	PROPN
fumecheng-10464	149	17	(	(	PUNCT
fumecheng-10464	149	18	=	=	NOUN
fumecheng-10464	149	19	x	x	X
fumecheng-10464	149	20	and	and	CCONJ
fumecheng-10464	149	21			X
fumecheng-10464	149	22			VERB
fumecheng-10464	149	23	=	=	PUNCT
fumecheng-10464	149	24	=	=	NOUN
fumecheng-10464	149	25	0	0	NUM
fumecheng-10464	149	26	)	)	PUNCT
fumecheng-10464	149	27	0	0	NUM
fumecheng-10464	150	1	(	(	PUNCT
fumecheng-10464	150	2	j	j	PROPN
fumecheng-10464	150	3	j	j	PROPN
fumecheng-10464	150	4	jx	jx	PROPN
fumecheng-10464	150	5			PROPN
fumecheng-10464	150	6	(	(	PUNCT
fumecheng-10464	150	7	7	7	NUM
fumecheng-10464	150	8	)	)	PUNCT
fumecheng-10464	150	9	where	where	SCONJ
fumecheng-10464	150	10	the	the	DET
fumecheng-10464	150	11	constants	constant	NOUN
fumecheng-10464	150	12	λi	λi	INTJ
fumecheng-10464	150	13	will	will	AUX
fumecheng-10464	150	14	be	be	AUX
fumecheng-10464	150	15	determined	determine	VERB
fumecheng-10464	150	16	later	later	ADV
fumecheng-10464	150	17	as	as	ADP
fumecheng-10464	150	18	a	a	DET
fumecheng-10464	150	19	function	function	NOUN
fumecheng-10464	150	20	of	of	ADP
fumecheng-10464	150	21	the	the	DET
fumecheng-10464	150	22	characteristics	characteristic	NOUN
fumecheng-10464	150	23	of	of	ADP
fumecheng-10464	150	24	the	the	DET
fumecheng-10464	150	25	given	give	VERB
fumecheng-10464	150	26	equation	equation	NOUN
fumecheng-10464	150	27	.	.	PUNCT
fumecheng-10464	151	1	6	6	NUM
fumecheng-10464	151	2	j.-h	j.-h	NOUN
fumecheng-10464	151	3	.	.	PUNCT
fumecheng-10464	152	1	he	he	PRON
fumecheng-10464	152	2	,	,	PUNCT
fumecheng-10464	152	3	g.	g.	PROPN
fumecheng-10464	152	4	m.	m.	PROPN
fumecheng-10464	152	5	moatimid	moatimid	PROPN
fumecheng-10464	152	6	,	,	PUNCT
fumecheng-10464	152	7	m.	m.	PROPN
fumecheng-10464	152	8	h.	h.	PROPN
fumecheng-10464	152	9	zekry	zekry	PROPN
fumecheng-10464	152	10	this	this	PRON
fumecheng-10464	152	11	will	will	AUX
fumecheng-10464	152	12	be	be	AUX
fumecheng-10464	152	13	done	do	VERB
fumecheng-10464	152	14	,	,	PUNCT
fumecheng-10464	152	15	together	together	ADV
fumecheng-10464	152	16	with	with	SCONJ
fumecheng-10464	152	17	the	the	DET
fumecheng-10464	152	18	parameters	parameter	NOUN
fumecheng-10464	152	19	σj	σj	VERB
fumecheng-10464	152	20	as	as	SCONJ
fumecheng-10464	152	21	given	give	VERB
fumecheng-10464	152	22	in	in	ADP
fumecheng-10464	152	23	eq	eq	ADP
fumecheng-10464	152	24	.	.	PUNCT
fumecheng-10464	153	1	(	(	PUNCT
fumecheng-10464	153	2	5	5	NUM
fumecheng-10464	153	3	)	)	PUNCT
fumecheng-10464	153	4	,	,	PUNCT
fumecheng-10464	153	5	in	in	ADP
fumecheng-10464	153	6	light	light	NOUN
fumecheng-10464	153	7	of	of	ADP
fumecheng-10464	153	8	the	the	DET
fumecheng-10464	153	9	cancellation	cancellation	NOUN
fumecheng-10464	153	10	of	of	ADP
fumecheng-10464	153	11	the	the	DET
fumecheng-10464	153	12	secular	secular	ADJ
fumecheng-10464	153	13	terms	term	NOUN
fumecheng-10464	153	14	.	.	PUNCT
fumecheng-10464	154	1	taking	take	VERB
fumecheng-10464	154	2	the	the	DET
fumecheng-10464	154	3	laplace	laplace	NOUN
fumecheng-10464	154	4	transforms	transform	VERB
fumecheng-10464	154	5	to	to	ADP
fumecheng-10464	154	6	eq	eq	PROPN
fumecheng-10464	154	7	.	.	PUNCT
fumecheng-10464	155	1	(	(	PUNCT
fumecheng-10464	155	2	6	6	NUM
fumecheng-10464	155	3	)	)	PUNCT
fumecheng-10464	155	4	,	,	PUNCT
fumecheng-10464	155	5	while	while	SCONJ
fumecheng-10464	155	6	considering	consider	VERB
fumecheng-10464	155	7	the	the	DET
fumecheng-10464	155	8	initial	initial	ADJ
fumecheng-10464	155	9	conditions	condition	NOUN
fumecheng-10464	155	10	given	give	VERB
fumecheng-10464	155	11	in	in	ADP
fumecheng-10464	155	12	eq	eq	ADP
fumecheng-10464	155	13	.	.	PUNCT
fumecheng-10464	156	1	(	(	PUNCT
fumecheng-10464	156	2	7	7	NUM
fumecheng-10464	156	3	)	)	PUNCT
fumecheng-10464	156	4	,	,	PUNCT
fumecheng-10464	156	5	the	the	DET
fumecheng-10464	156	6	result	result	NOUN
fumecheng-10464	156	7	becomes	become	VERB
fumecheng-10464	156	8	2	2	NUM
fumecheng-10464	156	9	30	30	NUM
fumecheng-10464	156	10	31	31	NUM
fumecheng-10464	156	11	2	2	NUM
fumecheng-10464	156	12	2	2	NUM
fumecheng-10464	156	13	2	2	NUM
fumecheng-10464	156	14	2	2	NUM
fumecheng-10464	156	15	2	2	NUM
fumecheng-10464	156	16	2	2	NUM
fumecheng-10464	156	17	2	2	NUM
fumecheng-10464	156	18	2	2	NUM
fumecheng-10464	156	19	2	2	NUM
fumecheng-10464	156	20	2	2	NUM
fumecheng-10464	156	21	2	2	NUM
fumecheng-10464	156	22	3	3	NUM
fumecheng-10464	156	23	1	1	NUM
fumecheng-10464	156	24	2	2	NUM
fumecheng-10464	156	25	32	32	NUM
fumecheng-10464	156	26	2	2	NUM
fumecheng-10464	156	27	{	{	PUNCT
fumecheng-10464	156	28	(	(	PUNCT
fumecheng-10464	156	29	;	;	PUNCT
fumecheng-10464	156	30	)	)	PUNCT
fumecheng-10464	156	31	}	}	PUNCT
fumecheng-10464	156	32	....	....	PUNCT
fumecheng-10464	157	1	1	1	X
fumecheng-10464	157	2	{	{	PUNCT
fumecheng-10464	157	3	(	(	PUNCT
fumecheng-10464	157	4	(	(	PUNCT
fumecheng-10464	157	5	1	1	X
fumecheng-10464	157	6	)	)	PUNCT
fumecheng-10464	157	7	(	(	PUNCT
fumecheng-10464	157	8	)	)	PUNCT
fumecheng-10464	157	9	cos	cos	PROPN
fumecheng-10464	157	10	)	)	PUNCT
fumecheng-10464	157	11	}	}	PUNCT
fumecheng-10464	157	12	.	.	PUNCT
fumecheng-10464	158	1	t	t	PROPN
fumecheng-10464	158	2	t	t	PROPN
fumecheng-10464	158	3	l	l	NOUN
fumecheng-10464	159	1	x	x	PUNCT
fumecheng-10464	159	2	t	t	NOUN
fumecheng-10464	159	3	s	s	X
fumecheng-10464	159	4	s	s	NOUN
fumecheng-10464	159	5	s	s	X
fumecheng-10464	159	6	s	s	NOUN
fumecheng-10464	159	7	l	l	NOUN
fumecheng-10464	159	8	x	x	PUNCT
fumecheng-10464	159	9	x	x	PUNCT
fumecheng-10464	159	10	x	x	PUNCT
fumecheng-10464	159	11	x	x	SYM
fumecheng-10464	159	12	f	f	PROPN
fumecheng-10464	159	13	t	t	PROPN
fumecheng-10464	159	14	s	s	PART
fumecheng-10464	159	15			ADJ
fumecheng-10464	159	16			NOUN
fumecheng-10464	159	17			ADJ
fumecheng-10464	159	18			ADP
fumecheng-10464	159	19			X
fumecheng-10464	159	20			X
fumecheng-10464	159	21			ADP
fumecheng-10464	159	22			PROPN
fumecheng-10464	159	23			X
fumecheng-10464	159	24			X
fumecheng-10464	159	25			X
fumecheng-10464	159	26			NOUN
fumecheng-10464	159	27			NOUN
fumecheng-10464	159	28			X
fumecheng-10464	159	29			PUNCT
fumecheng-10464	159	30			ADP
fumecheng-10464	159	31			PROPN
fumecheng-10464	159	32			NOUN
fumecheng-10464	159	33			PROPN
fumecheng-10464	159	34	=	=	PUNCT
fumecheng-10464	160	1	+	+	PUNCT
fumecheng-10464	161	1	+	+	PUNCT
fumecheng-10464	161	2	+	+	PUNCT
fumecheng-10464	161	3	+	+	PUNCT
fumecheng-10464	161	4	+	+	PUNCT
fumecheng-10464	161	5	+	+	PUNCT
fumecheng-10464	161	6	+	+	PUNCT
fumecheng-10464	161	7	+	+	NUM
fumecheng-10464	161	8	−	−	ADP
fumecheng-10464	161	9	−	−	NOUN
fumecheng-10464	161	10	−	−	PROPN
fumecheng-10464	162	1	+	+	CCONJ
fumecheng-10464	162	2	+	+	PUNCT
fumecheng-10464	162	3	+	+	CCONJ
fumecheng-10464	162	4	−	−	NUM
fumecheng-10464	162	5			PRON
fumecheng-10464	163	1	+	+	CCONJ
fumecheng-10464	163	2	(	(	PUNCT
fumecheng-10464	163	3	8)	8)	NUM
fumecheng-10464	163	4	employing	employ	VERB
fumecheng-10464	163	5	the	the	DET
fumecheng-10464	163	6	inverse	inverse	NOUN
fumecheng-10464	163	7	transform	transform	NOUN
fumecheng-10464	163	8	of	of	ADP
fumecheng-10464	163	9	both	both	DET
fumecheng-10464	163	10	sides	side	NOUN
fumecheng-10464	163	11	of	of	ADP
fumecheng-10464	163	12	eq	eq	PROPN
fumecheng-10464	163	13	.	.	PUNCT
fumecheng-10464	164	1	(	(	PUNCT
fumecheng-10464	164	2	8)	8)	NUM
fumecheng-10464	164	3	,	,	PUNCT
fumecheng-10464	164	4	one	one	PRON
fumecheng-10464	164	5	gets	get	VERB
fumecheng-10464	164	6	:	:	PUNCT
fumecheng-10464	164	7	2	2	NUM
fumecheng-10464	164	8	30	30	NUM
fumecheng-10464	164	9	31	31	NUM
fumecheng-10464	164	10	2	2	NUM
fumecheng-10464	164	11	1	1	NUM
fumecheng-10464	164	12	2	2	NUM
fumecheng-10464	164	13	2	2	NUM
fumecheng-10464	164	14	3	3	NUM
fumecheng-10464	164	15	1	1	NUM
fumecheng-10464	164	16	2	2	NUM
fumecheng-10464	164	17	32	32	NUM
fumecheng-10464	164	18	2	2	NUM
fumecheng-10464	164	19	(	(	PUNCT
fumecheng-10464	164	20	;	;	PUNCT
fumecheng-10464	164	21	)	)	PUNCT
fumecheng-10464	164	22	......	......	PUNCT
fumecheng-10464	165	1	sin	sin	NOUN
fumecheng-10464	165	2	1	1	NUM
fumecheng-10464	165	3	{	{	PUNCT
fumecheng-10464	165	4	(	(	PUNCT
fumecheng-10464	165	5	(	(	PUNCT
fumecheng-10464	165	6	1	1	X
fumecheng-10464	165	7	)	)	PUNCT
fumecheng-10464	165	8	(	(	PUNCT
fumecheng-10464	165	9	)	)	PUNCT
fumecheng-10464	165	10	cos	cos	PROPN
fumecheng-10464	165	11	)	)	PUNCT
fumecheng-10464	165	12	}	}	PUNCT
fumecheng-10464	165	13	t	t	NOUN
fumecheng-10464	165	14	t	t	PROPN
fumecheng-10464	165	15	x	x	PUNCT
fumecheng-10464	166	1	t	t	PROPN
fumecheng-10464	166	2	t	t	PROPN
fumecheng-10464	166	3	l	l	NOUN
fumecheng-10464	166	4	l	l	NOUN
fumecheng-10464	167	1	x	x	PUNCT
fumecheng-10464	167	2	x	x	PUNCT
fumecheng-10464	167	3	x	x	PUNCT
fumecheng-10464	167	4	x	x	SYM
fumecheng-10464	167	5	f	f	PROPN
fumecheng-10464	167	6	t	t	PROPN
fumecheng-10464	167	7	s	s	PART
fumecheng-10464	167	8			ADJ
fumecheng-10464	167	9			NOUN
fumecheng-10464	167	10			ADJ
fumecheng-10464	167	11			ADP
fumecheng-10464	167	12			X
fumecheng-10464	167	13			X
fumecheng-10464	167	14			ADP
fumecheng-10464	167	15			PROPN
fumecheng-10464	167	16			X
fumecheng-10464	167	17			X
fumecheng-10464	167	18			X
fumecheng-10464	167	19			X
fumecheng-10464	167	20			NOUN
fumecheng-10464	167	21			NOUN
fumecheng-10464	167	22			X
fumecheng-10464	167	23			PUNCT
fumecheng-10464	167	24			ADP
fumecheng-10464	167	25			PROPN
fumecheng-10464	167	26			PROPN
fumecheng-10464	167	27			PROPN
fumecheng-10464	167	28	−	−	PROPN
fumecheng-10464	167	29			NOUN
fumecheng-10464	167	30			NOUN
fumecheng-10464	167	31	=	=	PUNCT
fumecheng-10464	168	1	+	+	PUNCT
fumecheng-10464	169	1	+	+	PUNCT
fumecheng-10464	169	2	+	+	PUNCT
fumecheng-10464	169	3	+	+	CCONJ
fumecheng-10464	169	4	−	−	PROPN
fumecheng-10464	169	5			PROPN
fumecheng-10464	169	6			PROPN
fumecheng-10464	169	7			PROPN
fumecheng-10464	170	1			NUM
fumecheng-10464	170	2			NOUN
fumecheng-10464	170	3	−	−	PROPN
fumecheng-10464	171	1	−	−	PROPN
fumecheng-10464	172	1	+	+	CCONJ
fumecheng-10464	172	2	+	+	PUNCT
fumecheng-10464	172	3	+	+	CCONJ
fumecheng-10464	172	4	−	−	PROPN
fumecheng-10464	172	5			NOUN
fumecheng-10464	172	6			PUNCT
fumecheng-10464	173	1	+	+	CCONJ
fumecheng-10464	173	2			PROPN
fumecheng-10464	173	3			PROPN
fumecheng-10464	173	4	(	(	PUNCT
fumecheng-10464	173	5	9	9	NUM
fumecheng-10464	173	6	)	)	PUNCT
fumecheng-10464	173	7	by	by	ADP
fumecheng-10464	173	8	utilizing	utilize	VERB
fumecheng-10464	173	9	the	the	DET
fumecheng-10464	173	10	expansion	expansion	NOUN
fumecheng-10464	173	11	of	of	ADP
fumecheng-10464	173	12	the	the	DET
fumecheng-10464	173	13	dependent	dependent	ADJ
fumecheng-10464	173	14	parameter	parameter	NOUN
fumecheng-10464	173	15	x(t;ρ	x(t;ρ	PROPN
fumecheng-10464	173	16	)	)	PUNCT
fumecheng-10464	173	17	as	as	SCONJ
fumecheng-10464	173	18	given	give	VERB
fumecheng-10464	173	19	in	in	ADP
fumecheng-10464	173	20	eq	eq	ADP
fumecheng-10464	173	21	.	.	PUNCT
fumecheng-10464	174	1	(	(	PUNCT
fumecheng-10464	174	2	4	4	NUM
fumecheng-10464	174	3	)	)	PUNCT
fumecheng-10464	174	4	,	,	PUNCT
fumecheng-10464	174	5	and	and	CCONJ
fumecheng-10464	174	6	by	by	ADP
fumecheng-10464	174	7	equating	equate	VERB
fumecheng-10464	174	8	the	the	DET
fumecheng-10464	174	9	coefficients	coefficient	NOUN
fumecheng-10464	174	10	of	of	ADP
fumecheng-10464	174	11	like	like	ADP
fumecheng-10464	174	12	powers	power	NOUN
fumecheng-10464	174	13	ρ	ρ	NOUN
fumecheng-10464	174	14	on	on	ADP
fumecheng-10464	174	15	both	both	DET
fumecheng-10464	174	16	sides	side	NOUN
fumecheng-10464	174	17	,	,	PUNCT
fumecheng-10464	174	18	one	one	PRON
fumecheng-10464	174	19	gets	get	VERB
fumecheng-10464	174	20	,	,	PUNCT
fumecheng-10464	174	21	sin	sin	NOUN
fumecheng-10464	174	22	)	)	PUNCT
fumecheng-10464	174	23	(:	(:	VERB
fumecheng-10464	175	1	0	0	NUM
fumecheng-10464	175	2	0	0	SYM
fumecheng-10464	175	3	0	0	NUM
fumecheng-10464	175	4	ttx	ttx	PROPN
fumecheng-10464	175	5			PROPN
fumecheng-10464	175	6			PROPN
fumecheng-10464	175	7			ADJ
fumecheng-10464	175	8			X
fumecheng-10464	175	9	=	=	SYM
fumecheng-10464	175	10	(	(	PUNCT
fumecheng-10464	175	11	10	10	NUM
fumecheng-10464	175	12	)	)	SYM
fumecheng-10464	175	13	1	1	NUM
fumecheng-10464	175	14	2	2	NUM
fumecheng-10464	175	15	31	31	NUM
fumecheng-10464	175	16	1	1	NUM
fumecheng-10464	175	17	0	0	NUM
fumecheng-10464	175	18	0	0	NUM
fumecheng-10464	175	19	1	1	NUM
fumecheng-10464	175	20	0	0	NUM
fumecheng-10464	175	21	02	02	NUM
fumecheng-10464	175	22	2	2	NUM
fumecheng-10464	175	23	1	1	NUM
fumecheng-10464	175	24	:	:	PUNCT
fumecheng-10464	175	25	(	(	PUNCT
fumecheng-10464	175	26	)	)	PUNCT
fumecheng-10464	175	27	sin	sin	NOUN
fumecheng-10464	175	28	(	(	PUNCT
fumecheng-10464	175	29	)	)	PUNCT
fumecheng-10464	175	30	{	{	PUNCT
fumecheng-10464	175	31	(	(	PUNCT
fumecheng-10464	175	32	1	1	X
fumecheng-10464	175	33	)	)	PUNCT
fumecheng-10464	175	34	cos	co	NOUN
fumecheng-10464	175	35	}	}	PUNCT
fumecheng-10464	175	36	t	t	PROPN
fumecheng-10464	175	37	tx	tx	PROPN
fumecheng-10464	175	38	t	t	PROPN
fumecheng-10464	175	39	t	t	PROPN
fumecheng-10464	175	40	l	l	NOUN
fumecheng-10464	175	41	l	l	NOUN
fumecheng-10464	175	42	x	x	PUNCT
fumecheng-10464	175	43	x	x	PUNCT
fumecheng-10464	175	44	x	x	PUNCT
fumecheng-10464	175	45	x	x	SYM
fumecheng-10464	175	46	f	f	PROPN
fumecheng-10464	175	47	t	t	PROPN
fumecheng-10464	175	48	s	s	PART
fumecheng-10464	175	49			ADJ
fumecheng-10464	175	50			NOUN
fumecheng-10464	175	51			NUM
fumecheng-10464	175	52			NOUN
fumecheng-10464	175	53			PROPN
fumecheng-10464	175	54			NOUN
fumecheng-10464	175	55			X
fumecheng-10464	175	56			X
fumecheng-10464	175	57	−	−	NOUN
fumecheng-10464	175	58			NOUN
fumecheng-10464	176	1			PROPN
fumecheng-10464	176	2	=	=	PUNCT
fumecheng-10464	177	1	−	−	PROPN
fumecheng-10464	177	2	−	−	NUM
fumecheng-10464	177	3	−	−	PROPN
fumecheng-10464	177	4	+	+	CCONJ
fumecheng-10464	177	5	−	−	PROPN
fumecheng-10464	177	6			NOUN
fumecheng-10464	177	7			VERB
fumecheng-10464	178	1	+	+	NOUN
fumecheng-10464	178	2			PROPN
fumecheng-10464	178	3			PROPN
fumecheng-10464	178	4	(	(	PUNCT
fumecheng-10464	178	5	11	11	NUM
fumecheng-10464	178	6	)	)	PUNCT
fumecheng-10464	178	7	characteristically	characteristically	ADV
fumecheng-10464	178	8	,	,	PUNCT
fumecheng-10464	178	9	the	the	DET
fumecheng-10464	178	10	uniform	uniform	ADJ
fumecheng-10464	178	11	effective	effective	ADJ
fumecheng-10464	178	12	expansion	expansion	NOUN
fumecheng-10464	178	13	emerges	emerge	VERB
fumecheng-10464	178	14	from	from	ADP
fumecheng-10464	178	15	the	the	DET
fumecheng-10464	178	16	invalidation	invalidation	NOUN
fumecheng-10464	178	17	of	of	ADP
fumecheng-10464	178	18	the	the	DET
fumecheng-10464	178	19	secular	secular	ADJ
fumecheng-10464	178	20	terms	term	NOUN
fumecheng-10464	178	21	.	.	PUNCT
fumecheng-10464	179	1	for	for	ADP
fumecheng-10464	179	2	this	this	DET
fumecheng-10464	179	3	purpose	purpose	NOUN
fumecheng-10464	179	4	,	,	PUNCT
fumecheng-10464	179	5	one	one	PRON
fumecheng-10464	179	6	gets	get	VERB
fumecheng-10464	179	7	the	the	DET
fumecheng-10464	179	8	following	follow	VERB
fumecheng-10464	179	9	results	result	NOUN
fumecheng-10464	179	10	:	:	PUNCT
fumecheng-10464	179	11	▪	▪	X
fumecheng-10464	179	12	the	the	DET
fumecheng-10464	179	13	cancellation	cancellation	NOUN
fumecheng-10464	179	14	of	of	ADP
fumecheng-10464	179	15	the	the	DET
fumecheng-10464	179	16	secular	secular	ADJ
fumecheng-10464	179	17	terms	term	NOUN
fumecheng-10464	179	18	,	,	PUNCT
fumecheng-10464	179	19	i.e.	i.e.	X
fumecheng-10464	179	20	excluding	exclude	VERB
fumecheng-10464	179	21	the	the	DET
fumecheng-10464	179	22	coefficients	coefficient	NOUN
fumecheng-10464	179	23	of	of	ADP
fumecheng-10464	179	24	the	the	DET
fumecheng-10464	179	25	functions	function	NOUN
fumecheng-10464	179	26	sin	sin	VERB
fumecheng-10464	179	27	σt	σt	ADP
fumecheng-10464	179	28	and	and	CCONJ
fumecheng-10464	179	29	cos	cos	ADP
fumecheng-10464	179	30	σt	σt	PROPN
fumecheng-10464	179	31	gives	give	VERB
fumecheng-10464	179	32			PROPN
fumecheng-10464	179	33	20	20	NUM
fumecheng-10464	179	34	=	=	SYM
fumecheng-10464	179	35	(	(	PUNCT
fumecheng-10464	179	36	12	12	NUM
fumecheng-10464	179	37	)	)	PUNCT
fumecheng-10464	179	38	and	and	CCONJ
fumecheng-10464	179	39			NOUN
fumecheng-10464	179	40	31	31	NUM
fumecheng-10464	179	41	=	=	SYM
fumecheng-10464	179	42	(	(	PUNCT
fumecheng-10464	179	43	13	13	NUM
fumecheng-10464	179	44	)	)	PUNCT
fumecheng-10464	179	45	the	the	DET
fumecheng-10464	179	46	second	second	ADJ
fumecheng-10464	179	47	-	-	PUNCT
fumecheng-10464	179	48	order	order	NOUN
fumecheng-10464	179	49	of	of	ADP
fumecheng-10464	179	50	eq	eq	PROPN
fumecheng-10464	179	51	.	.	PUNCT
fumecheng-10464	180	1	(	(	PUNCT
fumecheng-10464	180	2	9	9	X
fumecheng-10464	180	3	)	)	PUNCT
fumecheng-10464	180	4	yields	yield	VERB
fumecheng-10464	180	5	2	2	NUM
fumecheng-10464	180	6	1	1	NUM
fumecheng-10464	180	7	2	2	NUM
fumecheng-10464	180	8	22	22	NUM
fumecheng-10464	180	9	2	2	NUM
fumecheng-10464	180	10	1	1	NUM
fumecheng-10464	180	11	0	0	NUM
fumecheng-10464	180	12	0	0	NUM
fumecheng-10464	180	13	0	0	NUM
fumecheng-10464	180	14	1	1	NUM
fumecheng-10464	180	15	1	1	NUM
fumecheng-10464	180	16	1	1	NUM
fumecheng-10464	180	17	2	2	NUM
fumecheng-10464	180	18	0	0	NUM
fumecheng-10464	180	19	0	0	NUM
fumecheng-10464	180	20	12	12	NUM
fumecheng-10464	180	21	2	2	NUM
fumecheng-10464	180	22	1	1	NUM
fumecheng-10464	180	23	:	:	PUNCT
fumecheng-10464	180	24	(	(	PUNCT
fumecheng-10464	180	25	)	)	PUNCT
fumecheng-10464	180	26	sin	sin	NOUN
fumecheng-10464	180	27	{	{	PUNCT
fumecheng-10464	180	28	(	(	PUNCT
fumecheng-10464	180	29	(	(	PUNCT
fumecheng-10464	180	30	1	1	NUM
fumecheng-10464	180	31	)	)	SYM
fumecheng-10464	180	32	2	2	NUM
fumecheng-10464	180	33	)	)	PUNCT
fumecheng-10464	180	34	3	3	NUM
fumecheng-10464	180	35	}	}	PUNCT
fumecheng-10464	180	36	t	t	PROPN
fumecheng-10464	180	37	tx	tx	PROPN
fumecheng-10464	180	38	t	t	PROPN
fumecheng-10464	180	39	t	t	PROPN
fumecheng-10464	180	40	l	l	NOUN
fumecheng-10464	180	41	l	l	NOUN
fumecheng-10464	180	42	x	x	PUNCT
fumecheng-10464	181	1	x	x	PUNCT
fumecheng-10464	181	2	x	x	PUNCT
fumecheng-10464	181	3	x	x	PUNCT
fumecheng-10464	181	4	x	x	PUNCT
fumecheng-10464	181	5	x	x	PUNCT
fumecheng-10464	181	6	x	x	PUNCT
fumecheng-10464	181	7	x	x	PUNCT
fumecheng-10464	181	8	x	x	SYM
fumecheng-10464	181	9	s	s	X
fumecheng-10464	181	10			ADJ
fumecheng-10464	181	11			NOUN
fumecheng-10464	181	12			NUM
fumecheng-10464	181	13			NOUN
fumecheng-10464	181	14			NOUN
fumecheng-10464	181	15			PROPN
fumecheng-10464	181	16			NOUN
fumecheng-10464	181	17			X
fumecheng-10464	181	18			X
fumecheng-10464	181	19	−	−	NOUN
fumecheng-10464	182	1			NOUN
fumecheng-10464	183	1			PROPN
fumecheng-10464	183	2	=	=	PUNCT
fumecheng-10464	184	1	−	−	PROPN
fumecheng-10464	184	2	−	−	PROPN
fumecheng-10464	185	1	+	+	CCONJ
fumecheng-10464	185	2	−	−	PROPN
fumecheng-10464	185	3	−	−	PRON
fumecheng-10464	186	1	+	+	NOUN
fumecheng-10464	186	2			NUM
fumecheng-10464	186	3			PUNCT
fumecheng-10464	187	1	+	+	NOUN
fumecheng-10464	187	2			PROPN
fumecheng-10464	187	3			PROPN
fumecheng-10464	187	4	(	(	PUNCT
fumecheng-10464	187	5	14	14	NUM
fumecheng-10464	187	6	)	)	PUNCT
fumecheng-10464	187	7	▪	▪	NOUN
fumecheng-10464	187	8	once	once	ADV
fumecheng-10464	187	9	more	more	ADV
fumecheng-10464	187	10	,	,	PUNCT
fumecheng-10464	187	11	the	the	DET
fumecheng-10464	187	12	cancellation	cancellation	NOUN
fumecheng-10464	187	13	of	of	ADP
fumecheng-10464	187	14	the	the	DET
fumecheng-10464	187	15	secular	secular	ADJ
fumecheng-10464	187	16	terms	term	NOUN
fumecheng-10464	187	17	needs	need	VERB
fumecheng-10464	187	18			SYM
fumecheng-10464	187	19	4/51	4/51	NUM
fumecheng-10464	187	20	−=	−=	NOUN
fumecheng-10464	187	21	(	(	PUNCT
fumecheng-10464	187	22	15	15	NUM
fumecheng-10464	187	23	)	)	PUNCT
fumecheng-10464	187	24	and	and	CCONJ
fumecheng-10464	187	25	2222	2222	NUM
fumecheng-10464	187	26	2	2	NUM
fumecheng-10464	187	27	8/)9	8/)9	NUM
fumecheng-10464	187	28	(	(	PUNCT
fumecheng-10464	187	29			NOUN
fumecheng-10464	188	1	+	+	NOUN
fumecheng-10464	188	2	−=	−=	PUNCT
fumecheng-10464	188	3	(	(	PUNCT
fumecheng-10464	188	4	16	16	NUM
fumecheng-10464	188	5	)	)	PUNCT
fumecheng-10464	188	6	the	the	DET
fumecheng-10464	188	7	third	third	ADJ
fumecheng-10464	188	8	-	-	PUNCT
fumecheng-10464	188	9	order	order	NOUN
fumecheng-10464	188	10	of	of	ADP
fumecheng-10464	188	11	eq	eq	PROPN
fumecheng-10464	188	12	.	.	PUNCT
fumecheng-10464	189	1	(	(	PUNCT
fumecheng-10464	189	2	9	9	X
fumecheng-10464	189	3	)	)	PUNCT
fumecheng-10464	189	4	results	result	NOUN
fumecheng-10464	189	5	in	in	ADP
fumecheng-10464	189	6	2	2	NUM
fumecheng-10464	189	7	2	2	NUM
fumecheng-10464	189	8	2	2	NUM
fumecheng-10464	189	9	0	0	NUM
fumecheng-10464	189	10	0	0	NUM
fumecheng-10464	189	11	1	1	NUM
fumecheng-10464	189	12	0	0	NUM
fumecheng-10464	189	13	2	2	NUM
fumecheng-10464	189	14	1	1	NUM
fumecheng-10464	189	15	0	0	NUM
fumecheng-10464	189	16	13	13	NUM
fumecheng-10464	189	17	13	13	NUM
fumecheng-10464	189	18	3	3	NUM
fumecheng-10464	189	19	2	2	NUM
fumecheng-10464	189	20	2	2	NUM
fumecheng-10464	189	21	2	2	NUM
fumecheng-10464	189	22	2	2	NUM
fumecheng-10464	189	23	1	1	NUM
fumecheng-10464	189	24	2	2	NUM
fumecheng-10464	189	25	2	2	NUM
fumecheng-10464	189	26	1	1	NUM
fumecheng-10464	189	27	3	3	NUM
fumecheng-10464	189	28	0	0	NUM
fumecheng-10464	189	29	0	0	NUM
fumecheng-10464	189	30	1	1	NUM
fumecheng-10464	189	31	2	2	NUM
fumecheng-10464	189	32	0	0	NUM
fumecheng-10464	189	33	(	(	PUNCT
fumecheng-10464	189	34	(	(	PUNCT
fumecheng-10464	189	35	1	1	X
fumecheng-10464	189	36	)	)	PUNCT
fumecheng-10464	189	37	(	(	PUNCT
fumecheng-10464	189	38	2	2	NUM
fumecheng-10464	189	39	)	)	PUNCT
fumecheng-10464	189	40	2	2	NUM
fumecheng-10464	189	41	)	)	PUNCT
fumecheng-10464	189	42	1	1	NUM
fumecheng-10464	189	43	:	:	PUNCT
fumecheng-10464	189	44	(	(	PUNCT
fumecheng-10464	189	45	)	)	PUNCT
fumecheng-10464	189	46	sin	sin	NOUN
fumecheng-10464	189	47	3	3	NUM
fumecheng-10464	189	48	(	(	PUNCT
fumecheng-10464	189	49	)	)	PUNCT
fumecheng-10464	189	50	t	t	NOUN
fumecheng-10464	189	51	t	t	NOUN
fumecheng-10464	189	52	x	x	PUNCT
fumecheng-10464	189	53	x	x	PUNCT
fumecheng-10464	189	54	x	x	PUNCT
fumecheng-10464	189	55	x	x	PUNCT
fumecheng-10464	189	56	x	x	PUNCT
fumecheng-10464	189	57	x	x	PUNCT
fumecheng-10464	189	58	x	x	PUNCT
fumecheng-10464	189	59	x	x	PUNCT
fumecheng-10464	189	60	x	x	PUNCT
fumecheng-10464	189	61	x	x	SYM
fumecheng-10464	189	62	t	t	NOUN
fumecheng-10464	189	63	t	t	PROPN
fumecheng-10464	189	64	l	l	NOUN
fumecheng-10464	189	65	l	l	NOUN
fumecheng-10464	189	66	s	s	X
fumecheng-10464	189	67	x	x	X
fumecheng-10464	189	68	x	x	PUNCT
fumecheng-10464	189	69	x	x	PUNCT
fumecheng-10464	189	70	x	x	PUNCT
fumecheng-10464	189	71	x	x	SYM
fumecheng-10464	189	72	x	x	SYM
fumecheng-10464	189	73	x	x	SYM
fumecheng-10464	189	74			PROPN
fumecheng-10464	189	75			NOUN
fumecheng-10464	189	76			PROPN
fumecheng-10464	189	77			X
fumecheng-10464	189	78			X
fumecheng-10464	189	79			X
fumecheng-10464	189	80			X
fumecheng-10464	189	81			PROPN
fumecheng-10464	189	82			NOUN
fumecheng-10464	189	83	−	−	NOUN
fumecheng-10464	189	84			ADP
fumecheng-10464	189	85			NOUN
fumecheng-10464	189	86	−	−	PRON
fumecheng-10464	190	1	+	+	PUNCT
fumecheng-10464	191	1	+	+	PUNCT
fumecheng-10464	191	2	+	+	CCONJ
fumecheng-10464	191	3	−	−	NUM
fumecheng-10464	191	4			NUM
fumecheng-10464	191	5			NOUN
fumecheng-10464	191	6	=	=	PUNCT
fumecheng-10464	192	1	−	−	PROPN
fumecheng-10464	192	2			NUM
fumecheng-10464	192	3			NUM
fumecheng-10464	192	4			VERB
fumecheng-10464	192	5	+	+	CCONJ
fumecheng-10464	192	6	−	−	ADP
fumecheng-10464	192	7	−	−	PROPN
fumecheng-10464	193	1	+	+	CCONJ
fumecheng-10464	193	2	+	+	ADJ
fumecheng-10464	193	3			NUM
fumecheng-10464	193	4			ADJ
fumecheng-10464	193	5			NOUN
fumecheng-10464	193	6			NOUN
fumecheng-10464	193	7			X
fumecheng-10464	193	8	(	(	PUNCT
fumecheng-10464	193	9	17	17	NUM
fumecheng-10464	193	10	)	)	PUNCT
fumecheng-10464	193	11	forced	force	VERB
fumecheng-10464	193	12	nonlinear	nonlinear	ADJ
fumecheng-10464	193	13	oscillator	oscillator	NOUN
fumecheng-10464	193	14	in	in	ADP
fumecheng-10464	193	15	a	a	DET
fumecheng-10464	193	16	fractal	fractal	ADJ
fumecheng-10464	193	17	space	space	NOUN
fumecheng-10464	193	18	7	7	NUM
fumecheng-10464	193	19	▪	▪	NOUN
fumecheng-10464	193	20	once	once	ADV
fumecheng-10464	193	21	more	more	ADV
fumecheng-10464	193	22	,	,	PUNCT
fumecheng-10464	193	23	the	the	DET
fumecheng-10464	193	24	cancellation	cancellation	NOUN
fumecheng-10464	193	25	of	of	ADP
fumecheng-10464	193	26	the	the	DET
fumecheng-10464	193	27	secular	secular	ADJ
fumecheng-10464	193	28	terms	term	NOUN
fumecheng-10464	193	29	necessitates	necessitate	VERB
fumecheng-10464	193	30	2	2	NUM
fumecheng-10464	193	31	2	2	NUM
fumecheng-10464	193	32	2	2	NUM
fumecheng-10464	193	33	2	2	NUM
fumecheng-10464	193	34	2	2	NUM
fumecheng-10464	193	35	2	2	NUM
fumecheng-10464	193	36	2	2	NUM
fumecheng-10464	193	37	2	2	NUM
fumecheng-10464	193	38	2	2	NUM
fumecheng-10464	193	39	4	4	NUM
fumecheng-10464	193	40	2	2	NUM
fumecheng-10464	193	41	2	2	NUM
fumecheng-10464	193	42	3	3	NUM
fumecheng-10464	193	43	4	4	NUM
fumecheng-10464	193	44	2	2	NUM
fumecheng-10464	193	45	2	2	NUM
fumecheng-10464	193	46	4	4	NUM
fumecheng-10464	193	47	2	2	NUM
fumecheng-10464	193	48	3	3	NUM
fumecheng-10464	193	49	2	2	NUM
fumecheng-10464	193	50	2	2	NUM
fumecheng-10464	193	51	2	2	NUM
fumecheng-10464	193	52	2	2	NUM
fumecheng-10464	193	53	2	2	NUM
fumecheng-10464	193	54	(	(	PUNCT
fumecheng-10464	193	55	81	81	NUM
fumecheng-10464	193	56	5	5	NUM
fumecheng-10464	193	57	)	)	PUNCT
fumecheng-10464	193	58	(	(	PUNCT
fumecheng-10464	193	59	)	)	PUNCT
fumecheng-10464	193	60	(	(	PUNCT
fumecheng-10464	193	61	9	9	NUM
fumecheng-10464	193	62	)	)	PUNCT
fumecheng-10464	193	63	72	72	NUM
fumecheng-10464	193	64	(	(	PUNCT
fumecheng-10464	193	65	9	9	NUM
fumecheng-10464	193	66	)	)	PUNCT
fumecheng-10464	193	67	24	24	NUM
fumecheng-10464	193	68	(	(	PUNCT
fumecheng-10464	193	69	69	69	NUM
fumecheng-10464	193	70	6	6	NUM
fumecheng-10464	193	71	)	)	PUNCT
fumecheng-10464	193	72	,	,	PUNCT
fumecheng-10464	193	73	96	96	NUM
fumecheng-10464	193	74	(	(	PUNCT
fumecheng-10464	193	75	)	)	PUNCT
fumecheng-10464	193	76	(	(	PUNCT
fumecheng-10464	193	77	9	9	X
fumecheng-10464	193	78	)	)	PUNCT
fumecheng-10464	193	79	f	f	NOUN
fumecheng-10464	193	80	f	f	ADV
fumecheng-10464	193	81			NOUN
fumecheng-10464	193	82			X
fumecheng-10464	193	83			X
fumecheng-10464	193	84			X
fumecheng-10464	193	85			X
fumecheng-10464	193	86			X
fumecheng-10464	193	87			X
fumecheng-10464	193	88			X
fumecheng-10464	193	89			X
fumecheng-10464	193	90			X
fumecheng-10464	193	91			X
fumecheng-10464	193	92			X
fumecheng-10464	193	93			X
fumecheng-10464	193	94	+	+	NUM
fumecheng-10464	193	95	−	−	PROPN
fumecheng-10464	193	96	−	−	PROPN
fumecheng-10464	193	97	−	−	PROPN
fumecheng-10464	193	98	−	−	NOUN
fumecheng-10464	193	99	+	+	CCONJ
fumecheng-10464	193	100	−	−	NUM
fumecheng-10464	193	101			NUM
fumecheng-10464	194	1	+	+	NOUN
fumecheng-10464	194	2			NOUN
fumecheng-10464	194	3	=	=	NOUN
fumecheng-10464	194	4	−	−	NOUN
fumecheng-10464	194	5	−	−	PROPN
fumecheng-10464	194	6	(	(	PUNCT
fumecheng-10464	194	7	18	18	NUM
fumecheng-10464	194	8	)	)	PUNCT
fumecheng-10464	194	9	and	and	CCONJ
fumecheng-10464	194	10	4222	4222	NUM
fumecheng-10464	194	11	3	3	NUM
fumecheng-10464	194	12	64/)9(9	64/)9(9	NOUN
fumecheng-10464	194	13			X
fumecheng-10464	195	1	+	+	NOUN
fumecheng-10464	195	2	=	=	SYM
fumecheng-10464	195	3	(	(	PUNCT
fumecheng-10464	195	4	19	19	NUM
fumecheng-10464	195	5	)	)	PUNCT
fumecheng-10464	195	6	it	it	PRON
fumecheng-10464	195	7	follows	follow	VERB
fumecheng-10464	195	8	that	that	SCONJ
fumecheng-10464	195	9	the	the	DET
fumecheng-10464	195	10	bounded	bounded	ADJ
fumecheng-10464	195	11	solution	solution	NOUN
fumecheng-10464	195	12	x1(t	x1(t	PUNCT
fumecheng-10464	195	13	)	)	PUNCT
fumecheng-10464	195	14	then	then	ADV
fumecheng-10464	195	15	becomes	become	VERB
fumecheng-10464	195	16	2	2	NUM
fumecheng-10464	195	17	2	2	NUM
fumecheng-10464	195	18	2	2	NUM
fumecheng-10464	195	19	2	2	NUM
fumecheng-10464	195	20	21	21	NUM
fumecheng-10464	195	21	1	1	NUM
fumecheng-10464	195	22	2	2	NUM
fumecheng-10464	195	23	2	2	NUM
fumecheng-10464	195	24	2	2	NUM
fumecheng-10464	195	25	2	2	NUM
fumecheng-10464	195	26	2	2	NUM
fumecheng-10464	195	27	2	2	NUM
fumecheng-10464	195	28	2	2	NUM
fumecheng-10464	195	29	1	1	NUM
fumecheng-10464	195	30	(	(	PUNCT
fumecheng-10464	195	31	)	)	PUNCT
fumecheng-10464	195	32	sin	sin	NOUN
fumecheng-10464	195	33	(	(	PUNCT
fumecheng-10464	195	34	(	(	PUNCT
fumecheng-10464	195	35	4	4	NUM
fumecheng-10464	195	36	(	(	PUNCT
fumecheng-10464	195	37	)	)	PUNCT
fumecheng-10464	195	38	)	)	PUNCT
fumecheng-10464	195	39	cos	cos	ADP
fumecheng-10464	195	40	3	3	NUM
fumecheng-10464	195	41	(	(	PUNCT
fumecheng-10464	195	42	)	)	PUNCT
fumecheng-10464	195	43	sin	sin	NOUN
fumecheng-10464	195	44	4	4	NUM
fumecheng-10464	195	45	cos	cos	ADP
fumecheng-10464	195	46	4	4	NUM
fumecheng-10464	195	47	(	(	PUNCT
fumecheng-10464	195	48	)	)	PUNCT
fumecheng-10464	195	49	(	(	PUNCT
fumecheng-10464	195	50	)	)	PUNCT
fumecheng-10464	195	51	cos3	cos3	PROPN
fumecheng-10464	195	52	(	(	PUNCT
fumecheng-10464	195	53	)	)	PUNCT
fumecheng-10464	195	54	sin	sin	NOUN
fumecheng-10464	195	55	3	3	NUM
fumecheng-10464	195	56	)	)	PUNCT
fumecheng-10464	195	57	.	.	PUNCT
fumecheng-10464	196	1	x	x	X
fumecheng-10464	197	1	t	t	PROPN
fumecheng-10464	197	2	t	t	X
fumecheng-10464	197	3	f	f	PROPN
fumecheng-10464	197	4	t	t	PROPN
fumecheng-10464	197	5	t	t	PROPN
fumecheng-10464	197	6	f	f	PROPN
fumecheng-10464	197	7	t	t	PROPN
fumecheng-10464	197	8	t	t	PROPN
fumecheng-10464	197	9	t	t	PROPN
fumecheng-10464	197	10			ADJ
fumecheng-10464	197	11			X
fumecheng-10464	197	12			X
fumecheng-10464	197	13			NOUN
fumecheng-10464	197	14			NOUN
fumecheng-10464	197	15			NOUN
fumecheng-10464	197	16			PROPN
fumecheng-10464	197	17			PROPN
fumecheng-10464	197	18			PROPN
fumecheng-10464	197	19			X
fumecheng-10464	197	20			X
fumecheng-10464	197	21			X
fumecheng-10464	197	22			X
fumecheng-10464	197	23			X
fumecheng-10464	197	24			X
fumecheng-10464	197	25			X
fumecheng-10464	197	26			PROPN
fumecheng-10464	197	27			NOUN
fumecheng-10464	197	28			X
fumecheng-10464	197	29			PROPN
fumecheng-10464	197	30	=	=	PUNCT
fumecheng-10464	198	1	+	+	NUM
fumecheng-10464	198	2	−	−	PROPN
fumecheng-10464	198	3	+	+	CCONJ
fumecheng-10464	198	4	−	−	PROPN
fumecheng-10464	198	5	+	+	CCONJ
fumecheng-10464	198	6	−	−	PROPN
fumecheng-10464	198	7	+	+	CCONJ
fumecheng-10464	198	8			NUM
fumecheng-10464	199	1	−	−	PROPN
fumecheng-10464	199	2	−	−	PROPN
fumecheng-10464	199	3	−	−	PROPN
fumecheng-10464	199	4	−	−	PROPN
fumecheng-10464	199	5	−	−	PROPN
fumecheng-10464	199	6	(	(	PUNCT
fumecheng-10464	199	7	20	20	NUM
fumecheng-10464	199	8	)	)	PUNCT
fumecheng-10464	199	9	as	as	SCONJ
fumecheng-10464	199	10	mentioned	mention	VERB
fumecheng-10464	199	11	before	before	ADV
fumecheng-10464	199	12	,	,	PUNCT
fumecheng-10464	199	13	for	for	ADP
fumecheng-10464	199	14	an	an	DET
fumecheng-10464	199	15	easy	easy	ADJ
fumecheng-10464	199	16	follow	follow	NOUN
fumecheng-10464	199	17	-	-	PUNCT
fumecheng-10464	199	18	up	up	NOUN
fumecheng-10464	199	19	of	of	ADP
fumecheng-10464	199	20	the	the	DET
fumecheng-10464	199	21	analysis	analysis	NOUN
fumecheng-10464	199	22	,	,	PUNCT
fumecheng-10464	199	23	the	the	DET
fumecheng-10464	199	24	function	function	NOUN
fumecheng-10464	199	25	x2(t	x2(t	PRON
fumecheng-10464	199	26	)	)	PUNCT
fumecheng-10464	199	27	will	will	AUX
fumecheng-10464	199	28	be	be	AUX
fumecheng-10464	199	29	given	give	VERB
fumecheng-10464	199	30	in	in	ADP
fumecheng-10464	199	31	the	the	DET
fumecheng-10464	199	32	appendix	appendix	NOUN
fumecheng-10464	199	33	.	.	PUNCT
fumecheng-10464	200	1	therefore	therefore	ADV
fumecheng-10464	200	2	,	,	PUNCT
fumecheng-10464	200	3	the	the	DET
fumecheng-10464	200	4	periodic	periodic	ADJ
fumecheng-10464	200	5	analytic	analytic	ADJ
fumecheng-10464	200	6	approximate	approximate	ADJ
fumecheng-10464	200	7	solution	solution	NOUN
fumecheng-10464	200	8	of	of	ADP
fumecheng-10464	200	9	the	the	DET
fumecheng-10464	200	10	governing	govern	VERB
fumecheng-10464	200	11	equation	equation	NOUN
fumecheng-10464	200	12	of	of	ADP
fumecheng-10464	200	13	motion	motion	NOUN
fumecheng-10464	200	14	given	give	VERB
fumecheng-10464	200	15	in	in	ADP
fumecheng-10464	200	16	eq	eq	ADP
fumecheng-10464	200	17	.	.	PUNCT
fumecheng-10464	201	1	(	(	PUNCT
fumecheng-10464	201	2	2	2	X
fumecheng-10464	201	3	)	)	PUNCT
fumecheng-10464	201	4	may	may	AUX
fumecheng-10464	201	5	be	be	AUX
fumecheng-10464	201	6	written	write	VERB
fumecheng-10464	201	7	as	as	SCONJ
fumecheng-10464	201	8	follows	follow	VERB
fumecheng-10464	201	9	:	:	PUNCT
fumecheng-10464	201	10	2	2	NUM
fumecheng-10464	201	11	0	0	NUM
fumecheng-10464	201	12	1	1	NUM
fumecheng-10464	201	13	2	2	NUM
fumecheng-10464	201	14	1	1	NUM
fumecheng-10464	201	15	(	(	PUNCT
fumecheng-10464	201	16	)	)	PUNCT
fumecheng-10464	201	17	lim	lim	PROPN
fumecheng-10464	201	18	(	(	PUNCT
fumecheng-10464	201	19	(	(	PUNCT
fumecheng-10464	201	20	)	)	PUNCT
fumecheng-10464	201	21	(	(	PUNCT
fumecheng-10464	201	22	)	)	PUNCT
fumecheng-10464	201	23	(	(	PUNCT
fumecheng-10464	201	24	)	)	PUNCT
fumecheng-10464	201	25	)	)	PUNCT
fumecheng-10464	202	1	x	x	SYM
fumecheng-10464	202	2	t	t	NOUN
fumecheng-10464	202	3	x	x	SYM
fumecheng-10464	202	4	t	t	NOUN
fumecheng-10464	202	5	x	x	SYM
fumecheng-10464	202	6	t	t	PROPN
fumecheng-10464	202	7	x	x	PROPN
fumecheng-10464	202	8	t	t	PROPN
fumecheng-10464	202	9			X
fumecheng-10464	202	10			ADP
fumecheng-10464	202	11			ADP
fumecheng-10464	202	12	→	→	PUNCT
fumecheng-10464	202	13	=	=	SYM
fumecheng-10464	203	1	+	+	PUNCT
fumecheng-10464	203	2	+	+	CCONJ
fumecheng-10464	203	3	(	(	PUNCT
fumecheng-10464	203	4	21	21	NUM
fumecheng-10464	203	5	)	)	PUNCT
fumecheng-10464	203	6	by	by	ADP
fumecheng-10464	203	7	the	the	DET
fumecheng-10464	203	8	inverse	inverse	NOUN
fumecheng-10464	203	9	of	of	ADP
fumecheng-10464	203	10	two	two	NUM
fumecheng-10464	203	11	-	-	PUNCT
fumecheng-10464	203	12	scale	scale	NOUN
fumecheng-10464	203	13	transforms	transform	NOUN
fumecheng-10464	203	14	,	,	PUNCT
fumecheng-10464	203	15	t=√aτα	t=√aτα	NUM
fumecheng-10464	203	16	,	,	PUNCT
fumecheng-10464	203	17	we	we	PRON
fumecheng-10464	203	18	can	can	AUX
fumecheng-10464	203	19	obtain	obtain	VERB
fumecheng-10464	203	20	the	the	DET
fumecheng-10464	203	21	following	follow	VERB
fumecheng-10464	203	22	solution	solution	NOUN
fumecheng-10464	203	23	of	of	ADP
fumecheng-10464	203	24	the	the	DET
fumecheng-10464	203	25	fractal	fractal	ADJ
fumecheng-10464	203	26	dvdp	dvdp	ADJ
fumecheng-10464	203	27	equation	equation	NOUN
fumecheng-10464	203	28	along	along	ADP
fumecheng-10464	203	29	with	with	ADP
fumecheng-10464	203	30	x0(√aτα)+	x0(√aτα)+	PROPN
fumecheng-10464	203	31	x1(√aτα)+	x1(√aτα)+	PROPN
fumecheng-10464	203	32	x2(√aτα	x2(√aτα	PROPN
fumecheng-10464	203	33	)	)	PUNCT
fumecheng-10464	203	34	.	.	PUNCT
fumecheng-10464	204	1	in	in	ADP
fumecheng-10464	204	2	fact	fact	NOUN
fumecheng-10464	204	3	,	,	PUNCT
fumecheng-10464	204	4	the	the	DET
fumecheng-10464	204	5	bounded	bounded	ADJ
fumecheng-10464	204	6	approximate	approximate	ADJ
fumecheng-10464	204	7	solution	solution	NOUN
fumecheng-10464	204	8	as	as	SCONJ
fumecheng-10464	204	9	given	give	VERB
fumecheng-10464	204	10	in	in	ADP
fumecheng-10464	204	11	eq	eq	ADP
fumecheng-10464	204	12	.	.	PUNCT
fumecheng-10464	205	1	(	(	PUNCT
fumecheng-10464	205	2	21	21	NUM
fumecheng-10464	205	3	)	)	PUNCT
fumecheng-10464	205	4	necessitates	necessitate	VERB
fumecheng-10464	205	5	that	that	SCONJ
fumecheng-10464	205	6	the	the	DET
fumecheng-10464	205	7	arguments	argument	NOUN
fumecheng-10464	205	8	of	of	ADP
fumecheng-10464	205	9	the	the	DET
fumecheng-10464	205	10	trigonometric	trigonometric	ADJ
fumecheng-10464	205	11	functions	function	NOUN
fumecheng-10464	205	12	are	be	AUX
fumecheng-10464	205	13	real	real	ADJ
fumecheng-10464	205	14	.	.	PUNCT
fumecheng-10464	206	1	for	for	ADP
fumecheng-10464	206	2	this	this	DET
fumecheng-10464	206	3	purpose	purpose	NOUN
fumecheng-10464	206	4	,	,	PUNCT
fumecheng-10464	206	5	combining	combine	VERB
fumecheng-10464	206	6	eqs	eqs	PROPN
fumecheng-10464	206	7	.	.	PUNCT
fumecheng-10464	207	1	(	(	PUNCT
fumecheng-10464	207	2	13	13	NUM
fumecheng-10464	207	3	)	)	PUNCT
fumecheng-10464	207	4	,	,	PUNCT
fumecheng-10464	207	5	(	(	PUNCT
fumecheng-10464	207	6	16	16	NUM
fumecheng-10464	207	7	)	)	PUNCT
fumecheng-10464	207	8	and	and	CCONJ
fumecheng-10464	207	9	(	(	PUNCT
fumecheng-10464	207	10	19	19	NUM
fumecheng-10464	207	11	)	)	PUNCT
fumecheng-10464	207	12	into	into	ADP
fumecheng-10464	207	13	eq	eq	NOUN
fumecheng-10464	207	14	.	.	PUNCT
fumecheng-10464	208	1	(	(	PUNCT
fumecheng-10464	208	2	5	5	NUM
fumecheng-10464	208	3	)	)	PUNCT
fumecheng-10464	208	4	,	,	PUNCT
fumecheng-10464	208	5	it	it	PRON
fumecheng-10464	208	6	follows	follow	VERB
fumecheng-10464	208	7	that	that	SCONJ
fumecheng-10464	208	8	the	the	DET
fumecheng-10464	208	9	synthetic	synthetic	ADJ
fumecheng-10464	208	10	frequency	frequency	NOUN
fumecheng-10464	208	11	satisfies	satisfy	VERB
fumecheng-10464	208	12	a	a	DET
fumecheng-10464	208	13	certain	certain	ADJ
fumecheng-10464	208	14	characteristic	characteristic	ADJ
fumecheng-10464	208	15	equation	equation	NOUN
fumecheng-10464	208	16	.	.	PUNCT
fumecheng-10464	209	1	the	the	DET
fumecheng-10464	209	2	calculation	calculation	NOUN
fumecheng-10464	209	3	showed	show	VERB
fumecheng-10464	209	4	that	that	SCONJ
fumecheng-10464	209	5	this	this	DET
fumecheng-10464	209	6	equation	equation	NOUN
fumecheng-10464	209	7	represents	represent	VERB
fumecheng-10464	209	8	a	a	DET
fumecheng-10464	209	9	polynomial	polynomial	NOUN
fumecheng-10464	209	10	of	of	ADP
fumecheng-10464	209	11	sixth	sixth	ADJ
fumecheng-10464	209	12	order	order	NOUN
fumecheng-10464	209	13	.	.	PUNCT
fumecheng-10464	210	1	once	once	ADV
fumecheng-10464	210	2	more	more	ADV
fumecheng-10464	210	3	,	,	PUNCT
fumecheng-10464	210	4	by	by	ADP
fumecheng-10464	210	5	means	mean	NOUN
fumecheng-10464	210	6	of	of	ADP
fumecheng-10464	210	7	hpm	hpm	NOUN
fumecheng-10464	210	8	,	,	PUNCT
fumecheng-10464	210	9	one	one	PRON
fumecheng-10464	210	10	may	may	AUX
fumecheng-10464	210	11	obtain	obtain	VERB
fumecheng-10464	210	12	the	the	DET
fumecheng-10464	210	13	approximate	approximate	ADJ
fumecheng-10464	210	14	solution	solution	NOUN
fumecheng-10464	210	15	as	as	SCONJ
fumecheng-10464	210	16	follows	follow	VERB
fumecheng-10464	210	17	:	:	PUNCT
fumecheng-10464	210	18	2	2	NUM
fumecheng-10464	210	19	4	4	NUM
fumecheng-10464	210	20	6	6	NUM
fumecheng-10464	210	21	(	(	PUNCT
fumecheng-10464	210	22	)	)	PUNCT
fumecheng-10464	210	23	,	,	PUNCT
fumecheng-10464	211	1	[	[	X
fumecheng-10464	211	2	0	0	NUM
fumecheng-10464	211	3	,	,	PUNCT
fumecheng-10464	211	4	1]a	1]a	NUM
fumecheng-10464	211	5	b	b	PROPN
fumecheng-10464	211	6	c	c	ADJ
fumecheng-10464	211	7			NUM
fumecheng-10464	211	8			X
fumecheng-10464	211	9			NUM
fumecheng-10464	211	10	=	=	NOUN
fumecheng-10464	211	11	+	+	CCONJ
fumecheng-10464	211	12	−	−	PROPN
fumecheng-10464	211	13			NOUN
fumecheng-10464	211	14	(	(	PUNCT
fumecheng-10464	211	15	22	22	NUM
fumecheng-10464	211	16	)	)	PUNCT
fumecheng-10464	211	17	where	where	SCONJ
fumecheng-10464	211	18	the	the	DET
fumecheng-10464	211	19	constants	constant	NOUN
fumecheng-10464	211	20	a	a	PRON
fumecheng-10464	211	21	,	,	PUNCT
fumecheng-10464	211	22	b	b	PROPN
fumecheng-10464	211	23	and	and	CCONJ
fumecheng-10464	211	24	c	c	NOUN
fumecheng-10464	211	25	,	,	PUNCT
fumecheng-10464	211	26	may	may	AUX
fumecheng-10464	211	27	be	be	AUX
fumecheng-10464	211	28	listed	list	VERB
fumecheng-10464	211	29	as	as	ADP
fumecheng-10464	211	30	:	:	PUNCT
fumecheng-10464	211	31	)	)	PUNCT
fumecheng-10464	211	32	8/(9	8/(9	PROPN
fumecheng-10464	211	33	22	22	NUM
fumecheng-10464	211	34			NOUN
fumecheng-10464	211	35	−=a	−=a	X
fumecheng-10464	211	36	,	,	PUNCT
fumecheng-10464	211	37	,	,	PUNCT
fumecheng-10464	211	38	)	)	PUNCT
fumecheng-10464	211	39	8(9/)819264	8(9/)819264	NUM
fumecheng-10464	211	40	(	(	PUNCT
fumecheng-10464	211	41	22	22	NUM
fumecheng-10464	211	42			ADJ
fumecheng-10464	211	43	−−+=b	−−+=b	NUM
fumecheng-10464	211	44	.)8(9/64	.)8(9/64	NOUN
fumecheng-10464	211	45	2	2	NUM
fumecheng-10464	211	46			NOUN
fumecheng-10464	211	47	−=c	−=c	PRON
fumecheng-10464	212	1	(	(	PUNCT
fumecheng-10464	212	2	23	23	NUM
fumecheng-10464	212	3	)	)	PUNCT
fumecheng-10464	212	4	following	follow	VERB
fumecheng-10464	212	5	a	a	DET
fumecheng-10464	212	6	similar	similar	ADJ
fumecheng-10464	212	7	procedure	procedure	NOUN
fumecheng-10464	212	8	as	as	SCONJ
fumecheng-10464	212	9	given	give	VERB
fumecheng-10464	212	10	above	above	ADV
fumecheng-10464	212	11	,	,	PUNCT
fumecheng-10464	212	12	an	an	DET
fumecheng-10464	212	13	approximate	approximate	ADJ
fumecheng-10464	212	14	solution	solution	NOUN
fumecheng-10464	212	15	up	up	ADP
fumecheng-10464	212	16	to	to	ADP
fumecheng-10464	212	17	the	the	DET
fumecheng-10464	212	18	second	second	ADJ
fumecheng-10464	212	19	-	-	PUNCT
fumecheng-10464	212	20	order	order	NOUN
fumecheng-10464	212	21	,	,	PUNCT
fumecheng-10464	212	22	of	of	ADP
fumecheng-10464	212	23	the	the	DET
fumecheng-10464	212	24	simulated	simulate	VERB
fumecheng-10464	212	25	frequency	frequency	NOUN
fumecheng-10464	212	26	,	,	PUNCT
fumecheng-10464	212	27	may	may	AUX
fumecheng-10464	212	28	be	be	AUX
fumecheng-10464	212	29	written	write	VERB
fumecheng-10464	212	30	as	as	ADP
fumecheng-10464	212	31	:	:	PUNCT
fumecheng-10464	212	32	2	2	NUM
fumecheng-10464	212	33	2	2	NUM
fumecheng-10464	212	34	10	10	NUM
fumecheng-10464	212	35	sss	sss	VERB
fumecheng-10464	212	36			PROPN
fumecheng-10464	212	37	+	+	PROPN
fumecheng-10464	212	38	+	+	PROPN
fumecheng-10464	212	39			PROPN
fumecheng-10464	212	40	(	(	PUNCT
fumecheng-10464	212	41	24	24	NUM
fumecheng-10464	212	42	)	)	PUNCT
fumecheng-10464	212	43	where	where	SCONJ
fumecheng-10464	212	44	the	the	DET
fumecheng-10464	212	45	constants	constant	NOUN
fumecheng-10464	212	46	si	si	X
fumecheng-10464	212	47	are	be	AUX
fumecheng-10464	212	48	given	give	VERB
fumecheng-10464	212	49	as	as	ADP
fumecheng-10464	212	50	:	:	PUNCT
fumecheng-10464	212	51	2/	2/	NUM
fumecheng-10464	212	52	)	)	PUNCT
fumecheng-10464	212	53	(	(	PUNCT
fumecheng-10464	212	54	,	,	PUNCT
fumecheng-10464	212	55	2/3	2/3	NUM
fumecheng-10464	212	56	10	10	NUM
fumecheng-10464	212	57	acbasas	acbasa	NOUN
fumecheng-10464	212	58	+	+	NOUN
fumecheng-10464	212	59	=	=	NOUN
fumecheng-10464	212	60	=	=	SYM
fumecheng-10464	212	61	(	(	PUNCT
fumecheng-10464	212	62	25	25	NUM
fumecheng-10464	212	63	)	)	PUNCT
fumecheng-10464	212	64	and	and	CCONJ
fumecheng-10464	212	65	)	)	PUNCT
fumecheng-10464	212	66	11187	11187	NUM
fumecheng-10464	212	67	(	(	PUNCT
fumecheng-10464	212	68	8	8	NUM
fumecheng-10464	212	69	1	1	NUM
fumecheng-10464	212	70	2222/5	2222/5	NUM
fumecheng-10464	212	71	2	2	NUM
fumecheng-10464	212	72	cacbabas	cacbaba	NOUN
fumecheng-10464	213	1	+	+	X
fumecheng-10464	213	2	+	+	NOUN
fumecheng-10464	213	3	=	=	X
fumecheng-10464	213	4	(	(	PUNCT
fumecheng-10464	213	5	26	26	NUM
fumecheng-10464	213	6	)	)	PUNCT
fumecheng-10464	213	7	in	in	ADP
fumecheng-10464	213	8	accordance	accordance	NOUN
fumecheng-10464	213	9	with	with	ADP
fumecheng-10464	213	10	the	the	DET
fumecheng-10464	213	11	real	real	ADJ
fumecheng-10464	213	12	value	value	NOUN
fumecheng-10464	213	13	of	of	ADP
fumecheng-10464	213	14	the	the	DET
fumecheng-10464	213	15	expanded	expand	VERB
fumecheng-10464	213	16	frequency	frequency	NOUN
fumecheng-10464	213	17	,	,	PUNCT
fumecheng-10464	213	18	the	the	DET
fumecheng-10464	213	19	approximate	approximate	ADJ
fumecheng-10464	213	20	bounded	bound	VERB
fumecheng-10464	213	21	solution	solution	NOUN
fumecheng-10464	213	22	requires	require	VERB
fumecheng-10464	213	23	the	the	DET
fumecheng-10464	213	24	following	follow	VERB
fumecheng-10464	213	25	criterion	criterion	NOUN
fumecheng-10464	213	26	:	:	PUNCT
fumecheng-10464	213	27	.08	.08	NUM
fumecheng-10464	213	28	2	2	NUM
fumecheng-10464	213	29	−	−	X
fumecheng-10464	213	30	(	(	PUNCT
fumecheng-10464	213	31	27	27	NUM
fumecheng-10464	213	32	)	)	SYM
fumecheng-10464	213	33	8	8	NUM
fumecheng-10464	213	34	j.-h	j.-h	NOUN
fumecheng-10464	213	35	.	.	PUNCT
fumecheng-10464	214	1	he	he	PRON
fumecheng-10464	214	2	,	,	PUNCT
fumecheng-10464	214	3	g.	g.	PROPN
fumecheng-10464	214	4	m.	m.	PROPN
fumecheng-10464	214	5	moatimid	moatimid	PROPN
fumecheng-10464	214	6	,	,	PUNCT
fumecheng-10464	214	7	m.	m.	PROPN
fumecheng-10464	214	8	h.	h.	PROPN
fumecheng-10464	214	9	zekry	zekry	PROPN
fumecheng-10464	214	10	eq	eq	PROPN
fumecheng-10464	214	11	.	.	PUNCT
fumecheng-10464	215	1	(	(	PUNCT
fumecheng-10464	215	2	27	27	NUM
fumecheng-10464	215	3	)	)	PUNCT
fumecheng-10464	215	4	reads	read	VERB
fumecheng-10464	215	5	that	that	SCONJ
fumecheng-10464	215	6	the	the	DET
fumecheng-10464	215	7	analytic	analytic	ADJ
fumecheng-10464	215	8	approximate	approximate	ADJ
fumecheng-10464	215	9	bounded	bound	VERB
fumecheng-10464	215	10	solution	solution	NOUN
fumecheng-10464	215	11	can	can	AUX
fumecheng-10464	215	12	not	not	PART
fumecheng-10464	215	13	be	be	AUX
fumecheng-10464	215	14	realized	realize	VERB
fumecheng-10464	215	15	where	where	SCONJ
fumecheng-10464	215	16	the	the	DET
fumecheng-10464	215	17	stiffness	stiffness	ADJ
fumecheng-10464	215	18	parameter	parameter	NOUN
fumecheng-10464	215	19	becomes	become	VERB
fumecheng-10464	215	20	negative	negative	ADJ
fumecheng-10464	215	21	.	.	PUNCT
fumecheng-10464	216	1	for	for	ADP
fumecheng-10464	216	2	more	more	ADJ
fumecheng-10464	216	3	opportunities	opportunity	NOUN
fumecheng-10464	216	4	,	,	PUNCT
fumecheng-10464	216	5	the	the	PRON
fumecheng-10464	216	6	attained	attain	VERB
fumecheng-10464	216	7	analytic	analytic	ADJ
fumecheng-10464	216	8	approximate	approximate	ADJ
fumecheng-10464	216	9	analytic	analytic	ADJ
fumecheng-10464	216	10	solution	solution	NOUN
fumecheng-10464	216	11	must	must	AUX
fumecheng-10464	216	12	validate	validate	VERB
fumecheng-10464	216	13	the	the	DET
fumecheng-10464	216	14	numerical	numerical	ADJ
fumecheng-10464	216	15	solution	solution	NOUN
fumecheng-10464	216	16	.	.	PUNCT
fumecheng-10464	217	1	for	for	ADP
fumecheng-10464	217	2	this	this	DET
fumecheng-10464	217	3	objective	objective	NOUN
fumecheng-10464	217	4	,	,	PUNCT
fumecheng-10464	217	5	the	the	DET
fumecheng-10464	217	6	fourth	fourth	ADJ
fumecheng-10464	217	7	-	-	PUNCT
fumecheng-10464	217	8	order	order	NOUN
fumecheng-10464	217	9	runge	runge	NOUN
fumecheng-10464	217	10	–	–	PUNCT
fumecheng-10464	217	11	kutta	kutta	NOUN
fumecheng-10464	217	12	method	method	NOUN
fumecheng-10464	217	13	(	(	PUNCT
fumecheng-10464	217	14	rk4	rk4	NOUN
fumecheng-10464	217	15	)	)	PUNCT
fumecheng-10464	217	16	it	it	PRON
fumecheng-10464	217	17	utilized	utilize	VERB
fumecheng-10464	217	18	to	to	PART
fumecheng-10464	217	19	confirm	confirm	VERB
fumecheng-10464	217	20	the	the	DET
fumecheng-10464	217	21	approximate	approximate	ADJ
fumecheng-10464	217	22	solution	solution	NOUN
fumecheng-10464	217	23	.	.	PUNCT
fumecheng-10464	218	1	therefore	therefore	ADV
fumecheng-10464	218	2	,	,	PUNCT
fumecheng-10464	218	3	fig	fig	NOUN
fumecheng-10464	218	4	.	.	PUNCT
fumecheng-10464	218	5	2	2	NUM
fumecheng-10464	218	6	is	be	AUX
fumecheng-10464	218	7	designed	design	VERB
fumecheng-10464	218	8	for	for	ADP
fumecheng-10464	218	9	demonstrating	demonstrate	VERB
fumecheng-10464	218	10	the	the	DET
fumecheng-10464	218	11	analytic	analytic	ADJ
fumecheng-10464	218	12	bounded	bound	VERB
fumecheng-10464	218	13	solution	solution	NOUN
fumecheng-10464	218	14	given	give	VERB
fumecheng-10464	218	15	from	from	ADP
fumecheng-10464	218	16	the	the	DET
fumecheng-10464	218	17	expanded	expand	VERB
fumecheng-10464	218	18	frequency	frequency	NOUN
fumecheng-10464	218	19	approach	approach	NOUN
fumecheng-10464	218	20	together	together	ADV
fumecheng-10464	218	21	with	with	ADP
fumecheng-10464	218	22	the	the	DET
fumecheng-10464	218	23	numerical	numerical	ADJ
fumecheng-10464	218	24	solution	solution	NOUN
fumecheng-10464	218	25	that	that	PRON
fumecheng-10464	218	26	is	be	AUX
fumecheng-10464	218	27	given	give	VERB
fumecheng-10464	218	28	by	by	ADP
fumecheng-10464	218	29	rk4	rk4	NOUN
fumecheng-10464	218	30	.	.	PUNCT
fumecheng-10464	219	1	through	through	ADP
fumecheng-10464	219	2	this	this	DET
fumecheng-10464	219	3	figure	figure	NOUN
fumecheng-10464	219	4	,	,	PUNCT
fumecheng-10464	219	5	the	the	DET
fumecheng-10464	219	6	usage	usage	NOUN
fumecheng-10464	219	7	of	of	ADP
fumecheng-10464	219	8	the	the	DET
fumecheng-10464	219	9	sample	sample	NOUN
fumecheng-10464	219	10	chosen	choose	VERB
fumecheng-10464	219	11	system	system	NOUN
fumecheng-10464	219	12	showed	show	VERB
fumecheng-10464	219	13	that	that	SCONJ
fumecheng-10464	219	14	the	the	DET
fumecheng-10464	219	15	approximate	approximate	ADJ
fumecheng-10464	219	16	value	value	NOUN
fumecheng-10464	219	17	of	of	ADP
fumecheng-10464	219	18	the	the	DET
fumecheng-10464	219	19	expanded	expand	VERB
fumecheng-10464	219	20	frequency	frequency	NOUN
fumecheng-10464	219	21	equals	equal	VERB
fumecheng-10464	219	22	σ≌	σ≌	PROPN
fumecheng-10464	219	23	3.29	3.29	NUM
fumecheng-10464	219	24	.	.	PUNCT
fumecheng-10464	220	1	additionally	additionally	ADV
fumecheng-10464	220	2	,	,	PUNCT
fumecheng-10464	220	3	the	the	DET
fumecheng-10464	220	4	calculations	calculation	NOUN
fumecheng-10464	220	5	revealed	reveal	VERB
fumecheng-10464	220	6	that	that	SCONJ
fumecheng-10464	220	7	the	the	DET
fumecheng-10464	220	8	initial	initial	ADJ
fumecheng-10464	220	9	condition	condition	NOUN
fumecheng-10464	220	10	becomes	become	VERB
fumecheng-10464	220	11	ẋ(0)=5.821	ẋ(0)=5.821	NOUN
fumecheng-10464	220	12	.	.	PUNCT
fumecheng-10464	221	1	as	as	SCONJ
fumecheng-10464	221	2	shown	show	VERB
fumecheng-10464	221	3	from	from	ADP
fumecheng-10464	221	4	this	this	DET
fumecheng-10464	221	5	figure	figure	NOUN
fumecheng-10464	221	6	,	,	PUNCT
fumecheng-10464	221	7	the	the	DET
fumecheng-10464	221	8	amplitudes	amplitude	NOUN
fumecheng-10464	221	9	of	of	ADP
fumecheng-10464	221	10	the	the	DET
fumecheng-10464	221	11	solution	solution	NOUN
fumecheng-10464	221	12	in	in	ADP
fumecheng-10464	221	13	the	the	DET
fumecheng-10464	221	14	two	two	NUM
fumecheng-10464	221	15	cases	case	NOUN
fumecheng-10464	221	16	are	be	AUX
fumecheng-10464	221	17	nearly	nearly	ADV
fumecheng-10464	221	18	coincident	coincident	ADJ
fumecheng-10464	221	19	.	.	PUNCT
fumecheng-10464	222	1	this	this	PRON
fumecheng-10464	222	2	indicates	indicate	VERB
fumecheng-10464	222	3	a	a	DET
fumecheng-10464	222	4	good	good	ADJ
fumecheng-10464	222	5	agreement	agreement	NOUN
fumecheng-10464	222	6	between	between	ADP
fumecheng-10464	222	7	the	the	DET
fumecheng-10464	222	8	two	two	NUM
fumecheng-10464	222	9	methodologies	methodology	NOUN
fumecheng-10464	222	10	.	.	PUNCT
fumecheng-10464	223	1	fig	fig	NOUN
fumecheng-10464	223	2	.	.	PUNCT
fumecheng-10464	224	1	2	2	NUM
fumecheng-10464	224	2	comparison	comparison	NOUN
fumecheng-10464	224	3	of	of	ADP
fumecheng-10464	224	4	the	the	DET
fumecheng-10464	224	5	approximate	approximate	ADJ
fumecheng-10464	224	6	solution	solution	NOUN
fumecheng-10464	224	7	that	that	PRON
fumecheng-10464	224	8	is	be	AUX
fumecheng-10464	224	9	given	give	VERB
fumecheng-10464	224	10	in	in	ADP
fumecheng-10464	224	11	eq	eq	ADP
fumecheng-10464	224	12	.	.	PUNCT
fumecheng-10464	225	1	(	(	PUNCT
fumecheng-10464	225	2	21	21	NUM
fumecheng-10464	225	3	)	)	PUNCT
fumecheng-10464	225	4	with	with	ADP
fumecheng-10464	225	5	the	the	DET
fumecheng-10464	225	6	numerical	numerical	ADJ
fumecheng-10464	225	7	one	one	NUM
fumecheng-10464	225	8	for	for	ADP
fumecheng-10464	225	9	the	the	DET
fumecheng-10464	225	10	case	case	NOUN
fumecheng-10464	225	11	:	:	PUNCT
fumecheng-10464	225	12	µ=0.2	µ=0.2	NUM
fumecheng-10464	225	13	,	,	PUNCT
fumecheng-10464	225	14	β=2	β=2	ADP
fumecheng-10464	225	15	,	,	PUNCT
fumecheng-10464	225	16	f=0.05	f=0.05	NOUN
fumecheng-10464	225	17	and	and	CCONJ
fumecheng-10464	225	18	ω=0.4	ω=0.4	NOUN
fumecheng-10464	225	19	additionally	additionally	ADV
fumecheng-10464	225	20	,	,	PUNCT
fumecheng-10464	225	21	the	the	DET
fumecheng-10464	225	22	bounded	bounded	ADJ
fumecheng-10464	225	23	solution	solution	NOUN
fumecheng-10464	225	24	of	of	ADP
fumecheng-10464	225	25	the	the	DET
fumecheng-10464	225	26	considered	consider	VERB
fumecheng-10464	225	27	dvdp	dvdp	ADJ
fumecheng-10464	225	28	will	will	AUX
fumecheng-10464	225	29	be	be	AUX
fumecheng-10464	225	30	graphed	graph	VERB
fumecheng-10464	225	31	.	.	PUNCT
fumecheng-10464	226	1	this	this	DET
fumecheng-10464	226	2	solution	solution	NOUN
fumecheng-10464	226	3	is	be	AUX
fumecheng-10464	226	4	given	give	VERB
fumecheng-10464	226	5	by	by	ADP
fumecheng-10464	226	6	eq	eq	PROPN
fumecheng-10464	226	7	.	.	PUNCT
fumecheng-10464	227	1	(	(	PUNCT
fumecheng-10464	227	2	21	21	NUM
fumecheng-10464	227	3	)	)	PUNCT
fumecheng-10464	227	4	.	.	PUNCT
fumecheng-10464	228	1	simultaneously	simultaneously	ADV
fumecheng-10464	228	2	,	,	PUNCT
fumecheng-10464	228	3	it	it	PRON
fumecheng-10464	228	4	depends	depend	VERB
fumecheng-10464	228	5	mainly	mainly	ADV
fumecheng-10464	228	6	on	on	ADP
fumecheng-10464	228	7	the	the	DET
fumecheng-10464	228	8	value	value	NOUN
fumecheng-10464	228	9	of	of	ADP
fumecheng-10464	228	10	the	the	DET
fumecheng-10464	228	11	expanded	expand	VERB
fumecheng-10464	228	12	frequency	frequency	NOUN
fumecheng-10464	228	13	(	(	PUNCT
fumecheng-10464	228	14	σ	σ	NOUN
fumecheng-10464	228	15	)	)	PUNCT
fumecheng-10464	228	16	that	that	PRON
fumecheng-10464	228	17	is	be	AUX
fumecheng-10464	228	18	given	give	VERB
fumecheng-10464	228	19	in	in	ADP
fumecheng-10464	228	20	eq	eq	ADP
fumecheng-10464	228	21	.	.	PUNCT
fumecheng-10464	229	1	(	(	PUNCT
fumecheng-10464	229	2	24	24	NUM
fumecheng-10464	229	3	)	)	PUNCT
fumecheng-10464	229	4	.	.	PUNCT
fumecheng-10464	230	1	it	it	PRON
fumecheng-10464	230	2	is	be	AUX
fumecheng-10464	230	3	obvious	obvious	ADJ
fumecheng-10464	230	4	that	that	SCONJ
fumecheng-10464	230	5	the	the	DET
fumecheng-10464	230	6	validation	validation	NOUN
fumecheng-10464	230	7	of	of	ADP
fumecheng-10464	230	8	the	the	DET
fumecheng-10464	230	9	value	value	NOUN
fumecheng-10464	230	10	σ	σ	PROPN
fumecheng-10464	230	11	requires	require	VERB
fumecheng-10464	230	12	that	that	SCONJ
fumecheng-10464	230	13	8β	8β	PRON
fumecheng-10464	231	1	>	>	X
fumecheng-10464	231	2	µ2	µ2	PROPN
fumecheng-10464	231	3	as	as	SCONJ
fumecheng-10464	231	4	specified	specify	VERB
fumecheng-10464	231	5	in	in	ADP
fumecheng-10464	231	6	the	the	DET
fumecheng-10464	231	7	inequality	inequality	NOUN
fumecheng-10464	231	8	(	(	PUNCT
fumecheng-10464	231	9	27	27	NUM
fumecheng-10464	231	10	)	)	PUNCT
fumecheng-10464	231	11	.	.	PUNCT
fumecheng-10464	232	1	to	to	PART
fumecheng-10464	232	2	prove	prove	VERB
fumecheng-10464	232	3	the	the	DET
fumecheng-10464	232	4	accuracy	accuracy	NOUN
fumecheng-10464	232	5	of	of	ADP
fumecheng-10464	232	6	the	the	DET
fumecheng-10464	232	7	method	method	NOUN
fumecheng-10464	232	8	,	,	PUNCT
fumecheng-10464	232	9	we	we	PRON
fumecheng-10464	232	10	depict	depict	VERB
fumecheng-10464	232	11	in	in	ADP
fumecheng-10464	232	12	fig	fig	NOUN
fumecheng-10464	232	13	.	.	PUNCT
fumecheng-10464	233	1	3	3	NUM
fumecheng-10464	233	2	,	,	PUNCT
fumecheng-10464	233	3	the	the	DET
fumecheng-10464	233	4	percent	percent	NOUN
fumecheng-10464	233	5	relative	relative	ADJ
fumecheng-10464	233	6	error	error	NOUN
fumecheng-10464	233	7	e(t)=x2(t)/(x0(t)+x1(t	e(t)=x2(t)/(x0(t)+x1(t	NUM
fumecheng-10464	233	8	)	)	PUNCT
fumecheng-10464	233	9	+	+	PROPN
fumecheng-10464	233	10	x2(t	x2(t	PROPN
fumecheng-10464	233	11	)	)	PUNCT
fumecheng-10464	233	12	)	)	PUNCT
fumecheng-10464	233	13	,	,	PUNCT
fumecheng-10464	233	14	i.e.	i.e.	X
fumecheng-10464	233	15	,	,	PUNCT
fumecheng-10464	233	16	the	the	DET
fumecheng-10464	233	17	stepwise	stepwise	NOUN
fumecheng-10464	233	18	error	error	NOUN
fumecheng-10464	233	19	,	,	PUNCT
fumecheng-10464	233	20	from	from	ADP
fumecheng-10464	233	21	the	the	DET
fumecheng-10464	233	22	results	result	NOUN
fumecheng-10464	233	23	depicted	depict	VERB
fumecheng-10464	233	24	in	in	ADP
fumecheng-10464	233	25	this	this	DET
fumecheng-10464	233	26	figure	figure	NOUN
fumecheng-10464	233	27	,	,	PUNCT
fumecheng-10464	233	28	we	we	PRON
fumecheng-10464	233	29	assure	assure	VERB
fumecheng-10464	233	30	the	the	DET
fumecheng-10464	233	31	accuracy	accuracy	NOUN
fumecheng-10464	233	32	as	as	ADV
fumecheng-10464	233	33	well	well	ADV
fumecheng-10464	233	34	as	as	ADP
fumecheng-10464	233	35	the	the	DET
fumecheng-10464	233	36	stability	stability	NOUN
fumecheng-10464	233	37	of	of	ADP
fumecheng-10464	233	38	raising	raise	VERB
fumecheng-10464	233	39	the	the	DET
fumecheng-10464	233	40	order	order	NOUN
fumecheng-10464	233	41	of	of	ADP
fumecheng-10464	233	42	the	the	DET
fumecheng-10464	233	43	approximation	approximation	NOUN
fumecheng-10464	233	44	.	.	PUNCT
fumecheng-10464	234	1	fig	fig	NOUN
fumecheng-10464	234	2	.	.	PUNCT
fumecheng-10464	235	1	3	3	NUM
fumecheng-10464	235	2	the	the	DET
fumecheng-10464	235	3	error	error	NOUN
fumecheng-10464	235	4	function	function	NOUN
fumecheng-10464	235	5	e(t	e(t	NOUN
fumecheng-10464	235	6	)	)	PUNCT
fumecheng-10464	235	7	for	for	ADP
fumecheng-10464	235	8	a	a	DET
fumecheng-10464	235	9	system	system	NOUN
fumecheng-10464	235	10	having	have	VERB
fumecheng-10464	235	11	the	the	DET
fumecheng-10464	235	12	particulars	particular	NOUN
fumecheng-10464	235	13	:	:	PUNCT
fumecheng-10464	235	14	µ=0.2	µ=0.2	ADJ
fumecheng-10464	235	15	,	,	PUNCT
fumecheng-10464	235	16	β=2	β=2	ADP
fumecheng-10464	235	17	,	,	PUNCT
fumecheng-10464	235	18	f=0.05	f=0.05	NOUN
fumecheng-10464	235	19	and	and	CCONJ
fumecheng-10464	235	20	ω=0.4	ω=0.4	NOUN
fumecheng-10464	235	21	forced	force	VERB
fumecheng-10464	235	22	nonlinear	nonlinear	ADJ
fumecheng-10464	235	23	oscillator	oscillator	NOUN
fumecheng-10464	235	24	in	in	ADP
fumecheng-10464	235	25	a	a	DET
fumecheng-10464	235	26	fractal	fractal	ADJ
fumecheng-10464	235	27	space	space	NOUN
fumecheng-10464	235	28	9	9	NUM
fumecheng-10464	235	29	along	along	ADP
fumecheng-10464	235	30	with	with	ADP
fumecheng-10464	235	31	these	these	DET
fumecheng-10464	235	32	restrictions	restriction	NOUN
fumecheng-10464	235	33	,	,	PUNCT
fumecheng-10464	235	34	in	in	ADP
fumecheng-10464	235	35	what	what	PRON
fumecheng-10464	235	36	follows	follow	VERB
fumecheng-10464	235	37	two	two	NUM
fumecheng-10464	235	38	graphs	graph	NOUN
fumecheng-10464	235	39	are	be	AUX
fumecheng-10464	235	40	plotted	plot	VERB
fumecheng-10464	235	41	for	for	ADP
fumecheng-10464	235	42	some	some	DET
fumecheng-10464	235	43	chosen	choose	VERB
fumecheng-10464	235	44	systems	system	NOUN
fumecheng-10464	235	45	to	to	PART
fumecheng-10464	235	46	indicate	indicate	VERB
fumecheng-10464	235	47	the	the	DET
fumecheng-10464	235	48	bounded	bounded	ADJ
fumecheng-10464	235	49	solutions	solution	NOUN
fumecheng-10464	235	50	,	,	PUNCT
fumecheng-10464	235	51	as	as	SCONJ
fumecheng-10464	235	52	shown	show	VERB
fumecheng-10464	235	53	in	in	ADP
fumecheng-10464	235	54	figs	fig	NOUN
fumecheng-10464	235	55	.	.	PUNCT
fumecheng-10464	236	1	4	4	NUM
fumecheng-10464	236	2	,	,	PUNCT
fumecheng-10464	236	3	and	and	CCONJ
fumecheng-10464	236	4	5	5	NUM
fumecheng-10464	236	5	.	.	X
fumecheng-10464	236	6	fig	fig	NOUN
fumecheng-10464	236	7	.	.	PUNCT
fumecheng-10464	237	1	3	3	NUM
fumecheng-10464	237	2	displays	display	VERB
fumecheng-10464	237	3	the	the	DET
fumecheng-10464	237	4	analytical	analytical	ADJ
fumecheng-10464	237	5	bounded	bound	VERB
fumecheng-10464	237	6	approximate	approximate	ADJ
fumecheng-10464	237	7	solution	solution	NOUN
fumecheng-10464	237	8	for	for	ADP
fumecheng-10464	237	9	a	a	DET
fumecheng-10464	237	10	sample	sample	NOUN
fumecheng-10464	237	11	chosen	choose	VERB
fumecheng-10464	237	12	system	system	NOUN
fumecheng-10464	237	13	.	.	PUNCT
fumecheng-10464	238	1	the	the	DET
fumecheng-10464	238	2	inspection	inspection	NOUN
fumecheng-10464	238	3	of	of	ADP
fumecheng-10464	238	4	this	this	DET
fumecheng-10464	238	5	figure	figure	NOUN
fumecheng-10464	238	6	indicates	indicate	VERB
fumecheng-10464	238	7	the	the	DET
fumecheng-10464	238	8	behavior	behavior	NOUN
fumecheng-10464	238	9	of	of	ADP
fumecheng-10464	238	10	the	the	DET
fumecheng-10464	238	11	solution	solution	NOUN
fumecheng-10464	238	12	,	,	PUNCT
fumecheng-10464	238	13	which	which	PRON
fumecheng-10464	238	14	is	be	AUX
fumecheng-10464	238	15	a	a	DET
fumecheng-10464	238	16	bounded	bounded	ADJ
fumecheng-10464	238	17	one	one	NUM
fumecheng-10464	238	18	.	.	PUNCT
fumecheng-10464	239	1	throughout	throughout	ADP
fumecheng-10464	239	2	this	this	DET
fumecheng-10464	239	3	figure	figure	NOUN
fumecheng-10464	239	4	,	,	PUNCT
fumecheng-10464	239	5	the	the	DET
fumecheng-10464	239	6	calculations	calculation	NOUN
fumecheng-10464	239	7	showed	show	VERB
fumecheng-10464	239	8	that	that	SCONJ
fumecheng-10464	239	9	the	the	DET
fumecheng-10464	239	10	approximate	approximate	ADJ
fumecheng-10464	239	11	value	value	NOUN
fumecheng-10464	239	12	of	of	ADP
fumecheng-10464	239	13	the	the	DET
fumecheng-10464	239	14	expanded	expand	VERB
fumecheng-10464	239	15	frequency	frequency	NOUN
fumecheng-10464	239	16	equals	equal	VERB
fumecheng-10464	239	17	σ≌	σ≌	PROPN
fumecheng-10464	239	18	8.716	8.716	NUM
fumecheng-10464	239	19	.	.	PUNCT
fumecheng-10464	240	1	additionally	additionally	ADV
fumecheng-10464	240	2	,	,	PUNCT
fumecheng-10464	240	3	the	the	DET
fumecheng-10464	240	4	calculations	calculation	NOUN
fumecheng-10464	240	5	illustrated	illustrate	VERB
fumecheng-10464	240	6	that	that	SCONJ
fumecheng-10464	240	7	the	the	DET
fumecheng-10464	240	8	initial	initial	ADJ
fumecheng-10464	240	9	condition	condition	NOUN
fumecheng-10464	240	10	developed	develop	VERB
fumecheng-10464	240	11	as	as	ADP
fumecheng-10464	240	12	ẋ(0)=13.017	ẋ(0)=13.017	ADP
fumecheng-10464	240	13	.	.	PUNCT
fumecheng-10464	240	14	fig	fig	NOUN
fumecheng-10464	240	15	.	.	PUNCT
fumecheng-10464	241	1	4	4	NUM
fumecheng-10464	241	2	the	the	DET
fumecheng-10464	241	3	approximate	approximate	ADJ
fumecheng-10464	241	4	solution	solution	NOUN
fumecheng-10464	241	5	that	that	PRON
fumecheng-10464	241	6	is	be	AUX
fumecheng-10464	241	7	given	give	VERB
fumecheng-10464	241	8	in	in	ADP
fumecheng-10464	241	9	eq	eq	ADP
fumecheng-10464	241	10	.	.	PUNCT
fumecheng-10464	242	1	(	(	PUNCT
fumecheng-10464	242	2	21	21	NUM
fumecheng-10464	242	3	)	)	PUNCT
fumecheng-10464	242	4	for	for	ADP
fumecheng-10464	242	5	a	a	DET
fumecheng-10464	242	6	system	system	NOUN
fumecheng-10464	242	7	having	have	VERB
fumecheng-10464	242	8	the	the	DET
fumecheng-10464	242	9	particulars	particular	NOUN
fumecheng-10464	242	10	:	:	PUNCT
fumecheng-10464	242	11	µ=0.2	µ=0.2	ADJ
fumecheng-10464	242	12	,	,	PUNCT
fumecheng-10464	242	13	β=2	β=2	ADP
fumecheng-10464	242	14	,	,	PUNCT
fumecheng-10464	242	15	f=50	f=50	PROPN
fumecheng-10464	242	16	and	and	CCONJ
fumecheng-10464	242	17	ω=4	ω=4	PUNCT
fumecheng-10464	242	18	by	by	ADP
fumecheng-10464	242	19	contrast	contrast	NOUN
fumecheng-10464	242	20	,	,	PUNCT
fumecheng-10464	242	21	fig	fig	NOUN
fumecheng-10464	242	22	.	.	PUNCT
fumecheng-10464	242	23	4	4	NUM
fumecheng-10464	242	24	represents	represent	VERB
fumecheng-10464	242	25	a	a	DET
fumecheng-10464	242	26	system	system	NOUN
fumecheng-10464	242	27	whose	whose	DET
fumecheng-10464	242	28	particulars	particular	NOUN
fumecheng-10464	242	29	are	be	AUX
fumecheng-10464	242	30	held	hold	VERB
fumecheng-10464	242	31	fixed	fix	VERB
fumecheng-10464	242	32	,	,	PUNCT
fumecheng-10464	242	33	except	except	SCONJ
fumecheng-10464	242	34	for	for	ADP
fumecheng-10464	242	35	the	the	DET
fumecheng-10464	242	36	values	value	NOUN
fumecheng-10464	242	37	of	of	ADP
fumecheng-10464	242	38	the	the	DET
fumecheng-10464	242	39	parameter	parameter	NOUN
fumecheng-10464	242	40	f.	f.	PROPN
fumecheng-10464	242	41	as	as	SCONJ
fumecheng-10464	242	42	shown	show	VERB
fumecheng-10464	242	43	from	from	ADP
fumecheng-10464	242	44	this	this	DET
fumecheng-10464	242	45	figure	figure	NOUN
fumecheng-10464	242	46	,	,	PUNCT
fumecheng-10464	242	47	the	the	DET
fumecheng-10464	242	48	amplitude	amplitude	NOUN
fumecheng-10464	242	49	of	of	ADP
fumecheng-10464	242	50	the	the	DET
fumecheng-10464	242	51	wave	wave	NOUN
fumecheng-10464	242	52	solution	solution	NOUN
fumecheng-10464	242	53	increases	increase	VERB
fumecheng-10464	242	54	as	as	SCONJ
fumecheng-10464	242	55	f	f	PROPN
fumecheng-10464	242	56	also	also	ADV
fumecheng-10464	242	57	increases	increase	VERB
fumecheng-10464	242	58	.	.	PUNCT
fumecheng-10464	243	1	this	this	PRON
fumecheng-10464	243	2	shows	show	VERB
fumecheng-10464	243	3	a	a	DET
fumecheng-10464	243	4	destabilizing	destabilizing	ADJ
fumecheng-10464	243	5	influence	influence	NOUN
fumecheng-10464	243	6	of	of	ADP
fumecheng-10464	243	7	this	this	DET
fumecheng-10464	243	8	parameter	parameter	NOUN
fumecheng-10464	243	9	.	.	PUNCT
fumecheng-10464	244	1	physically	physically	ADV
fumecheng-10464	244	2	,	,	PUNCT
fumecheng-10464	244	3	it	it	PRON
fumecheng-10464	244	4	is	be	AUX
fumecheng-10464	244	5	a	a	DET
fumecheng-10464	244	6	convenient	convenient	ADJ
fumecheng-10464	244	7	evidence	evidence	NOUN
fumecheng-10464	244	8	because	because	SCONJ
fumecheng-10464	244	9	of	of	ADP
fumecheng-10464	244	10	the	the	DET
fumecheng-10464	244	11	excitation	excitation	NOUN
fumecheng-10464	244	12	of	of	ADP
fumecheng-10464	244	13	the	the	DET
fumecheng-10464	244	14	external	external	ADJ
fumecheng-10464	244	15	force	force	NOUN
fumecheng-10464	244	16	.	.	PUNCT
fumecheng-10464	245	1	it	it	PRON
fumecheng-10464	245	2	should	should	AUX
fumecheng-10464	245	3	be	be	AUX
fumecheng-10464	245	4	noticed	notice	VERB
fumecheng-10464	245	5	that	that	SCONJ
fumecheng-10464	245	6	the	the	DET
fumecheng-10464	245	7	domain	domain	NOUN
fumecheng-10464	245	8	of	of	ADP
fumecheng-10464	245	9	the	the	DET
fumecheng-10464	245	10	solution	solution	NOUN
fumecheng-10464	245	11	function	function	NOUN
fumecheng-10464	245	12	is	be	AUX
fumecheng-10464	245	13	much	much	ADV
fumecheng-10464	245	14	shorter	short	ADJ
fumecheng-10464	245	15	than	than	ADP
fumecheng-10464	245	16	the	the	DET
fumecheng-10464	245	17	previous	previous	ADJ
fumecheng-10464	245	18	one	one	NUM
fumecheng-10464	245	19	.	.	PUNCT
fumecheng-10464	246	1	this	this	PRON
fumecheng-10464	246	2	occurs	occur	VERB
fumecheng-10464	246	3	only	only	ADV
fumecheng-10464	246	4	to	to	PART
fumecheng-10464	246	5	clearly	clearly	ADV
fumecheng-10464	246	6	indicate	indicate	VERB
fumecheng-10464	246	7	the	the	DET
fumecheng-10464	246	8	influence	influence	NOUN
fumecheng-10464	246	9	.	.	PUNCT
fumecheng-10464	247	1	fig	fig	NOUN
fumecheng-10464	247	2	.	.	PUNCT
fumecheng-10464	248	1	5	5	NUM
fumecheng-10464	248	2	the	the	DET
fumecheng-10464	248	3	approximate	approximate	ADJ
fumecheng-10464	248	4	solution	solution	NOUN
fumecheng-10464	248	5	that	that	PRON
fumecheng-10464	248	6	is	be	AUX
fumecheng-10464	248	7	given	give	VERB
fumecheng-10464	248	8	in	in	ADP
fumecheng-10464	248	9	eq	eq	ADP
fumecheng-10464	248	10	.	.	PUNCT
fumecheng-10464	249	1	(	(	PUNCT
fumecheng-10464	249	2	21	21	NUM
fumecheng-10464	249	3	)	)	PUNCT
fumecheng-10464	249	4	,	,	PUNCT
fumecheng-10464	249	5	for	for	ADP
fumecheng-10464	249	6	a	a	DET
fumecheng-10464	249	7	system	system	NOUN
fumecheng-10464	249	8	having	have	VERB
fumecheng-10464	249	9	the	the	DET
fumecheng-10464	249	10	particulars	particular	NOUN
fumecheng-10464	249	11	given	give	VERB
fumecheng-10464	249	12	in	in	ADP
fumecheng-10464	249	13	fig	fig	NOUN
fumecheng-10464	249	14	.	.	PUNCT
fumecheng-10464	250	1	2	2	NUM
fumecheng-10464	251	1	but	but	CCONJ
fumecheng-10464	251	2	for	for	ADP
fumecheng-10464	251	3	the	the	DET
fumecheng-10464	251	4	variation	variation	NOUN
fumecheng-10464	251	5	of	of	ADP
fumecheng-10464	251	6	the	the	DET
fumecheng-10464	251	7	parameter	parameter	NOUN
fumecheng-10464	251	8	f.	f.	PROPN
fumecheng-10464	251	9	10	10	NUM
fumecheng-10464	251	10	j.-h	j.-h	NOUN
fumecheng-10464	251	11	.	.	PUNCT
fumecheng-10464	252	1	he	he	PRON
fumecheng-10464	252	2	,	,	PUNCT
fumecheng-10464	252	3	g.	g.	PROPN
fumecheng-10464	252	4	m.	m.	PROPN
fumecheng-10464	252	5	moatimid	moatimid	PROPN
fumecheng-10464	252	6	,	,	PUNCT
fumecheng-10464	252	7	m.	m.	PROPN
fumecheng-10464	252	8	h.	h.	PROPN
fumecheng-10464	252	9	zekry	zekry	PROPN
fumecheng-10464	252	10	3	3	X
fumecheng-10464	252	11	.	.	PUNCT
fumecheng-10464	252	12	linearized	linearize	VERB
fumecheng-10464	252	13	stability	stability	NOUN
fumecheng-10464	252	14	of	of	ADP
fumecheng-10464	252	15	the	the	DET
fumecheng-10464	252	16	autonomous	autonomous	ADJ
fumecheng-10464	252	17	system	system	NOUN
fumecheng-10464	252	18	the	the	DET
fumecheng-10464	252	19	analysis	analysis	NOUN
fumecheng-10464	252	20	here	here	ADV
fumecheng-10464	252	21	is	be	AUX
fumecheng-10464	252	22	concerned	concern	VERB
fumecheng-10464	252	23	with	with	ADP
fumecheng-10464	252	24	the	the	DET
fumecheng-10464	252	25	governing	govern	VERB
fumecheng-10464	252	26	dvdp	dvdp	ADJ
fumecheng-10464	252	27	equation	equation	NOUN
fumecheng-10464	252	28	at	at	ADP
fumecheng-10464	252	29	which	which	PRON
fumecheng-10464	252	30	the	the	DET
fumecheng-10464	252	31	external	external	ADJ
fumecheng-10464	252	32	force	force	NOUN
fumecheng-10464	252	33	is	be	AUX
fumecheng-10464	252	34	absent	absent	ADJ
fumecheng-10464	252	35	as	as	ADP
fumecheng-10464	252	36	(	(	PUNCT
fumecheng-10464	252	37	f→	f→	PROPN
fumecheng-10464	252	38	0	0	NUM
fumecheng-10464	252	39	)	)	PUNCT
fumecheng-10464	252	40	.	.	PUNCT
fumecheng-10464	253	1	for	for	ADP
fumecheng-10464	253	2	this	this	DET
fumecheng-10464	253	3	purpose	purpose	NOUN
fumecheng-10464	253	4	,	,	PUNCT
fumecheng-10464	253	5	consider	consider	VERB
fumecheng-10464	253	6	the	the	DET
fumecheng-10464	253	7	following	follow	VERB
fumecheng-10464	253	8	transformations	transformation	NOUN
fumecheng-10464	253	9	:	:	PUNCT
fumecheng-10464	253	10	,	,	PUNCT
fumecheng-10464	253	11	yx	yx	NOUN
fumecheng-10464	253	12	=	=	NOUN
fumecheng-10464	253	13			PROPN
fumecheng-10464	253	14	and	and	CCONJ
fumecheng-10464	253	15	.yx	.yx	PUNCT
fumecheng-10464	253	16			PROPN
fumecheng-10464	253	17	=	=	SYM
fumecheng-10464	253	18	(	(	PUNCT
fumecheng-10464	253	19	28	28	NUM
fumecheng-10464	253	20	)	)	PUNCT
fumecheng-10464	253	21	it	it	PRON
fumecheng-10464	253	22	follows	follow	VERB
fumecheng-10464	253	23	that	that	SCONJ
fumecheng-10464	253	24	the	the	DET
fumecheng-10464	253	25	governing	govern	VERB
fumecheng-10464	253	26	equation	equation	NOUN
fumecheng-10464	253	27	that	that	PRON
fumecheng-10464	253	28	is	be	AUX
fumecheng-10464	253	29	given	give	VERB
fumecheng-10464	253	30	by	by	ADP
fumecheng-10464	253	31	eq	eq	PROPN
fumecheng-10464	253	32	.	.	PUNCT
fumecheng-10464	254	1	(	(	PUNCT
fumecheng-10464	254	2	2	2	X
fumecheng-10464	254	3	)	)	PUNCT
fumecheng-10464	254	4	may	may	AUX
fumecheng-10464	254	5	be	be	AUX
fumecheng-10464	254	6	represented	represent	VERB
fumecheng-10464	254	7	by	by	ADP
fumecheng-10464	254	8	the	the	DET
fumecheng-10464	254	9	following	follow	VERB
fumecheng-10464	254	10	first	first	ADJ
fumecheng-10464	254	11	-order	-order	PROPN
fumecheng-10464	254	12	nonlinear	nonlinear	ADJ
fumecheng-10464	254	13	ordinary	ordinary	ADJ
fumecheng-10464	254	14	differential	differential	ADJ
fumecheng-10464	254	15	equations	equation	NOUN
fumecheng-10464	254	16	:	:	PUNCT
fumecheng-10464	254	17	)	)	PUNCT
fumecheng-10464	254	18	,	,	PUNCT
fumecheng-10464	254	19	(	(	PUNCT
fumecheng-10464	254	20	yxfx	yxfx	NOUN
fumecheng-10464	254	21	=	=	NOUN
fumecheng-10464	254	22			PROPN
fumecheng-10464	254	23	and	and	CCONJ
fumecheng-10464	254	24	,	,	PUNCT
fumecheng-10464	254	25	)	)	PUNCT
fumecheng-10464	254	26	,	,	PUNCT
fumecheng-10464	254	27	(	(	PUNCT
fumecheng-10464	254	28	yxhy	yxhy	NOUN
fumecheng-10464	254	29	=	=	NOUN
fumecheng-10464	254	30			NOUN
fumecheng-10464	254	31	(	(	PUNCT
fumecheng-10464	254	32	29	29	NUM
fumecheng-10464	254	33	)	)	PUNCT
fumecheng-10464	254	34	where	where	SCONJ
fumecheng-10464	254	35	f(x	f(x	PROPN
fumecheng-10464	254	36	,	,	PUNCT
fumecheng-10464	254	37	y)=y	y)=y	NOUN
fumecheng-10464	254	38	and	and	CCONJ
fumecheng-10464	254	39	h(x	h(x	PROPN
fumecheng-10464	254	40	,	,	PUNCT
fumecheng-10464	254	41	y)=-x+µ(1−x2)y−β	y)=-x+µ(1−x2)y−β	NOUN
fumecheng-10464	254	42	x3	x3	ADJ
fumecheng-10464	254	43	.	.	PUNCT
fumecheng-10464	255	1	the	the	DET
fumecheng-10464	255	2	details	detail	NOUN
fumecheng-10464	255	3	of	of	ADP
fumecheng-10464	255	4	the	the	DET
fumecheng-10464	255	5	current	current	ADJ
fumecheng-10464	255	6	approach	approach	NOUN
fumecheng-10464	255	7	are	be	AUX
fumecheng-10464	255	8	given	give	VERB
fumecheng-10464	255	9	in	in	ADP
fumecheng-10464	255	10	our	our	PRON
fumecheng-10464	255	11	previous	previous	ADJ
fumecheng-10464	255	12	recent	recent	ADJ
fumecheng-10464	255	13	work	work	NOUN
fumecheng-10464	255	14	[	[	X
fumecheng-10464	255	15	42	42	NUM
fumecheng-10464	255	16	]	]	PUNCT
fumecheng-10464	255	17	.	.	PUNCT
fumecheng-10464	256	1	to	to	PART
fumecheng-10464	256	2	restrict	restrict	VERB
fumecheng-10464	256	3	the	the	DET
fumecheng-10464	256	4	length	length	NOUN
fumecheng-10464	256	5	of	of	ADP
fumecheng-10464	256	6	the	the	DET
fumecheng-10464	256	7	paper	paper	NOUN
fumecheng-10464	256	8	,	,	PUNCT
fumecheng-10464	256	9	they	they	PRON
fumecheng-10464	256	10	will	will	AUX
fumecheng-10464	256	11	be	be	AUX
fumecheng-10464	256	12	omitted	omit	VERB
fumecheng-10464	256	13	.	.	PUNCT
fumecheng-10464	257	1	for	for	ADP
fumecheng-10464	257	2	more	more	ADJ
fumecheng-10464	257	3	opportunities	opportunity	NOUN
fumecheng-10464	257	4	,	,	PUNCT
fumecheng-10464	257	5	some	some	DET
fumecheng-10464	257	6	numerical	numerical	ADJ
fumecheng-10464	257	7	calculations	calculation	NOUN
fumecheng-10464	257	8	are	be	AUX
fumecheng-10464	257	9	given	give	VERB
fumecheng-10464	257	10	here	here	ADV
fumecheng-10464	257	11	to	to	PART
fumecheng-10464	257	12	indicate	indicate	VERB
fumecheng-10464	257	13	the	the	DET
fumecheng-10464	257	14	nature	nature	NOUN
fumecheng-10464	257	15	of	of	ADP
fumecheng-10464	257	16	the	the	DET
fumecheng-10464	257	17	characteristic	characteristic	ADJ
fumecheng-10464	257	18	eigenvalues	eigenvalue	NOUN
fumecheng-10464	257	19	and	and	CCONJ
fumecheng-10464	257	20	consequences	consequence	NOUN
fumecheng-10464	257	21	.	.	PUNCT
fumecheng-10464	258	1	therefore	therefore	ADV
fumecheng-10464	258	2	,	,	PUNCT
fumecheng-10464	258	3	the	the	DET
fumecheng-10464	258	4	phase	phase	NOUN
fumecheng-10464	258	5	portraits	portrait	NOUN
fumecheng-10464	258	6	are	be	AUX
fumecheng-10464	258	7	plotted	plot	VERB
fumecheng-10464	258	8	.	.	PUNCT
fumecheng-10464	259	1	table	table	NOUN
fumecheng-10464	259	2	1	1	NUM
fumecheng-10464	259	3	illustration	illustration	NOUN
fumecheng-10464	259	4	of	of	ADP
fumecheng-10464	259	5	some	some	DET
fumecheng-10464	259	6	sample	sample	NOUN
fumecheng-10464	259	7	values	value	NOUN
fumecheng-10464	259	8	of	of	ADP
fumecheng-10464	259	9	the	the	DET
fumecheng-10464	259	10	eigenvalues	eigenvalue	NOUN
fumecheng-10464	259	11	and	and	CCONJ
fumecheng-10464	259	12	the	the	DET
fumecheng-10464	259	13	corresponding	corresponding	ADJ
fumecheng-10464	259	14	stability	stability	NOUN
fumecheng-10464	259	15	/	/	SYM
fumecheng-10464	259	16	instability	instability	NOUN
fumecheng-10464	259	17	sample	sample	NOUN
fumecheng-10464	259	18	chosen	choose	VERB
fumecheng-10464	259	19	system	system	NOUN
fumecheng-10464	259	20	fixed	fix	VERB
fumecheng-10464	259	21	point	point	NOUN
fumecheng-10464	259	22	roots	root	NOUN
fumecheng-10464	259	23	of	of	ADP
fumecheng-10464	259	24	the	the	DET
fumecheng-10464	259	25	eigenvalues	eigenvalue	NOUN
fumecheng-10464	259	26	stability	stability	NOUN
fumecheng-10464	259	27	/	/	SYM
fumecheng-10464	259	28	instability	instability	NOUN
fumecheng-10464	259	29	1	1	NUM
fumecheng-10464	259	30	0,1	0,1	NUM
fumecheng-10464	259	31	=	=	X
fumecheng-10464	259	32	=	=	SYM
fumecheng-10464	259	33			PROPN
fumecheng-10464	259	34	(	(	PUNCT
fumecheng-10464	259	35	0,0	0,0	NOUN
fumecheng-10464	259	36	)	)	PUNCT
fumecheng-10464	259	37	pure	pure	ADJ
fumecheng-10464	259	38	imaginary	imaginary	ADJ
fumecheng-10464	259	39	.2,1	.2,1	NOUN
fumecheng-10464	260	1	i=	i=	ADJ
fumecheng-10464	260	2	a	a	DET
fumecheng-10464	260	3	stable	stable	ADJ
fumecheng-10464	260	4	center	center	NOUN
fumecheng-10464	260	5	see	see	VERB
fumecheng-10464	260	6	fig	fig	NOUN
fumecheng-10464	260	7	.	.	PUNCT
fumecheng-10464	261	1	6	6	NUM
fumecheng-10464	261	2	2	2	NUM
fumecheng-10464	261	3	1,1	1,1	NUM
fumecheng-10464	261	4	=	=	NOUN
fumecheng-10464	261	5	−=	−=	ADP
fumecheng-10464	261	6			PROPN
fumecheng-10464	261	7	(	(	PUNCT
fumecheng-10464	261	8	1,0)	1,0)	PROPN
fumecheng-10464	261	9	real	real	ADJ
fumecheng-10464	261	10	,	,	PUNCT
fumecheng-10464	261	11	equal	equal	ADJ
fumecheng-10464	261	12	,	,	PUNCT
fumecheng-10464	261	13	and	and	CCONJ
fumecheng-10464	261	14	of	of	ADP
fumecheng-10464	261	15	different	different	ADJ
fumecheng-10464	261	16	signs	sign	NOUN
fumecheng-10464	261	17	.414.1,414.1	.414.1,414.1	PUNCT
fumecheng-10464	261	18	21	21	NUM
fumecheng-10464	261	19	−==	−==	ADJ
fumecheng-10464	261	20	saddle	saddle	NOUN
fumecheng-10464	261	21	point	point	NOUN
fumecheng-10464	261	22	(	(	PUNCT
fumecheng-10464	261	23	unstable	unstable	ADJ
fumecheng-10464	261	24	)	)	PUNCT
fumecheng-10464	261	25	see	see	VERB
fumecheng-10464	261	26	fig	fig	NOUN
fumecheng-10464	261	27	.	.	PUNCT
fumecheng-10464	262	1	7	7	NUM
fumecheng-10464	262	2	3	3	NUM
fumecheng-10464	262	3	5.0,2	5.0,2	NOUN
fumecheng-10464	262	4	=	=	NUM
fumecheng-10464	262	5	−=	−=	NOUN
fumecheng-10464	262	6			PROPN
fumecheng-10464	262	7	1	1	NUM
fumecheng-10464	262	8	,	,	PUNCT
fumecheng-10464	262	9	0	0	NUM
fumecheng-10464	262	10	2	2	NUM
fumecheng-10464	262	11			NOUN
fumecheng-10464	262	12			NOUN
fumecheng-10464	262	13			PUNCT
fumecheng-10464	262	14			PROPN
fumecheng-10464	263	1			ADJ
fumecheng-10464	263	2			NOUN
fumecheng-10464	263	3	real	real	ADJ
fumecheng-10464	263	4	,	,	PUNCT
fumecheng-10464	263	5	distinct	distinct	ADJ
fumecheng-10464	263	6	,	,	PUNCT
fumecheng-10464	263	7	and	and	CCONJ
fumecheng-10464	263	8	of	of	ADP
fumecheng-10464	263	9	different	different	ADJ
fumecheng-10464	263	10	signs	sign	NOUN
fumecheng-10464	263	11	.29473.1	.29473.1	PUNCT
fumecheng-10464	263	12	,	,	PUNCT
fumecheng-10464	263	13	54473.1	54473.1	NUM
fumecheng-10464	263	14	2	2	NUM
fumecheng-10464	263	15	1	1	NUM
fumecheng-10464	263	16	−=	−=	NOUN
fumecheng-10464	263	17	=	=	NOUN
fumecheng-10464	263	18			NOUN
fumecheng-10464	263	19	saddle	saddle	NOUN
fumecheng-10464	263	20	point	point	NOUN
fumecheng-10464	263	21	(	(	PUNCT
fumecheng-10464	263	22	unstable	unstable	ADJ
fumecheng-10464	263	23	)	)	PUNCT
fumecheng-10464	263	24	see	see	VERB
fumecheng-10464	263	25	fig	fig	NOUN
fumecheng-10464	263	26	.	.	PUNCT
fumecheng-10464	264	1	8	8	NUM
fumecheng-10464	264	2	4	4	NUM
fumecheng-10464	264	3	1,1	1,1	NUM
fumecheng-10464	264	4	−=−=	−=−=	NOUN
fumecheng-10464	264	5			PROPN
fumecheng-10464	264	6	(	(	PUNCT
fumecheng-10464	264	7	0,0	0,0	NUM
fumecheng-10464	264	8	)	)	PUNCT
fumecheng-10464	264	9	complex	complex	ADJ
fumecheng-10464	264	10	conjugates	conjugate	NOUN
fumecheng-10464	264	11	with	with	ADP
fumecheng-10464	264	12	negative	negative	ADJ
fumecheng-10464	264	13	real	real	ADJ
fumecheng-10464	264	14	part	part	NOUN
fumecheng-10464	264	15	)	)	PUNCT
fumecheng-10464	264	16	31	31	NUM
fumecheng-10464	264	17	(	(	PUNCT
fumecheng-10464	264	18	2	2	NUM
fumecheng-10464	264	19	1	1	NUM
fumecheng-10464	264	20	1	1	NUM
fumecheng-10464	264	21	i−=	i−=	NOUN
fumecheng-10464	264	22	stable	stable	ADJ
fumecheng-10464	264	23	focus	focus	NOUN
fumecheng-10464	264	24	see	see	VERB
fumecheng-10464	264	25	fig	fig	NOUN
fumecheng-10464	264	26	.	.	PUNCT
fumecheng-10464	265	1	9	9	NUM
fumecheng-10464	265	2	unfortunately	unfortunately	ADV
fumecheng-10464	265	3	,	,	PUNCT
fumecheng-10464	265	4	the	the	DET
fumecheng-10464	265	5	previous	previous	ADJ
fumecheng-10464	265	6	criterion	criterion	NOUN
fumecheng-10464	265	7	ignores	ignore	VERB
fumecheng-10464	265	8	the	the	DET
fumecheng-10464	265	9	contribution	contribution	NOUN
fumecheng-10464	265	10	of	of	ADP
fumecheng-10464	265	11	the	the	DET
fumecheng-10464	265	12	external	external	ADJ
fumecheng-10464	265	13	excitation	excitation	NOUN
fumecheng-10464	265	14	force	force	NOUN
fumecheng-10464	265	15	.	.	PUNCT
fumecheng-10464	266	1	therefore	therefore	ADV
fumecheng-10464	266	2	,	,	PUNCT
fumecheng-10464	266	3	the	the	DET
fumecheng-10464	266	4	following	follow	VERB
fumecheng-10464	266	5	analysis	analysis	NOUN
fumecheng-10464	266	6	will	will	AUX
fumecheng-10464	266	7	be	be	AUX
fumecheng-10464	266	8	included	include	VERB
fumecheng-10464	266	9	to	to	PART
fumecheng-10464	266	10	indicate	indicate	VERB
fumecheng-10464	266	11	this	this	DET
fumecheng-10464	266	12	influence	influence	NOUN
fumecheng-10464	266	13	throughout	throughout	ADP
fumecheng-10464	266	14	the	the	DET
fumecheng-10464	266	15	multiple	multiple	ADJ
fumecheng-10464	266	16	scale	scale	NOUN
fumecheng-10464	266	17	technique	technique	NOUN
fumecheng-10464	266	18	.	.	PUNCT
fumecheng-10464	267	1	forced	force	VERB
fumecheng-10464	267	2	nonlinear	nonlinear	ADJ
fumecheng-10464	267	3	oscillator	oscillator	NOUN
fumecheng-10464	267	4	in	in	ADP
fumecheng-10464	267	5	a	a	DET
fumecheng-10464	267	6	fractal	fractal	ADJ
fumecheng-10464	267	7	space	space	NOUN
fumecheng-10464	267	8	11	11	NUM
fumecheng-10464	267	9	fig	fig	NOUN
fumecheng-10464	267	10	.	.	PUNCT
fumecheng-10464	268	1	6	6	NUM
fumecheng-10464	268	2	the	the	DET
fumecheng-10464	268	3	phase	phase	NOUN
fumecheng-10464	268	4	portrait	portrait	NOUN
fumecheng-10464	268	5	of	of	ADP
fumecheng-10464	268	6	a	a	DET
fumecheng-10464	268	7	system	system	NOUN
fumecheng-10464	268	8	having	have	VERB
fumecheng-10464	268	9	the	the	DET
fumecheng-10464	268	10	particular	particular	ADJ
fumecheng-10464	268	11	:	:	PUNCT
fumecheng-10464	268	12	β	β	X
fumecheng-10464	268	13	=	=	NOUN
fumecheng-10464	268	14	1	1	NUM
fumecheng-10464	268	15	and	and	CCONJ
fumecheng-10464	268	16	µ=0	µ=0	PROPN
fumecheng-10464	268	17	.	.	PUNCT
fumecheng-10464	268	18	fig	fig	NOUN
fumecheng-10464	268	19	.	.	PUNCT
fumecheng-10464	268	20	7	7	NUM
fumecheng-10464	269	1	the	the	DET
fumecheng-10464	269	2	phase	phase	NOUN
fumecheng-10464	269	3	portrait	portrait	NOUN
fumecheng-10464	269	4	of	of	ADP
fumecheng-10464	269	5	a	a	DET
fumecheng-10464	269	6	system	system	NOUN
fumecheng-10464	269	7	having	have	VERB
fumecheng-10464	269	8	the	the	DET
fumecheng-10464	269	9	particular	particular	ADJ
fumecheng-10464	269	10	:	:	PUNCT
fumecheng-10464	269	11	β	β	X
fumecheng-10464	269	12	=	=	NOUN
fumecheng-10464	269	13	−1	−1	NOUN
fumecheng-10464	269	14	and	and	CCONJ
fumecheng-10464	269	15	µ=1	µ=1	PROPN
fumecheng-10464	269	16	.	.	PUNCT
fumecheng-10464	270	1	fig	fig	NOUN
fumecheng-10464	270	2	.	.	PUNCT
fumecheng-10464	270	3	8	8	NUM
fumecheng-10464	271	1	the	the	DET
fumecheng-10464	271	2	phase	phase	NOUN
fumecheng-10464	271	3	portrait	portrait	NOUN
fumecheng-10464	271	4	of	of	ADP
fumecheng-10464	271	5	a	a	DET
fumecheng-10464	271	6	system	system	NOUN
fumecheng-10464	271	7	having	have	VERB
fumecheng-10464	271	8	the	the	DET
fumecheng-10464	271	9	particular	particular	ADJ
fumecheng-10464	271	10	:	:	PUNCT
fumecheng-10464	271	11	β	β	X
fumecheng-10464	271	12	=	=	PUNCT
fumecheng-10464	271	13	−2	−2	NOUN
fumecheng-10464	271	14	and	and	CCONJ
fumecheng-10464	271	15	µ=0.5	µ=0.5	NOUN
fumecheng-10464	271	16	.	.	PUNCT
fumecheng-10464	272	1	fig	fig	NOUN
fumecheng-10464	272	2	.	.	PUNCT
fumecheng-10464	273	1	9	9	NUM
fumecheng-10464	273	2	the	the	DET
fumecheng-10464	273	3	phase	phase	NOUN
fumecheng-10464	273	4	portrait	portrait	NOUN
fumecheng-10464	273	5	of	of	ADP
fumecheng-10464	273	6	a	a	DET
fumecheng-10464	273	7	system	system	NOUN
fumecheng-10464	273	8	having	have	VERB
fumecheng-10464	273	9	the	the	DET
fumecheng-10464	273	10	particular	particular	ADJ
fumecheng-10464	273	11	:	:	PUNCT
fumecheng-10464	274	1	β	β	X
fumecheng-10464	274	2	=	=	NOUN
fumecheng-10464	274	3	−1	−1	NOUN
fumecheng-10464	274	4	and	and	CCONJ
fumecheng-10464	274	5	µ=−1	µ=−1	VERB
fumecheng-10464	274	6	.	.	NOUN
fumecheng-10464	275	1	4	4	X
fumecheng-10464	275	2	.	.	X
fumecheng-10464	276	1	the	the	DET
fumecheng-10464	276	2	stability	stability	NOUN
fumecheng-10464	276	3	analysis	analysis	NOUN
fumecheng-10464	276	4	along	along	ADP
fumecheng-10464	276	5	the	the	DET
fumecheng-10464	276	6	multiple	multiple	ADJ
fumecheng-10464	276	7	-	-	PUNCT
fumecheng-10464	276	8	time	time	NOUN
fumecheng-10464	276	9	scale	scale	NOUN
fumecheng-10464	276	10	technique	technique	NOUN
fumecheng-10464	276	11	as	as	SCONJ
fumecheng-10464	276	12	known	know	VERB
fumecheng-10464	276	13	the	the	DET
fumecheng-10464	276	14	poincare	poincare	PROPN
fumecheng-10464	276	15	-	-	PUNCT
fumecheng-10464	276	16	lindstedt	lindstedt	VERB
fumecheng-10464	276	17	method	method	NOUN
fumecheng-10464	276	18	is	be	AUX
fumecheng-10464	276	19	an	an	DET
fumecheng-10464	276	20	approach	approach	NOUN
fumecheng-10464	276	21	to	to	PART
fumecheng-10464	276	22	postulate	postulate	VERB
fumecheng-10464	276	23	an	an	DET
fumecheng-10464	276	24	asymptotic	asymptotic	ADJ
fumecheng-10464	276	25	approximation	approximation	NOUN
fumecheng-10464	276	26	of	of	ADP
fumecheng-10464	276	27	the	the	DET
fumecheng-10464	276	28	periodic	periodic	ADJ
fumecheng-10464	276	29	solution	solution	NOUN
fumecheng-10464	276	30	.	.	PUNCT
fumecheng-10464	277	1	on	on	ADP
fumecheng-10464	277	2	the	the	DET
fumecheng-10464	277	3	other	other	ADJ
fumecheng-10464	277	4	hand	hand	NOUN
fumecheng-10464	277	5	,	,	PUNCT
fumecheng-10464	277	6	it	it	PRON
fumecheng-10464	277	7	can	can	AUX
fumecheng-10464	277	8	not	not	PART
fumecheng-10464	277	9	be	be	AUX
fumecheng-10464	277	10	used	use	VERB
fumecheng-10464	277	11	to	to	PART
fumecheng-10464	277	12	attain	attain	VERB
fumecheng-10464	277	13	solutions	solution	NOUN
fumecheng-10464	277	14	that	that	PRON
fumecheng-10464	277	15	develop	develop	VERB
fumecheng-10464	277	16	periodically	periodically	ADV
fumecheng-10464	277	17	on	on	ADP
fumecheng-10464	277	18	a	a	DET
fumecheng-10464	277	19	slow	slow	ADJ
fumecheng-10464	277	20	timescale	timescale	NOUN
fumecheng-10464	277	21	.	.	PUNCT
fumecheng-10464	278	1	the	the	DET
fumecheng-10464	278	2	method	method	NOUN
fumecheng-10464	278	3	of	of	ADP
fumecheng-10464	278	4	multiple	multiple	ADJ
fumecheng-10464	278	5	scales	scale	NOUN
fumecheng-10464	278	6	is	be	AUX
fumecheng-10464	278	7	a	a	DET
fumecheng-10464	278	8	more	more	ADV
fumecheng-10464	278	9	general	general	ADJ
fumecheng-10464	278	10	approach	approach	NOUN
fumecheng-10464	278	11	that	that	PRON
fumecheng-10464	278	12	involves	involve	VERB
fumecheng-10464	278	13	two	two	NUM
fumecheng-10464	278	14	key	key	ADJ
fumecheng-10464	278	15	tricks	trick	NOUN
fumecheng-10464	278	16	.	.	PUNCT
fumecheng-10464	279	1	therefore	therefore	ADV
fumecheng-10464	279	2	,	,	PUNCT
fumecheng-10464	279	3	the	the	DET
fumecheng-10464	279	4	method	method	NOUN
fumecheng-10464	279	5	of	of	ADP
fumecheng-10464	279	6	multiple	multiple	ADJ
fumecheng-10464	279	7	scales	scale	NOUN
fumecheng-10464	279	8	encompasses	encompass	VERB
fumecheng-10464	279	9	a	a	DET
fumecheng-10464	279	10	technique	technique	NOUN
fumecheng-10464	279	11	that	that	PRON
fumecheng-10464	279	12	is	be	AUX
fumecheng-10464	279	13	used	use	VERB
fumecheng-10464	279	14	to	to	PART
fumecheng-10464	279	15	establish	establish	VERB
fumecheng-10464	279	16	a	a	DET
fumecheng-10464	279	17	uniform	uniform	ADJ
fumecheng-10464	279	18	valid	valid	ADJ
fumecheng-10464	279	19	approximation	approximation	NOUN
fumecheng-10464	279	20	to	to	ADP
fumecheng-10464	279	21	the	the	DET
fumecheng-10464	279	22	general	general	ADJ
fumecheng-10464	279	23	solution	solution	NOUN
fumecheng-10464	279	24	of	of	ADP
fumecheng-10464	279	25	perturbation	perturbation	NOUN
fumecheng-10464	279	26	problems	problem	NOUN
fumecheng-10464	279	27	in	in	ADP
fumecheng-10464	279	28	which	which	PRON
fumecheng-10464	279	29	the	the	DET
fumecheng-10464	279	30	solution	solution	NOUN
fumecheng-10464	279	31	depends	depend	VERB
fumecheng-10464	279	32	on	on	ADP
fumecheng-10464	279	33	extensively	extensively	ADV
fumecheng-10464	279	34	diverse	diverse	ADJ
fumecheng-10464	279	35	scales	scale	NOUN
fumecheng-10464	279	36	.	.	PUNCT
fumecheng-10464	280	1	nayfeh	nayfeh	PROPN
fumecheng-10464	281	1	[	[	X
fumecheng-10464	281	2	43	43	NUM
fumecheng-10464	281	3	]	]	PUNCT
fumecheng-10464	281	4	divided	divide	VERB
fumecheng-10464	281	5	the	the	DET
fumecheng-10464	281	6	time	time	NOUN
fumecheng-10464	281	7	into	into	ADP
fumecheng-10464	281	8	several	several	ADJ
fumecheng-10464	281	9	time	time	NOUN
fumecheng-10464	281	10	scales	scale	NOUN
fumecheng-10464	281	11	which	which	PRON
fumecheng-10464	281	12	will	will	AUX
fumecheng-10464	281	13	be	be	AUX
fumecheng-10464	281	14	considered	consider	VERB
fumecheng-10464	281	15	to	to	PART
fumecheng-10464	281	16	be	be	AUX
fumecheng-10464	281	17	independent	independent	ADJ
fumecheng-10464	281	18	variables	variable	NOUN
fumecheng-10464	281	19	.	.	PUNCT
fumecheng-10464	282	1	based	base	VERB
fumecheng-10464	282	2	on	on	ADP
fumecheng-10464	282	3	this	this	DET
fumecheng-10464	282	4	conception	conception	NOUN
fumecheng-10464	282	5	,	,	PUNCT
fumecheng-10464	282	6	nayfeh	nayfeh	PROPN
fumecheng-10464	282	7	formulated	formulate	VERB
fumecheng-10464	282	8	his	his	PRON
fumecheng-10464	282	9	theory	theory	NOUN
fumecheng-10464	282	10	.	.	PUNCT
fumecheng-10464	283	1	in	in	ADP
fumecheng-10464	283	2	agreement	agreement	NOUN
fumecheng-10464	283	3	with	with	ADP
fumecheng-10464	283	4	the	the	DET
fumecheng-10464	283	5	transformation	transformation	NOUN
fumecheng-10464	283	6	of	of	ADP
fumecheng-10464	283	7	the	the	DET
fumecheng-10464	283	8	derivatives	derivative	NOUN
fumecheng-10464	283	9	,	,	PUNCT
fumecheng-10464	283	10	the	the	DET
fumecheng-10464	283	11	original	original	ADJ
fumecheng-10464	283	12	differential	differential	NOUN
fumecheng-10464	283	13	equation	equation	NOUN
fumecheng-10464	283	14	is	be	AUX
fumecheng-10464	283	15	divided	divide	VERB
fumecheng-10464	283	16	into	into	ADP
fumecheng-10464	283	17	a	a	DET
fumecheng-10464	283	18	set	set	NOUN
fumecheng-10464	283	19	of	of	ADP
fumecheng-10464	283	20	partial	partial	ADJ
fumecheng-10464	283	21	differential	differential	NOUN
fumecheng-10464	283	22	equations	equation	NOUN
fumecheng-10464	283	23	.	.	PUNCT
fumecheng-10464	284	1	subsequently	subsequently	ADV
fumecheng-10464	284	2	,	,	PUNCT
fumecheng-10464	284	3	it	it	PRON
fumecheng-10464	284	4	seems	seem	VERB
fumecheng-10464	284	5	that	that	SCONJ
fumecheng-10464	284	6	12	12	NUM
fumecheng-10464	284	7	j.-h	j.-h	NOUN
fumecheng-10464	284	8	.	.	PUNCT
fumecheng-10464	285	1	he	he	PRON
fumecheng-10464	285	2	,	,	PUNCT
fumecheng-10464	285	3	g.	g.	PROPN
fumecheng-10464	285	4	m.	m.	PROPN
fumecheng-10464	285	5	moatimid	moatimid	PROPN
fumecheng-10464	285	6	,	,	PUNCT
fumecheng-10464	285	7	m.	m.	PROPN
fumecheng-10464	285	8	h.	h.	PROPN
fumecheng-10464	285	9	zekry	zekry	PROPN
fumecheng-10464	285	10	the	the	DET
fumecheng-10464	285	11	problem	problem	NOUN
fumecheng-10464	285	12	has	have	AUX
fumecheng-10464	285	13	been	be	AUX
fumecheng-10464	285	14	complicated	complicate	VERB
fumecheng-10464	285	15	.	.	PUNCT
fumecheng-10464	286	1	the	the	DET
fumecheng-10464	286	2	results	result	NOUN
fumecheng-10464	286	3	obtained	obtain	VERB
fumecheng-10464	286	4	from	from	ADP
fumecheng-10464	286	5	this	this	DET
fumecheng-10464	286	6	approach	approach	NOUN
fumecheng-10464	286	7	have	have	AUX
fumecheng-10464	286	8	shown	show	VERB
fumecheng-10464	286	9	that	that	SCONJ
fumecheng-10464	286	10	there	there	PRON
fumecheng-10464	286	11	are	be	VERB
fumecheng-10464	286	12	disadvantages	disadvantage	NOUN
fumecheng-10464	286	13	of	of	ADP
fumecheng-10464	286	14	this	this	DET
fumecheng-10464	286	15	complexity	complexity	NOUN
fumecheng-10464	286	16	,	,	PUNCT
fumecheng-10464	286	17	which	which	PRON
fumecheng-10464	286	18	are	be	AUX
fumecheng-10464	286	19	far	far	ADV
fumecheng-10464	286	20	overbalanced	overbalance	VERB
fumecheng-10464	286	21	by	by	ADP
fumecheng-10464	286	22	more	more	ADJ
fumecheng-10464	286	23	compensations	compensation	NOUN
fumecheng-10464	286	24	.	.	PUNCT
fumecheng-10464	287	1	this	this	DET
fumecheng-10464	287	2	technique	technique	NOUN
fumecheng-10464	287	3	does	do	AUX
fumecheng-10464	287	4	not	not	PART
fumecheng-10464	287	5	only	only	ADV
fumecheng-10464	287	6	offer	offer	VERB
fumecheng-10464	287	7	a	a	DET
fumecheng-10464	287	8	uniform	uniform	ADJ
fumecheng-10464	287	9	expansion	expansion	NOUN
fumecheng-10464	287	10	,	,	PUNCT
fumecheng-10464	287	11	but	but	CCONJ
fumecheng-10464	287	12	it	it	PRON
fumecheng-10464	287	13	is	be	AUX
fumecheng-10464	287	14	also	also	ADV
fumecheng-10464	287	15	still	still	ADV
fumecheng-10464	287	16	valid	valid	ADJ
fumecheng-10464	287	17	to	to	PART
fumecheng-10464	287	18	be	be	AUX
fumecheng-10464	287	19	applied	apply	VERB
fumecheng-10464	287	20	to	to	ADP
fumecheng-10464	287	21	numerous	numerous	ADJ
fumecheng-10464	287	22	extremely	extremely	ADV
fumecheng-10464	287	23	nonlinear	nonlinear	ADJ
fumecheng-10464	287	24	problems	problem	NOUN
fumecheng-10464	287	25	in	in	ADP
fumecheng-10464	287	26	extensive	extensive	ADJ
fumecheng-10464	287	27	several	several	ADJ
fumecheng-10464	287	28	areas	area	NOUN
fumecheng-10464	287	29	of	of	ADP
fumecheng-10464	287	30	practical	practical	ADJ
fumecheng-10464	287	31	applications	application	NOUN
fumecheng-10464	287	32	and	and	CCONJ
fumecheng-10464	287	33	engineering	engineering	NOUN
fumecheng-10464	287	34	.	.	PUNCT
fumecheng-10464	288	1	now	now	ADV
fumecheng-10464	288	2	,	,	PUNCT
fumecheng-10464	288	3	one	one	PRON
fumecheng-10464	288	4	seeks	seek	VERB
fumecheng-10464	288	5	a	a	DET
fumecheng-10464	288	6	uniform	uniform	ADJ
fumecheng-10464	288	7	approximate	approximate	ADJ
fumecheng-10464	288	8	solution	solution	NOUN
fumecheng-10464	288	9	eq	eq	ADP
fumecheng-10464	288	10	.	.	PUNCT
fumecheng-10464	289	1	(	(	PUNCT
fumecheng-10464	289	2	2	2	NUM
fumecheng-10464	289	3	)	)	PUNCT
fumecheng-10464	289	4	in	in	ADP
fumecheng-10464	289	5	the	the	DET
fumecheng-10464	289	6	following	follow	VERB
fumecheng-10464	289	7	form	form	NOUN
fumecheng-10464	289	8	:	:	PUNCT
fumecheng-10464	289	9	)	)	PUNCT
fumecheng-10464	289	10	(	(	PUNCT
fumecheng-10464	289	11	)	)	PUNCT
fumecheng-10464	289	12	,	,	PUNCT
fumecheng-10464	289	13	(	(	PUNCT
fumecheng-10464	289	14	)	)	PUNCT
fumecheng-10464	289	15	,	,	PUNCT
fumecheng-10464	289	16	(	(	PUNCT
fumecheng-10464	289	17	)	)	PUNCT
fumecheng-10464	289	18	;	;	PUNCT
fumecheng-10464	289	19	(	(	PUNCT
fumecheng-10464	289	20	2	2	NUM
fumecheng-10464	289	21	101100	101100	NUM
fumecheng-10464	289	22			NOUN
fumecheng-10464	289	23	ottxttxtx	ottxttxtx	NOUN
fumecheng-10464	290	1	+	+	PROPN
fumecheng-10464	290	2	+	+	NOUN
fumecheng-10464	290	3	=	=	X
fumecheng-10464	290	4	(	(	PUNCT
fumecheng-10464	290	5	30	30	NUM
fumecheng-10464	290	6	)	)	PUNCT
fumecheng-10464	290	7	it	it	PRON
fumecheng-10464	290	8	should	should	AUX
fumecheng-10464	290	9	be	be	AUX
fumecheng-10464	290	10	noted	note	VERB
fumecheng-10464	290	11	that	that	SCONJ
fumecheng-10464	290	12	the	the	DET
fumecheng-10464	290	13	number	number	NOUN
fumecheng-10464	290	14	of	of	ADP
fumecheng-10464	290	15	the	the	DET
fumecheng-10464	290	16	independent	independent	ADJ
fumecheng-10464	290	17	time	time	NOUN
fumecheng-10464	290	18	scales	scale	NOUN
fumecheng-10464	290	19	generates	generate	VERB
fumecheng-10464	290	20	the	the	DET
fumecheng-10464	290	21	appropriate	appropriate	ADJ
fumecheng-10464	290	22	order	order	NOUN
fumecheng-10464	290	23	of	of	ADP
fumecheng-10464	290	24	expansion	expansion	NOUN
fumecheng-10464	290	25	.	.	PUNCT
fumecheng-10464	291	1	specifically	specifically	ADV
fumecheng-10464	291	2	,	,	PUNCT
fumecheng-10464	291	3	if	if	SCONJ
fumecheng-10464	291	4	the	the	DET
fumecheng-10464	291	5	expansion	expansion	NOUN
fumecheng-10464	291	6	is	be	AUX
fumecheng-10464	291	7	carried	carry	VERB
fumecheng-10464	291	8	out	out	ADP
fumecheng-10464	291	9	up	up	ADP
fumecheng-10464	291	10	to	to	ADP
fumecheng-10464	291	11	the	the	DET
fumecheng-10464	291	12	second	second	ADJ
fumecheng-10464	291	13	-	-	PUNCT
fumecheng-10464	291	14	order	order	NOUN
fumecheng-10464	291	15	,	,	PUNCT
fumecheng-10464	291	16	then	then	ADV
fumecheng-10464	291	17	only	only	ADV
fumecheng-10464	291	18	three	three	NUM
fumecheng-10464	291	19	scales	scale	NOUN
fumecheng-10464	291	20	t0	t0	NOUN
fumecheng-10464	291	21	,	,	PUNCT
fumecheng-10464	291	22	t1	t1	NOUN
fumecheng-10464	291	23	and	and	CCONJ
fumecheng-10464	291	24	t2	t2	NOUN
fumecheng-10464	291	25	are	be	AUX
fumecheng-10464	291	26	required	require	VERB
fumecheng-10464	291	27	.	.	PUNCT
fumecheng-10464	292	1	replacing	replace	VERB
fumecheng-10464	292	2	eq	eq	ADP
fumecheng-10464	292	3	.	.	PUNCT
fumecheng-10464	293	1	(	(	PUNCT
fumecheng-10464	293	2	30	30	NUM
fumecheng-10464	293	3	)	)	PUNCT
fumecheng-10464	293	4	as	as	ADV
fumecheng-10464	293	5	well	well	ADV
fumecheng-10464	293	6	as	as	ADP
fumecheng-10464	293	7	the	the	DET
fumecheng-10464	293	8	transformation	transformation	NOUN
fumecheng-10464	293	9	of	of	ADP
fumecheng-10464	293	10	the	the	DET
fumecheng-10464	293	11	derivatives	derivative	NOUN
fumecheng-10464	293	12	given	give	VERB
fumecheng-10464	293	13	below	below	ADV
fumecheng-10464	293	14	in	in	ADP
fumecheng-10464	293	15	the	the	DET
fumecheng-10464	293	16	homotopy	homotopy	NOUN
fumecheng-10464	293	17	equation	equation	NOUN
fumecheng-10464	293	18	eq	eq	ADJ
fumecheng-10464	293	19	.	.	PUNCT
fumecheng-10464	294	1	(	(	PUNCT
fumecheng-10464	294	2	5	5	NUM
fumecheng-10464	294	3	)	)	PUNCT
fumecheng-10464	294	4	,	,	PUNCT
fumecheng-10464	294	5	and	and	CCONJ
fumecheng-10464	294	6	then	then	ADV
fumecheng-10464	294	7	comparing	compare	VERB
fumecheng-10464	294	8	the	the	DET
fumecheng-10464	294	9	coefficient	coefficient	NOUN
fumecheng-10464	294	10	of	of	ADP
fumecheng-10464	294	11	like	like	ADP
fumecheng-10464	294	12	powers	power	NOUN
fumecheng-10464	294	13	ρ	ρ	NOUN
fumecheng-10464	294	14	,	,	PUNCT
fumecheng-10464	294	15	one	one	PRON
fumecheng-10464	294	16	finds	find	VERB
fumecheng-10464	294	17	the	the	DET
fumecheng-10464	294	18	following	follow	VERB
fumecheng-10464	294	19	equations	equation	NOUN
fumecheng-10464	294	20	:	:	PUNCT
fumecheng-10464	294	21	0	0	NUM
fumecheng-10464	294	22	2	2	NUM
fumecheng-10464	294	23	0	0	NUM
fumecheng-10464	294	24	0	0	NUM
fumecheng-10464	294	25	:	:	PUNCT
fumecheng-10464	294	26	(	(	PUNCT
fumecheng-10464	294	27	1	1	X
fumecheng-10464	294	28	)	)	PUNCT
fumecheng-10464	294	29	0d	0d	NOUN
fumecheng-10464	294	30	x	x	NOUN
fumecheng-10464	295	1	+	+	CCONJ
fumecheng-10464	295	2	=	=	SYM
fumecheng-10464	295	3	(	(	PUNCT
fumecheng-10464	295	4	31	31	NUM
fumecheng-10464	295	5	)	)	PUNCT
fumecheng-10464	295	6	and	and	CCONJ
fumecheng-10464	295	7	0	0	NUM
fumecheng-10464	295	8	02	02	NUM
fumecheng-10464	295	9	2	2	NUM
fumecheng-10464	295	10	3	3	NUM
fumecheng-10464	295	11	0	0	NUM
fumecheng-10464	295	12	1	1	NUM
fumecheng-10464	295	13	0	0	NUM
fumecheng-10464	295	14	1	1	NUM
fumecheng-10464	295	15	0	0	NUM
fumecheng-10464	295	16	0	0	NUM
fumecheng-10464	295	17	0	0	NUM
fumecheng-10464	295	18	0	0	NUM
fumecheng-10464	295	19	0	0	NUM
fumecheng-10464	295	20	:	:	PUNCT
fumecheng-10464	295	21	(	(	PUNCT
fumecheng-10464	295	22	1	1	X
fumecheng-10464	295	23	)	)	SYM
fumecheng-10464	295	24	2	2	NUM
fumecheng-10464	295	25	(	(	PUNCT
fumecheng-10464	295	26	1	1	NUM
fumecheng-10464	295	27	)	)	PUNCT
fumecheng-10464	295	28	(	(	PUNCT
fumecheng-10464	295	29	)	)	PUNCT
fumecheng-10464	295	30	2	2	NUM
fumecheng-10464	296	1	i	i	PRON
fumecheng-10464	296	2	t	t	VERB
fumecheng-10464	297	1	i	i	PRON
fumecheng-10464	297	2	tf	tf	INTJ
fumecheng-10464	298	1	d	d	NOUN
fumecheng-10464	298	2	x	x	PUNCT
fumecheng-10464	299	1	d	d	NOUN
fumecheng-10464	299	2	d	d	X
fumecheng-10464	299	3	x	x	X
fumecheng-10464	299	4	x	x	PUNCT
fumecheng-10464	299	5	d	d	NOUN
fumecheng-10464	299	6	x	x	SYM
fumecheng-10464	299	7	x	x	X
fumecheng-10464	299	8	e	e	PROPN
fumecheng-10464	299	9	e	e	PROPN
fumecheng-10464	299	10			NOUN
fumecheng-10464	299	11			PROPN
fumecheng-10464	299	12			PROPN
fumecheng-10464	299	13	−	−	PROPN
fumecheng-10464	299	14			PROPN
fumecheng-10464	300	1	+	+	CCONJ
fumecheng-10464	300	2	=	=	SYM
fumecheng-10464	300	3	−	−	PROPN
fumecheng-10464	300	4	−	−	NUM
fumecheng-10464	301	1	−	−	NOUN
fumecheng-10464	301	2	−	−	PROPN
fumecheng-10464	302	1	+	+	CCONJ
fumecheng-10464	302	2	+	+	CCONJ
fumecheng-10464	302	3	(	(	PUNCT
fumecheng-10464	302	4	32	32	NUM
fumecheng-10464	302	5	)	)	PUNCT
fumecheng-10464	303	1	where	where	SCONJ
fumecheng-10464	303	2	.......	.......	SYM
fumecheng-10464	303	3	2	2	NUM
fumecheng-10464	303	4	2	2	NUM
fumecheng-10464	303	5	10	10	NUM
fumecheng-10464	303	6	2	2	NUM
fumecheng-10464	303	7	2	2	NUM
fumecheng-10464	303	8	1	1	NUM
fumecheng-10464	303	9	1	1	NUM
fumecheng-10464	303	10	0	0	NUM
fumecheng-10464	303	11	0	0	NUM
fumecheng-10464	304	1	+	+	ADJ
fumecheng-10464	304	2	+	+	ADJ
fumecheng-10464	304	3	+	+	ADJ
fumecheng-10464	304	4	=	=	ADJ
fumecheng-10464	304	5	+	+	ADJ
fumecheng-10464	304	6			ADJ
fumecheng-10464	304	7			ADJ
fumecheng-10464	304	8	+	+	CCONJ
fumecheng-10464	304	9			ADJ
fumecheng-10464	304	10			ADJ
fumecheng-10464	304	11	+	+	CCONJ
fumecheng-10464	304	12			ADJ
fumecheng-10464	304	13			ADJ
fumecheng-10464	304	14			PROPN
fumecheng-10464	304	15	ddd	ddd	PROPN
fumecheng-10464	304	16	tdt	tdt	PROPN
fumecheng-10464	304	17	dt	dt	X
fumecheng-10464	304	18	tdt	tdt	PROPN
fumecheng-10464	304	19	dt	dt	X
fumecheng-10464	304	20	tdt	tdt	PROPN
fumecheng-10464	305	1	dt	dt	X
fumecheng-10464	305	2	dt	dt	X
fumecheng-10464	306	1	d	d	X
fumecheng-10464	306	2			NOUN
fumecheng-10464	306	3	and	and	CCONJ
fumecheng-10464	306	4	2	2	NUM
fumecheng-10464	306	5	2	2	NUM
fumecheng-10464	306	6	2	2	NUM
fumecheng-10464	306	7	2	2	NUM
fumecheng-10464	306	8	0	0	NUM
fumecheng-10464	306	9	0	0	NUM
fumecheng-10464	306	10	1	1	NUM
fumecheng-10464	306	11	1	1	NUM
fumecheng-10464	306	12	0	0	NUM
fumecheng-10464	306	13	22	22	NUM
fumecheng-10464	306	14	2	2	NUM
fumecheng-10464	306	15	(	(	PUNCT
fumecheng-10464	306	16	2	2	NUM
fumecheng-10464	306	17	)	)	PUNCT
fumecheng-10464	306	18	...	...	PUNCT
fumecheng-10464	306	19	,	,	PUNCT
fumecheng-10464	306	20	n	n	CCONJ
fumecheng-10464	306	21	n	n	NOUN
fumecheng-10464	307	1	d	d	NOUN
fumecheng-10464	307	2	d	d	PROPN
fumecheng-10464	307	3	d	d	PROPN
fumecheng-10464	307	4	d	d	PROPN
fumecheng-10464	307	5	d	d	PROPN
fumecheng-10464	307	6	d	d	PROPN
fumecheng-10464	307	7	d	d	X
fumecheng-10464	307	8	d	d	X
fumecheng-10464	307	9	tdt	tdt	PROPN
fumecheng-10464	307	10			ADV
fumecheng-10464	307	11			ADP
fumecheng-10464	307	12			ADJ
fumecheng-10464	307	13			PROPN
fumecheng-10464	307	14	+	+	PROPN
fumecheng-10464	307	15	+	+	PUNCT
fumecheng-10464	307	16	+	+	CCONJ
fumecheng-10464	307	17	+	+	CCONJ
fumecheng-10464	307	18			PROPN
fumecheng-10464	307	19			NOUN
fumecheng-10464	307	20	therefore	therefore	ADV
fumecheng-10464	307	21	,	,	PUNCT
fumecheng-10464	307	22	it	it	PRON
fumecheng-10464	307	23	is	be	AUX
fumecheng-10464	307	24	convenient	convenient	ADJ
fumecheng-10464	307	25	to	to	PART
fumecheng-10464	307	26	write	write	VERB
fumecheng-10464	307	27	the	the	DET
fumecheng-10464	307	28	solution	solution	NOUN
fumecheng-10464	307	29	of	of	ADP
fumecheng-10464	307	30	eq	eq	PROPN
fumecheng-10464	307	31	.	.	PUNCT
fumecheng-10464	308	1	(	(	PUNCT
fumecheng-10464	308	2	32	32	NUM
fumecheng-10464	308	3	)	)	PUNCT
fumecheng-10464	308	4	in	in	ADP
fumecheng-10464	308	5	the	the	DET
fumecheng-10464	308	6	following	follow	VERB
fumecheng-10464	308	7	form	form	NOUN
fumecheng-10464	308	8	:	:	PUNCT
fumecheng-10464	308	9	.	.	PUNCT
fumecheng-10464	308	10	,	,	PUNCT
fumecheng-10464	308	11	.	.	PUNCT
fumecheng-10464	308	12	)	)	PUNCT
fumecheng-10464	309	1	(	(	PUNCT
fumecheng-10464	309	2	)	)	PUNCT
fumecheng-10464	309	3	,	,	PUNCT
fumecheng-10464	309	4	(	(	PUNCT
fumecheng-10464	309	5	0	0	NUM
fumecheng-10464	309	6	1100	1100	NUM
fumecheng-10464	309	7	ccetattx	ccetattx	VERB
fumecheng-10464	309	8	it	it	PRON
fumecheng-10464	310	1	+	+	PROPN
fumecheng-10464	310	2	=	=	X
fumecheng-10464	310	3	(	(	PUNCT
fumecheng-10464	310	4	33	33	NUM
fumecheng-10464	310	5	)	)	PUNCT
fumecheng-10464	310	6	where	where	SCONJ
fumecheng-10464	310	7	a(t1	a(t1	NOUN
fumecheng-10464	310	8	)	)	PUNCT
fumecheng-10464	310	9	is	be	AUX
fumecheng-10464	310	10	an	an	DET
fumecheng-10464	310	11	unknown	unknown	ADJ
fumecheng-10464	310	12	complex	complex	ADJ
fumecheng-10464	310	13	function	function	NOUN
fumecheng-10464	310	14	of	of	ADP
fumecheng-10464	310	15	the	the	DET
fumecheng-10464	310	16	time	time	NOUN
fumecheng-10464	310	17	scale	scale	NOUN
fumecheng-10464	310	18	t1	t1	NOUN
fumecheng-10464	310	19	,	,	PUNCT
fumecheng-10464	310	20	and	and	CCONJ
fumecheng-10464	310	21	..	..	PUNCT
fumecheng-10464	310	22	cc	cc	PUNCT
fumecheng-10464	310	23	characterizes	characterize	VERB
fumecheng-10464	310	24	the	the	DET
fumecheng-10464	310	25	complex	complex	ADJ
fumecheng-10464	310	26	conjugate	conjugate	NOUN
fumecheng-10464	310	27	of	of	ADP
fumecheng-10464	310	28	the	the	DET
fumecheng-10464	310	29	foregoing	forego	VERB
fumecheng-10464	310	30	terms	term	NOUN
fumecheng-10464	310	31	.	.	PUNCT
fumecheng-10464	311	1	the	the	DET
fumecheng-10464	311	2	governing	govern	VERB
fumecheng-10464	311	3	equation	equation	NOUN
fumecheng-10464	311	4	of	of	ADP
fumecheng-10464	311	5	the	the	DET
fumecheng-10464	311	6	complex	complex	ADJ
fumecheng-10464	311	7	function	function	NOUN
fumecheng-10464	311	8	a(t1	a(t1	NOUN
fumecheng-10464	311	9	)	)	PUNCT
fumecheng-10464	311	10	is	be	AUX
fumecheng-10464	311	11	obtained	obtain	VERB
fumecheng-10464	311	12	in	in	ADP
fumecheng-10464	311	13	such	such	DET
fumecheng-10464	311	14	a	a	DET
fumecheng-10464	311	15	way	way	NOUN
fumecheng-10464	311	16	that	that	PRON
fumecheng-10464	311	17	the	the	DET
fumecheng-10464	311	18	time	time	NOUN
fumecheng-10464	311	19	-	-	PUNCT
fumecheng-10464	311	20	dependent	dependent	ADJ
fumecheng-10464	311	21	functions	function	NOUN
fumecheng-10464	311	22	x1	x1	PRON
fumecheng-10464	311	23	must	must	AUX
fumecheng-10464	311	24	be	be	AUX
fumecheng-10464	311	25	of	of	ADP
fumecheng-10464	311	26	an	an	DET
fumecheng-10464	311	27	oscillatory	oscillatory	ADJ
fumecheng-10464	311	28	nature	nature	NOUN
fumecheng-10464	311	29	.	.	PUNCT
fumecheng-10464	312	1	substituting	substitute	VERB
fumecheng-10464	312	2	eq	eq	ADP
fumecheng-10464	312	3	.	.	PUNCT
fumecheng-10464	313	1	(	(	PUNCT
fumecheng-10464	313	2	33	33	NUM
fumecheng-10464	313	3	)	)	PUNCT
fumecheng-10464	313	4	into	into	ADP
fumecheng-10464	313	5	eq	eq	NOUN
fumecheng-10464	313	6	.	.	PUNCT
fumecheng-10464	314	1	(	(	PUNCT
fumecheng-10464	314	2	32	32	NUM
fumecheng-10464	314	3	)	)	PUNCT
fumecheng-10464	314	4	,	,	PUNCT
fumecheng-10464	314	5	one	one	PRON
fumecheng-10464	314	6	finds	find	VERB
fumecheng-10464	314	7	0	0	NUM
fumecheng-10464	314	8	0	0	NUM
fumecheng-10464	314	9	032	032	NUM
fumecheng-10464	314	10	2	2	NUM
fumecheng-10464	314	11	3	3	NUM
fumecheng-10464	314	12	0	0	NUM
fumecheng-10464	314	13	1	1	NUM
fumecheng-10464	314	14	1	1	NUM
fumecheng-10464	314	15	1	1	NUM
fumecheng-10464	314	16	(	(	PUNCT
fumecheng-10464	314	17	1	1	NUM
fumecheng-10464	314	18	)	)	PUNCT
fumecheng-10464	314	19	(	(	PUNCT
fumecheng-10464	314	20	2	2	NUM
fumecheng-10464	314	21	(	(	PUNCT
fumecheng-10464	314	22	3	3	NUM
fumecheng-10464	314	23	)	)	PUNCT
fumecheng-10464	314	24	)	)	PUNCT
fumecheng-10464	315	1	(	(	PUNCT
fumecheng-10464	315	2	)	)	PUNCT
fumecheng-10464	315	3	.	.	PUNCT
fumecheng-10464	316	1	.	.	PUNCT
fumecheng-10464	317	1	,	,	PUNCT
fumecheng-10464	317	2	2	2	NUM
fumecheng-10464	317	3	it	it	PRON
fumecheng-10464	317	4	it	it	PRON
fumecheng-10464	318	1	i	i	INTJ
fumecheng-10464	318	2	t	t	X
fumecheng-10464	319	1	d	d	NOUN
fumecheng-10464	319	2	x	x	PUNCT
fumecheng-10464	319	3	i	i	PROPN
fumecheng-10464	319	4	d	d	PROPN
fumecheng-10464	319	5	a	a	X
fumecheng-10464	320	1	i	i	PRON
fumecheng-10464	320	2	a	a	PRON
fumecheng-10464	320	3	i	i	PRON
fumecheng-10464	321	1	a	a	DET
fumecheng-10464	321	2	a	a	X
fumecheng-10464	321	3	e	e	NOUN
fumecheng-10464	321	4	i	i	PRON
fumecheng-10464	321	5	a	a	DET
fumecheng-10464	321	6	e	e	X
fumecheng-10464	321	7	fe	fe	X
fumecheng-10464	321	8	c	c	NOUN
fumecheng-10464	321	9	c	c	NUM
fumecheng-10464	321	10			NOUN
fumecheng-10464	321	11			NOUN
fumecheng-10464	321	12			NOUN
fumecheng-10464	321	13			NOUN
fumecheng-10464	321	14			PROPN
fumecheng-10464	322	1	+	+	CCONJ
fumecheng-10464	322	2	=	=	SYM
fumecheng-10464	323	1	−	−	PROPN
fumecheng-10464	324	1	+	+	CCONJ
fumecheng-10464	324	2	−	−	PROPN
fumecheng-10464	325	1	+	+	CCONJ
fumecheng-10464	325	2	−	−	PROPN
fumecheng-10464	326	1	+	+	CCONJ
fumecheng-10464	326	2	+	+	PUNCT
fumecheng-10464	326	3	+	+	CCONJ
fumecheng-10464	326	4	(	(	PUNCT
fumecheng-10464	326	5	34	34	NUM
fumecheng-10464	326	6	)	)	PUNCT
fumecheng-10464	326	7	where	where	SCONJ
fumecheng-10464	326	8	the	the	DET
fumecheng-10464	326	9	function	function	NOUN
fumecheng-10464	326	10	ā	ā	NOUN
fumecheng-10464	326	11	represents	represent	VERB
fumecheng-10464	326	12	the	the	DET
fumecheng-10464	326	13	complex	complex	ADJ
fumecheng-10464	326	14	conjugate	conjugate	NOUN
fumecheng-10464	326	15	of	of	ADP
fumecheng-10464	326	16	the	the	DET
fumecheng-10464	326	17	function	function	NOUN
fumecheng-10464	326	18	a.	a.	NOUN
fumecheng-10464	326	19	the	the	DET
fumecheng-10464	326	20	uniform	uniform	ADJ
fumecheng-10464	326	21	valid	valid	ADJ
fumecheng-10464	326	22	expansion	expansion	NOUN
fumecheng-10464	326	23	of	of	ADP
fumecheng-10464	326	24	the	the	DET
fumecheng-10464	326	25	function	function	NOUN
fumecheng-10464	326	26	x1	x1	PROPN
fumecheng-10464	326	27	requires	require	VERB
fumecheng-10464	326	28	a	a	DET
fumecheng-10464	326	29	cancellation	cancellation	NOUN
fumecheng-10464	326	30	of	of	ADP
fumecheng-10464	326	31	the	the	DET
fumecheng-10464	326	32	secular	secular	ADJ
fumecheng-10464	326	33	term	term	NOUN
fumecheng-10464	326	34	.	.	PUNCT
fumecheng-10464	327	1	accordingly	accordingly	ADV
fumecheng-10464	327	2	,	,	PUNCT
fumecheng-10464	327	3	in	in	ADP
fumecheng-10464	327	4	order	order	NOUN
fumecheng-10464	327	5	to	to	PART
fumecheng-10464	327	6	attain	attain	VERB
fumecheng-10464	327	7	a	a	DET
fumecheng-10464	327	8	uniform	uniform	ADJ
fumecheng-10464	327	9	valid	valid	ADJ
fumecheng-10464	327	10	expansion	expansion	NOUN
fumecheng-10464	327	11	,	,	PUNCT
fumecheng-10464	327	12	the	the	DET
fumecheng-10464	327	13	secular	secular	ADJ
fumecheng-10464	327	14	terms	term	NOUN
fumecheng-10464	327	15	must	must	AUX
fumecheng-10464	327	16	be	be	AUX
fumecheng-10464	327	17	omitted	omit	VERB
fumecheng-10464	327	18	.	.	PUNCT
fumecheng-10464	328	1	the	the	DET
fumecheng-10464	328	2	invalidation	invalidation	NOUN
fumecheng-10464	328	3	of	of	ADP
fumecheng-10464	328	4	these	these	DET
fumecheng-10464	328	5	secular	secular	ADJ
fumecheng-10464	328	6	terms	term	NOUN
fumecheng-10464	328	7	arises	arise	VERB
fumecheng-10464	328	8	from	from	ADP
fumecheng-10464	328	9	the	the	DET
fumecheng-10464	328	10	coefficients	coefficient	NOUN
fumecheng-10464	328	11	of	of	ADP
fumecheng-10464	328	12	the	the	DET
fumecheng-10464	328	13	exponentials	exponential	NOUN
fumecheng-10464	328	14	exp(±it0	exp(±it0	PROPN
fumecheng-10464	328	15	)	)	PUNCT
fumecheng-10464	328	16	.	.	PUNCT
fumecheng-10464	329	1	therefore	therefore	ADV
fumecheng-10464	329	2	,	,	PUNCT
fumecheng-10464	329	3	the	the	DET
fumecheng-10464	329	4	uniform	uniform	ADJ
fumecheng-10464	329	5	valid	valid	ADJ
fumecheng-10464	329	6	expansion	expansion	NOUN
fumecheng-10464	329	7	requires	require	VERB
fumecheng-10464	329	8	0)3(2	0)3(2	NUM
fumecheng-10464	329	9	2	2	NUM
fumecheng-10464	329	10	1	1	NUM
fumecheng-10464	329	11	=	=	SYM
fumecheng-10464	329	12	+	+	NOUN
fumecheng-10464	329	13	−+−	−+−	ADJ
fumecheng-10464	329	14	aaiaiaid	aaiaiaid	VERB
fumecheng-10464	329	15			PROPN
fumecheng-10464	329	16	(	(	PUNCT
fumecheng-10464	329	17	35	35	NUM
fumecheng-10464	329	18	)	)	PUNCT
fumecheng-10464	329	19	forced	force	VERB
fumecheng-10464	329	20	nonlinear	nonlinear	ADJ
fumecheng-10464	329	21	oscillator	oscillator	NOUN
fumecheng-10464	329	22	in	in	ADP
fumecheng-10464	329	23	a	a	DET
fumecheng-10464	329	24	fractal	fractal	ADJ
fumecheng-10464	329	25	space	space	NOUN
fumecheng-10464	329	26	13	13	NUM
fumecheng-10464	329	27	eq	eq	NOUN
fumecheng-10464	329	28	.	.	PUNCT
fumecheng-10464	330	1	(	(	PUNCT
fumecheng-10464	330	2	35	35	NUM
fumecheng-10464	330	3	)	)	PUNCT
fumecheng-10464	330	4	is	be	AUX
fumecheng-10464	330	5	a	a	DET
fumecheng-10464	330	6	nonlinear	nonlinear	ADJ
fumecheng-10464	330	7	first	first	ADJ
fumecheng-10464	330	8	-	-	PUNCT
fumecheng-10464	330	9	order	order	NOUN
fumecheng-10464	330	10	differential	differential	ADJ
fumecheng-10464	330	11	equation	equation	NOUN
fumecheng-10464	330	12	with	with	ADP
fumecheng-10464	330	13	complex	complex	ADJ
fumecheng-10464	330	14	coefficients	coefficient	NOUN
fumecheng-10464	330	15	.	.	PUNCT
fumecheng-10464	331	1	it	it	PRON
fumecheng-10464	331	2	is	be	AUX
fumecheng-10464	331	3	known	know	VERB
fumecheng-10464	331	4	as	as	ADP
fumecheng-10464	331	5	the	the	DET
fumecheng-10464	331	6	amplitude	amplitude	NOUN
fumecheng-10464	331	7	equation	equation	NOUN
fumecheng-10464	331	8	.	.	PUNCT
fumecheng-10464	332	1	occasionally	occasionally	ADV
fumecheng-10464	332	2	,	,	PUNCT
fumecheng-10464	332	3	it	it	PRON
fumecheng-10464	332	4	is	be	AUX
fumecheng-10464	332	5	called	call	VERB
fumecheng-10464	332	6	the	the	DET
fumecheng-10464	332	7	solvability	solvability	NOUN
fumecheng-10464	332	8	condition	condition	NOUN
fumecheng-10464	332	9	.	.	PUNCT
fumecheng-10464	333	1	it	it	PRON
fumecheng-10464	333	2	follows	follow	VERB
fumecheng-10464	333	3	that	that	SCONJ
fumecheng-10464	333	4	uniform	uniform	ADJ
fumecheng-10464	333	5	solution	solution	NOUN
fumecheng-10464	333	6	of	of	ADP
fumecheng-10464	333	7	the	the	DET
fumecheng-10464	333	8	particular	particular	ADJ
fumecheng-10464	333	9	solution	solution	NOUN
fumecheng-10464	333	10	of	of	ADP
fumecheng-10464	333	11	eq	eq	PROPN
fumecheng-10464	333	12	.	.	PUNCT
fumecheng-10464	334	1	(	(	PUNCT
fumecheng-10464	334	2	34	34	NUM
fumecheng-10464	334	3	)	)	PUNCT
fumecheng-10464	334	4	may	may	AUX
fumecheng-10464	334	5	be	be	AUX
fumecheng-10464	334	6	formulated	formulate	VERB
fumecheng-10464	334	7	as	as	ADP
fumecheng-10464	334	8	..	..	PUNCT
fumecheng-10464	334	9	)	)	PUNCT
fumecheng-10464	335	1	1(2	1(2	NUM
fumecheng-10464	335	2	1	1	NUM
fumecheng-10464	335	3	)	)	PUNCT
fumecheng-10464	335	4	(	(	PUNCT
fumecheng-10464	335	5	8	8	NUM
fumecheng-10464	335	6	1	1	NUM
fumecheng-10464	335	7	)	)	PUNCT
fumecheng-10464	335	8	,	,	PUNCT
fumecheng-10464	335	9	(	(	PUNCT
fumecheng-10464	335	10	00	00	NUM
fumecheng-10464	335	11	2	2	NUM
fumecheng-10464	335	12	33	33	NUM
fumecheng-10464	335	13	101	101	NUM
fumecheng-10464	335	14	ccfeeaittx	ccfeeaittx	ADJ
fumecheng-10464	335	15	tiit	tiit	NOUN
fumecheng-10464	335	16	+	+	CCONJ
fumecheng-10464	335	17	−	−	NOUN
fumecheng-10464	335	18	+	+	PROPN
fumecheng-10464	335	19	+	+	NOUN
fumecheng-10464	335	20	=	=	SYM
fumecheng-10464	335	21			ADJ
fumecheng-10464	335	22	(	(	PUNCT
fumecheng-10464	335	23	36	36	NUM
fumecheng-10464	335	24	)	)	PUNCT
fumecheng-10464	335	25	4.1	4.1	NUM
fumecheng-10464	335	26	.	.	PUNCT
fumecheng-10464	336	1	stability	stability	NOUN
fumecheng-10464	336	2	analysis	analysis	NOUN
fumecheng-10464	336	3	in	in	ADP
fumecheng-10464	336	4	the	the	DET
fumecheng-10464	336	5	non	non	ADJ
fumecheng-10464	336	6	-	-	ADJ
fumecheng-10464	336	7	resonance	resonance	ADJ
fumecheng-10464	336	8	case	case	NOUN
fumecheng-10464	336	9	to	to	PART
fumecheng-10464	336	10	complete	complete	VERB
fumecheng-10464	336	11	the	the	DET
fumecheng-10464	336	12	stability	stability	NOUN
fumecheng-10464	336	13	profile	profile	NOUN
fumecheng-10464	336	14	,	,	PUNCT
fumecheng-10464	336	15	along	along	ADP
fumecheng-10464	336	16	with	with	ADP
fumecheng-10464	336	17	the	the	DET
fumecheng-10464	336	18	non	non	ADJ
fumecheng-10464	336	19	-	-	ADJ
fumecheng-10464	336	20	resonance	resonance	NOUN
fumecheng-10464	336	21	case	case	NOUN
fumecheng-10464	336	22	,	,	PUNCT
fumecheng-10464	336	23	one	one	PRON
fumecheng-10464	336	24	goes	go	VERB
fumecheng-10464	336	25	back	back	ADV
fumecheng-10464	336	26	to	to	ADP
fumecheng-10464	336	27	the	the	DET
fumecheng-10464	336	28	amplitude	amplitude	NOUN
fumecheng-10464	336	29	eq	eq	NOUN
fumecheng-10464	336	30	.	.	PUNCT
fumecheng-10464	337	1	(	(	PUNCT
fumecheng-10464	337	2	35	35	NUM
fumecheng-10464	337	3	)	)	PUNCT
fumecheng-10464	337	4	.	.	PUNCT
fumecheng-10464	338	1	essentially	essentially	ADV
fumecheng-10464	338	2	,	,	PUNCT
fumecheng-10464	338	3	this	this	DET
fumecheng-10464	338	4	equation	equation	NOUN
fumecheng-10464	338	5	might	might	AUX
fumecheng-10464	338	6	be	be	AUX
fumecheng-10464	338	7	utilized	utilize	VERB
fumecheng-10464	338	8	to	to	PART
fumecheng-10464	338	9	regulate	regulate	VERB
fumecheng-10464	338	10	the	the	DET
fumecheng-10464	338	11	indefinite	indefinite	ADJ
fumecheng-10464	338	12	function	function	NOUN
fumecheng-10464	338	13	a	a	PRON
fumecheng-10464	338	14	in	in	ADP
fumecheng-10464	338	15	terms	term	NOUN
fumecheng-10464	338	16	of	of	ADP
fumecheng-10464	338	17	the	the	DET
fumecheng-10464	338	18	time	time	NOUN
fumecheng-10464	338	19	-	-	PUNCT
fumecheng-10464	338	20	independent	independent	ADJ
fumecheng-10464	338	21	variable	variable	ADJ
fumecheng-10464	338	22	t1	t1	NOUN
fumecheng-10464	338	23	.	.	PUNCT
fumecheng-10464	339	1	additionally	additionally	ADV
fumecheng-10464	339	2	,	,	PUNCT
fumecheng-10464	339	3	the	the	DET
fumecheng-10464	339	4	stability	stability	NOUN
fumecheng-10464	339	5	presentation	presentation	NOUN
fumecheng-10464	339	6	is	be	AUX
fumecheng-10464	339	7	contingent	contingent	ADJ
fumecheng-10464	339	8	principally	principally	ADV
fumecheng-10464	339	9	on	on	ADP
fumecheng-10464	339	10	the	the	DET
fumecheng-10464	339	11	nature	nature	NOUN
fumecheng-10464	339	12	of	of	ADP
fumecheng-10464	339	13	this	this	DET
fumecheng-10464	339	14	function	function	NOUN
fumecheng-10464	339	15	.	.	PUNCT
fumecheng-10464	340	1	for	for	ADP
fumecheng-10464	340	2	this	this	DET
fumecheng-10464	340	3	determination	determination	NOUN
fumecheng-10464	340	4	,	,	PUNCT
fumecheng-10464	340	5	one	one	PRON
fumecheng-10464	340	6	may	may	AUX
fumecheng-10464	340	7	apply	apply	VERB
fumecheng-10464	340	8	the	the	DET
fumecheng-10464	340	9	polar	polar	ADJ
fumecheng-10464	340	10	form	form	NOUN
fumecheng-10464	340	11	solution	solution	NOUN
fumecheng-10464	340	12	as	as	ADP
fumecheng-10464	340	13	:	:	PUNCT
fumecheng-10464	340	14	)	)	PUNCT
fumecheng-10464	340	15	(	(	PUNCT
fumecheng-10464	340	16	11	11	NUM
fumecheng-10464	340	17	1	1	NUM
fumecheng-10464	340	18	)	)	PUNCT
fumecheng-10464	340	19	(	(	PUNCT
fumecheng-10464	340	20	2	2	NUM
fumecheng-10464	340	21	1	1	NUM
fumecheng-10464	340	22	)	)	PUNCT
fumecheng-10464	340	23	(	(	PUNCT
fumecheng-10464	340	24	ti	ti	X
fumecheng-10464	340	25	etta	etta	PROPN
fumecheng-10464	340	26	=	=	PROPN
fumecheng-10464	340	27	(	(	PUNCT
fumecheng-10464	340	28	37	37	NUM
fumecheng-10464	340	29	)	)	PUNCT
fumecheng-10464	340	30	where	where	SCONJ
fumecheng-10464	340	31	the	the	DET
fumecheng-10464	340	32	functions	function	NOUN
fumecheng-10464	340	33	ζ	ζ	X
fumecheng-10464	340	34	(	(	PUNCT
fumecheng-10464	340	35	t1	t1	NOUN
fumecheng-10464	340	36	)	)	PUNCT
fumecheng-10464	340	37	and	and	CCONJ
fumecheng-10464	340	38	𝛾(t1	𝛾(t1	NOUN
fumecheng-10464	340	39	)	)	PUNCT
fumecheng-10464	340	40	are	be	AUX
fumecheng-10464	340	41	two	two	NUM
fumecheng-10464	340	42	real	real	ADJ
fumecheng-10464	340	43	functions	function	NOUN
fumecheng-10464	340	44	on	on	ADP
fumecheng-10464	340	45	the	the	DET
fumecheng-10464	340	46	time	time	NOUN
fumecheng-10464	340	47	scale	scale	NOUN
fumecheng-10464	340	48	1	1	NUM
fumecheng-10464	340	49	t	t	NOUN
fumecheng-10464	340	50	.	.	PUNCT
fumecheng-10464	341	1	substituting	substitute	VERB
fumecheng-10464	341	2	eq	eq	ADP
fumecheng-10464	341	3	.	.	PUNCT
fumecheng-10464	342	1	(	(	PUNCT
fumecheng-10464	342	2	37	37	NUM
fumecheng-10464	342	3	)	)	PUNCT
fumecheng-10464	342	4	into	into	ADP
fumecheng-10464	342	5	eq	eq	NOUN
fumecheng-10464	342	6	.	.	PUNCT
fumecheng-10464	343	1	(	(	PUNCT
fumecheng-10464	343	2	35	35	NUM
fumecheng-10464	343	3	)	)	PUNCT
fumecheng-10464	343	4	,	,	PUNCT
fumecheng-10464	343	5	and	and	CCONJ
fumecheng-10464	343	6	then	then	ADV
fumecheng-10464	343	7	associating	associate	VERB
fumecheng-10464	343	8	the	the	DET
fumecheng-10464	343	9	real	real	ADJ
fumecheng-10464	343	10	and	and	CCONJ
fumecheng-10464	343	11	imaginary	imaginary	ADJ
fumecheng-10464	343	12	parts	part	NOUN
fumecheng-10464	343	13	on	on	ADP
fumecheng-10464	343	14	the	the	DET
fumecheng-10464	343	15	two	two	NUM
fumecheng-10464	343	16	sides	side	NOUN
fumecheng-10464	343	17	,	,	PUNCT
fumecheng-10464	343	18	one	one	PRON
fumecheng-10464	343	19	gets	get	VERB
fumecheng-10464	343	20	the	the	DET
fumecheng-10464	343	21	following	follow	VERB
fumecheng-10464	343	22	differential	differential	ADJ
fumecheng-10464	343	23	equations	equation	NOUN
fumecheng-10464	343	24	:	:	PUNCT
fumecheng-10464	343	25	3	3	NUM
fumecheng-10464	343	26	1	1	NUM
fumecheng-10464	343	27	82	82	NUM
fumecheng-10464	343	28			NOUN
fumecheng-10464	343	29			NOUN
fumecheng-10464	343	30			X
fumecheng-10464	344	1			PROPN
fumecheng-10464	344	2	−=	−=	NOUN
fumecheng-10464	344	3	dt	dt	PROPN
fumecheng-10464	345	1	d	d	X
fumecheng-10464	345	2	(	(	PUNCT
fumecheng-10464	345	3	38	38	NUM
fumecheng-10464	345	4	)	)	PUNCT
fumecheng-10464	345	5	and	and	CCONJ
fumecheng-10464	345	6	2	2	NUM
fumecheng-10464	345	7	1	1	NUM
fumecheng-10464	345	8	8	8	NUM
fumecheng-10464	345	9	3	3	NUM
fumecheng-10464	345	10			NOUN
fumecheng-10464	345	11			PUNCT
fumecheng-10464	345	12	=	=	PUNCT
fumecheng-10464	345	13	dt	dt	X
fumecheng-10464	345	14	d	d	X
fumecheng-10464	345	15	(	(	PUNCT
fumecheng-10464	345	16	39	39	NUM
fumecheng-10464	345	17	)	)	PUNCT
fumecheng-10464	345	18	eqs	eqs	PROPN
fumecheng-10464	345	19	.	.	PUNCT
fumecheng-10464	345	20	(	(	PUNCT
fumecheng-10464	345	21	38	38	NUM
fumecheng-10464	345	22	)	)	PUNCT
fumecheng-10464	345	23	and	and	CCONJ
fumecheng-10464	345	24	(	(	PUNCT
fumecheng-10464	345	25	39	39	NUM
fumecheng-10464	345	26	)	)	PUNCT
fumecheng-10464	345	27	are	be	AUX
fumecheng-10464	345	28	coupled	couple	VERB
fumecheng-10464	345	29	first	first	ADJ
fumecheng-10464	345	30	-	-	PUNCT
fumecheng-10464	345	31	order	order	NOUN
fumecheng-10464	345	32	differential	differential	ADJ
fumecheng-10464	345	33	equations	equation	NOUN
fumecheng-10464	345	34	with	with	ADP
fumecheng-10464	345	35	real	real	ADJ
fumecheng-10464	345	36	coefficients	coefficient	NOUN
fumecheng-10464	345	37	.	.	PUNCT
fumecheng-10464	346	1	as	as	ADP
fumecheng-10464	346	2	ρ→1	ρ→1	X
fumecheng-10464	346	3	,	,	PUNCT
fumecheng-10464	346	4	the	the	DET
fumecheng-10464	346	5	parameter	parameter	NOUN
fumecheng-10464	346	6	t1	t1	PROPN
fumecheng-10464	346	7	will	will	AUX
fumecheng-10464	346	8	be	be	AUX
fumecheng-10464	346	9	transformed	transform	VERB
fumecheng-10464	346	10	into	into	ADP
fumecheng-10464	346	11	t.	t.	PROPN
fumecheng-10464	346	12	certainly	certainly	ADV
fumecheng-10464	346	13	,	,	PUNCT
fumecheng-10464	346	14	the	the	DET
fumecheng-10464	346	15	stability	stability	NOUN
fumecheng-10464	346	16	conditions	condition	NOUN
fumecheng-10464	346	17	need	need	VERB
fumecheng-10464	346	18	that	that	SCONJ
fumecheng-10464	346	19	both	both	PRON
fumecheng-10464	346	20	of	of	ADP
fumecheng-10464	346	21	the	the	DET
fumecheng-10464	346	22	functions	function	NOUN
fumecheng-10464	346	23	ζ(t	ζ(t	VERB
fumecheng-10464	346	24	)	)	PUNCT
fumecheng-10464	346	25	and	and	CCONJ
fumecheng-10464	346	26	𝛾(t	𝛾(t	NOUN
fumecheng-10464	346	27	)	)	PUNCT
fumecheng-10464	346	28	become	become	VERB
fumecheng-10464	346	29	bounded	bounded	ADJ
fumecheng-10464	346	30	functions	function	NOUN
fumecheng-10464	346	31	.	.	PUNCT
fumecheng-10464	347	1	for	for	ADP
fumecheng-10464	347	2	straightforwardness	straightforwardness	NOUN
fumecheng-10464	347	3	,	,	PUNCT
fumecheng-10464	347	4	these	these	DET
fumecheng-10464	347	5	equations	equation	NOUN
fumecheng-10464	347	6	may	may	AUX
fumecheng-10464	347	7	be	be	AUX
fumecheng-10464	347	8	solved	solve	VERB
fumecheng-10464	347	9	by	by	ADP
fumecheng-10464	347	10	using	use	VERB
fumecheng-10464	347	11	a	a	DET
fumecheng-10464	347	12	perturbation	perturbation	NOUN
fumecheng-10464	347	13	approach	approach	NOUN
fumecheng-10464	347	14	as	as	SCONJ
fumecheng-10464	347	15	follows	follow	VERB
fumecheng-10464	347	16	:	:	PUNCT
fumecheng-10464	347	17	consider	consider	VERB
fumecheng-10464	347	18	that	that	SCONJ
fumecheng-10464	347	19	the	the	DET
fumecheng-10464	347	20	function	function	NOUN
fumecheng-10464	347	21	ζ	ζ	NOUN
fumecheng-10464	347	22	(	(	PUNCT
fumecheng-10464	347	23	t	t	NOUN
fumecheng-10464	347	24	)	)	PUNCT
fumecheng-10464	347	25	may	may	AUX
fumecheng-10464	347	26	be	be	AUX
fumecheng-10464	347	27	perturbed	perturb	VERB
fumecheng-10464	347	28	around	around	ADP
fumecheng-10464	347	29	a	a	DET
fumecheng-10464	347	30	steady	steady	ADJ
fumecheng-10464	347	31	-	-	PUNCT
fumecheng-10464	347	32	state	state	NOUN
fumecheng-10464	347	33	response	response	NOUN
fumecheng-10464	347	34	as	as	ADP
fumecheng-10464	347	35	:	:	PUNCT
fumecheng-10464	347	36	ζ	ζ	NOUN
fumecheng-10464	347	37	(	(	PUNCT
fumecheng-10464	347	38	t)=	t)=	NOUN
fumecheng-10464	347	39	ζ	ζ	NOUN
fumecheng-10464	347	40	0	0	NUM
fumecheng-10464	347	41	+	+	NUM
fumecheng-10464	347	42	ζ	ζ	NOUN
fumecheng-10464	347	43	1(t	1(t	NUM
fumecheng-10464	347	44	)	)	PUNCT
fumecheng-10464	347	45	.	.	PUNCT
fumecheng-10464	348	1	in	in	ADP
fumecheng-10464	348	2	this	this	DET
fumecheng-10464	348	3	case	case	NOUN
fumecheng-10464	348	4	,	,	PUNCT
fumecheng-10464	348	5	the	the	DET
fumecheng-10464	348	6	zero	zero	NUM
fumecheng-10464	348	7	-	-	PUNCT
fumecheng-10464	348	8	order	order	NOUN
fumecheng-10464	348	9	solution	solution	NOUN
fumecheng-10464	348	10	yields	yield	VERB
fumecheng-10464	348	11	20	20	NUM
fumecheng-10464	348	12	=	=	NUM
fumecheng-10464	348	13			X
fumecheng-10464	348	14	(	(	PUNCT
fumecheng-10464	348	15	40	40	NUM
fumecheng-10464	348	16	)	)	PUNCT
fumecheng-10464	348	17	it	it	PRON
fumecheng-10464	348	18	follows	follow	VERB
fumecheng-10464	348	19	that	that	SCONJ
fumecheng-10464	348	20	the	the	DET
fumecheng-10464	348	21	first	first	ADJ
fumecheng-10464	348	22	-	-	PUNCT
fumecheng-10464	348	23	order	order	NOUN
fumecheng-10464	348	24	solution	solution	NOUN
fumecheng-10464	348	25	becomes	become	VERB
fumecheng-10464	348	26	tet	tet	NOUN
fumecheng-10464	348	27			PROPN
fumecheng-10464	348	28	−=)(1	−=)(1	NOUN
fumecheng-10464	348	29	(	(	PUNCT
fumecheng-10464	348	30	41	41	NUM
fumecheng-10464	348	31	)	)	PUNCT
fumecheng-10464	348	32	in	in	ADP
fumecheng-10464	348	33	order	order	NOUN
fumecheng-10464	348	34	to	to	PART
fumecheng-10464	348	35	obtain	obtain	VERB
fumecheng-10464	348	36	a	a	DET
fumecheng-10464	348	37	finite	finite	ADJ
fumecheng-10464	348	38	solution	solution	NOUN
fumecheng-10464	348	39	,	,	PUNCT
fumecheng-10464	348	40	the	the	DET
fumecheng-10464	348	41	coefficient	coefficient	NOUN
fumecheng-10464	348	42	of	of	ADP
fumecheng-10464	348	43	the	the	DET
fumecheng-10464	348	44	damped	damped	NOUN
fumecheng-10464	348	45	parameter	parameter	NOUN
fumecheng-10464	348	46	(	(	PUNCT
fumecheng-10464	348	47	µ	µ	NOUN
fumecheng-10464	348	48	)	)	PUNCT
fumecheng-10464	348	49	must	must	AUX
fumecheng-10464	348	50	be	be	AUX
fumecheng-10464	348	51	positive	positive	ADJ
fumecheng-10464	348	52	.	.	PUNCT
fumecheng-10464	349	1	combining	combine	VERB
fumecheng-10464	349	2	equations	equation	NOUN
fumecheng-10464	349	3	(	(	PUNCT
fumecheng-10464	349	4	40	40	NUM
fumecheng-10464	349	5	)	)	PUNCT
fumecheng-10464	349	6	,	,	PUNCT
fumecheng-10464	349	7	(	(	PUNCT
fumecheng-10464	349	8	41	41	NUM
fumecheng-10464	349	9	)	)	PUNCT
fumecheng-10464	349	10	and	and	CCONJ
fumecheng-10464	349	11	(	(	PUNCT
fumecheng-10464	349	12	39	39	NUM
fumecheng-10464	349	13	)	)	PUNCT
fumecheng-10464	349	14	,	,	PUNCT
fumecheng-10464	349	15	the	the	DET
fumecheng-10464	349	16	first	first	ADJ
fumecheng-10464	349	17	-	-	PUNCT
fumecheng-10464	349	18	order	order	NOUN
fumecheng-10464	349	19	solution	solution	NOUN
fumecheng-10464	349	20	of	of	ADP
fumecheng-10464	349	21	the	the	DET
fumecheng-10464	349	22	function	function	NOUN
fumecheng-10464	349	23	𝛾1(t	𝛾1(t	PART
fumecheng-10464	349	24	)	)	PUNCT
fumecheng-10464	349	25	may	may	AUX
fumecheng-10464	349	26	be	be	AUX
fumecheng-10464	349	27	written	write	VERB
fumecheng-10464	349	28	as	as	ADP
fumecheng-10464	349	29	:	:	PUNCT
fumecheng-10464	349	30	1	1	NUM
fumecheng-10464	349	31	3	3	NUM
fumecheng-10464	349	32	(	(	PUNCT
fumecheng-10464	349	33	)	)	PUNCT
fumecheng-10464	349	34	(	(	PUNCT
fumecheng-10464	349	35	1	1	NUM
fumecheng-10464	349	36	)	)	PUNCT
fumecheng-10464	349	37	,	,	PUNCT
fumecheng-10464	349	38	2	2	NUM
fumecheng-10464	349	39	tt	tt	PROPN
fumecheng-10464	349	40	e	e	PROPN
fumecheng-10464	349	41			PROPN
fumecheng-10464	349	42			PROPN
fumecheng-10464	349	43			NOUN
fumecheng-10464	349	44	−=	−=	NOUN
fumecheng-10464	349	45	−	−	PROPN
fumecheng-10464	349	46	(	(	PUNCT
fumecheng-10464	349	47	42	42	NUM
fumecheng-10464	349	48	)	)	PUNCT
fumecheng-10464	349	49	where	where	SCONJ
fumecheng-10464	349	50	the	the	DET
fumecheng-10464	349	51	initial	initial	ADJ
fumecheng-10464	349	52	condition	condition	NOUN
fumecheng-10464	349	53	:	:	PUNCT
fumecheng-10464	349	54	𝛾1(0)=0	𝛾1(0)=0	ADJ
fumecheng-10464	349	55	is	be	AUX
fumecheng-10464	349	56	used	use	VERB
fumecheng-10464	349	57	.	.	PUNCT
fumecheng-10464	350	1	14	14	NUM
fumecheng-10464	350	2	j.-h	j.-h	NOUN
fumecheng-10464	350	3	.	.	PUNCT
fumecheng-10464	351	1	he	he	PRON
fumecheng-10464	351	2	,	,	PUNCT
fumecheng-10464	351	3	g.	g.	PROPN
fumecheng-10464	351	4	m.	m.	PROPN
fumecheng-10464	351	5	moatimid	moatimid	PROPN
fumecheng-10464	351	6	,	,	PUNCT
fumecheng-10464	351	7	m.	m.	PROPN
fumecheng-10464	351	8	h.	h.	PROPN
fumecheng-10464	351	9	zekry	zekry	PROPN
fumecheng-10464	351	10	it	it	PRON
fumecheng-10464	351	11	is	be	AUX
fumecheng-10464	351	12	worthy	worthy	ADJ
fumecheng-10464	351	13	to	to	PART
fumecheng-10464	351	14	notice	notice	VERB
fumecheng-10464	351	15	that	that	SCONJ
fumecheng-10464	351	16	the	the	DET
fumecheng-10464	351	17	stability	stability	NOUN
fumecheng-10464	351	18	occurs	occur	VERB
fumecheng-10464	351	19	regardless	regardless	ADV
fumecheng-10464	351	20	of	of	ADP
fumecheng-10464	351	21	the	the	DET
fumecheng-10464	351	22	sign	sign	NOUN
fumecheng-10464	351	23	of	of	ADP
fumecheng-10464	351	24	the	the	DET
fumecheng-10464	351	25	parameter	parameter	NOUN
fumecheng-10464	351	26	β	β	NOUN
fumecheng-10464	351	27	,	,	PUNCT
fumecheng-10464	351	28	provided	provide	VERB
fumecheng-10464	351	29	that	that	SCONJ
fumecheng-10464	351	30	𝜇	𝜇	ADP
fumecheng-10464	351	31	>	>	X
fumecheng-10464	351	32	0	0	NUM
fumecheng-10464	351	33	.	.	PUNCT
fumecheng-10464	352	1	as	as	ADP
fumecheng-10464	352	2	a	a	DET
fumecheng-10464	352	3	final	final	ADJ
fumecheng-10464	352	4	result	result	NOUN
fumecheng-10464	352	5	in	in	ADP
fumecheng-10464	352	6	the	the	DET
fumecheng-10464	352	7	case	case	NOUN
fumecheng-10464	352	8	of	of	ADP
fumecheng-10464	352	9	non	non	ADJ
fumecheng-10464	352	10	-	-	ADJ
fumecheng-10464	352	11	resonant	resonant	ADJ
fumecheng-10464	352	12	,	,	PUNCT
fumecheng-10464	352	13	the	the	DET
fumecheng-10464	352	14	approximate	approximate	ADJ
fumecheng-10464	352	15	periodic	periodic	ADJ
fumecheng-10464	352	16	solution	solution	NOUN
fumecheng-10464	352	17	of	of	ADP
fumecheng-10464	352	18	the	the	DET
fumecheng-10464	352	19	dvdp	dvdp	ADJ
fumecheng-10464	352	20	given	give	VERB
fumecheng-10464	352	21	in	in	ADP
fumecheng-10464	352	22	eq	eq	ADP
fumecheng-10464	352	23	.	.	PUNCT
fumecheng-10464	353	1	(	(	PUNCT
fumecheng-10464	353	2	2	2	X
fumecheng-10464	353	3	)	)	PUNCT
fumecheng-10464	353	4	may	may	AUX
fumecheng-10464	353	5	be	be	AUX
fumecheng-10464	353	6	written	write	VERB
fumecheng-10464	353	7	as	as	SCONJ
fumecheng-10464	353	8	follows	follow	VERB
fumecheng-10464	353	9	:	:	PUNCT
fumecheng-10464	353	10	0	0	NUM
fumecheng-10464	353	11	1	1	NUM
fumecheng-10464	353	12	1	1	NUM
fumecheng-10464	353	13	(	(	PUNCT
fumecheng-10464	353	14	)	)	PUNCT
fumecheng-10464	353	15	lim	lim	PROPN
fumecheng-10464	353	16	(	(	PUNCT
fumecheng-10464	353	17	(	(	PUNCT
fumecheng-10464	353	18	)	)	PUNCT
fumecheng-10464	353	19	(	(	PUNCT
fumecheng-10464	353	20	)	)	PUNCT
fumecheng-10464	353	21	)	)	PUNCT
fumecheng-10464	354	1	x	x	SYM
fumecheng-10464	354	2	t	t	NOUN
fumecheng-10464	354	3	x	x	SYM
fumecheng-10464	354	4	t	t	PROPN
fumecheng-10464	354	5	x	x	PROPN
fumecheng-10464	354	6	t	t	PROPN
fumecheng-10464	354	7			X
fumecheng-10464	354	8			ADV
fumecheng-10464	354	9	→	→	PUNCT
fumecheng-10464	354	10	=	=	SYM
fumecheng-10464	355	1	+	+	PUNCT
fumecheng-10464	355	2	(	(	PUNCT
fumecheng-10464	355	3	43	43	NUM
fumecheng-10464	355	4	)	)	PUNCT
fumecheng-10464	355	5	where	where	SCONJ
fumecheng-10464	355	6	x0(t	x0(t	NUM
fumecheng-10464	355	7	)	)	PUNCT
fumecheng-10464	355	8	and	and	CCONJ
fumecheng-10464	355	9	x1(t	x1(t	X
fumecheng-10464	355	10	)	)	PUNCT
fumecheng-10464	355	11	are	be	AUX
fumecheng-10464	355	12	the	the	DET
fumecheng-10464	355	13	time	time	NOUN
fumecheng-10464	355	14	-	-	PUNCT
fumecheng-10464	355	15	dependent	dependent	ADJ
fumecheng-10464	355	16	functions	function	NOUN
fumecheng-10464	355	17	obtained	obtain	VERB
fumecheng-10464	355	18	from	from	ADP
fumecheng-10464	355	19	eqs	eqs	PROPN
fumecheng-10464	355	20	.	.	PUNCT
fumecheng-10464	356	1	(	(	PUNCT
fumecheng-10464	356	2	33	33	NUM
fumecheng-10464	356	3	)	)	PUNCT
fumecheng-10464	356	4	and	and	CCONJ
fumecheng-10464	356	5	(	(	PUNCT
fumecheng-10464	356	6	36	36	NUM
fumecheng-10464	356	7	)	)	PUNCT
fumecheng-10464	356	8	,	,	PUNCT
fumecheng-10464	356	9	respectively	respectively	ADV
fumecheng-10464	356	10	.	.	PUNCT
fumecheng-10464	357	1	because	because	SCONJ
fumecheng-10464	357	2	of	of	ADP
fumecheng-10464	357	3	the	the	DET
fumecheng-10464	357	4	presence	presence	NOUN
fumecheng-10464	357	5	of	of	ADP
fumecheng-10464	357	6	the	the	DET
fumecheng-10464	357	7	non	non	ADJ
fumecheng-10464	357	8	-	-	ADJ
fumecheng-10464	357	9	homogeneous	homogeneous	ADJ
fumecheng-10464	357	10	oscillatory	oscillatory	ADJ
fumecheng-10464	357	11	term	term	NOUN
fumecheng-10464	357	12	through	through	ADP
fumecheng-10464	357	13	the	the	DET
fumecheng-10464	357	14	nonresonance	nonresonance	NOUN
fumecheng-10464	357	15	case	case	NOUN
fumecheng-10464	357	16	,	,	PUNCT
fumecheng-10464	357	17	the	the	DET
fumecheng-10464	357	18	analysis	analysis	NOUN
fumecheng-10464	357	19	will	will	AUX
fumecheng-10464	357	20	examine	examine	VERB
fumecheng-10464	357	21	the	the	DET
fumecheng-10464	357	22	resonance	resonance	NOUN
fumecheng-10464	357	23	cases	case	NOUN
fumecheng-10464	357	24	.	.	PUNCT
fumecheng-10464	358	1	therefore	therefore	ADV
fumecheng-10464	358	2	,	,	PUNCT
fumecheng-10464	358	3	the	the	DET
fumecheng-10464	358	4	following	follow	VERB
fumecheng-10464	358	5	subsection	subsection	NOUN
fumecheng-10464	358	6	discusses	discuss	VERB
fumecheng-10464	358	7	the	the	DET
fumecheng-10464	358	8	resonance	resonance	NOUN
fumecheng-10464	358	9	case	case	NOUN
fumecheng-10464	358	10	.	.	PUNCT
fumecheng-10464	359	1	4.2	4.2	NUM
fumecheng-10464	359	2	.	.	PUNCT
fumecheng-10464	360	1	stability	stability	NOUN
fumecheng-10464	360	2	analysis	analysis	NOUN
fumecheng-10464	360	3	of	of	ADP
fumecheng-10464	360	4	the	the	DET
fumecheng-10464	360	5	resonance	resonance	NOUN
fumecheng-10464	360	6	case	case	NOUN
fumecheng-10464	360	7	as	as	SCONJ
fumecheng-10464	360	8	seen	see	VERB
fumecheng-10464	360	9	from	from	ADP
fumecheng-10464	360	10	the	the	DET
fumecheng-10464	360	11	previous	previous	ADJ
fumecheng-10464	360	12	subsection	subsection	NOUN
fumecheng-10464	360	13	,	,	PUNCT
fumecheng-10464	360	14	the	the	DET
fumecheng-10464	360	15	non	non	ADJ
fumecheng-10464	360	16	-	-	ADJ
fumecheng-10464	360	17	resonance	resonance	NOUN
fumecheng-10464	360	18	case	case	NOUN
fumecheng-10464	360	19	fails	fail	VERB
fumecheng-10464	360	20	to	to	PART
fumecheng-10464	360	21	contain	contain	VERB
fumecheng-10464	360	22	all	all	DET
fumecheng-10464	360	23	parameters	parameter	NOUN
fumecheng-10464	360	24	of	of	ADP
fumecheng-10464	360	25	the	the	DET
fumecheng-10464	360	26	problem	problem	NOUN
fumecheng-10464	360	27	at	at	ADP
fumecheng-10464	360	28	hand	hand	NOUN
fumecheng-10464	360	29	during	during	ADP
fumecheng-10464	360	30	the	the	DET
fumecheng-10464	360	31	stability	stability	NOUN
fumecheng-10464	360	32	criteria	criterion	NOUN
fumecheng-10464	360	33	.	.	PUNCT
fumecheng-10464	361	1	consequently	consequently	ADV
fumecheng-10464	361	2	,	,	PUNCT
fumecheng-10464	361	3	the	the	DET
fumecheng-10464	361	4	following	follow	VERB
fumecheng-10464	361	5	discussion	discussion	NOUN
fumecheng-10464	361	6	is	be	AUX
fumecheng-10464	361	7	devoted	devote	VERB
fumecheng-10464	361	8	to	to	ADP
fumecheng-10464	361	9	presenting	present	VERB
fumecheng-10464	361	10	resonance	resonance	NOUN
fumecheng-10464	361	11	cases	case	NOUN
fumecheng-10464	361	12	.	.	PUNCT
fumecheng-10464	362	1	typically	typically	ADV
fumecheng-10464	362	2	,	,	PUNCT
fumecheng-10464	362	3	only	only	ADV
fumecheng-10464	362	4	the	the	DET
fumecheng-10464	362	5	resonance	resonance	NOUN
fumecheng-10464	362	6	case	case	NOUN
fumecheng-10464	362	7	is	be	AUX
fumecheng-10464	362	8	obtained	obtain	VERB
fumecheng-10464	362	9	.	.	PUNCT
fumecheng-10464	363	1	this	this	DET
fumecheng-10464	363	2	case	case	NOUN
fumecheng-10464	363	3	is	be	AUX
fumecheng-10464	363	4	definitely	definitely	ADV
fumecheng-10464	363	5	harmonic	harmonic	ADJ
fumecheng-10464	363	6	resonance	resonance	NOUN
fumecheng-10464	363	7	.	.	PUNCT
fumecheng-10464	364	1	it	it	PRON
fumecheng-10464	364	2	is	be	AUX
fumecheng-10464	364	3	defined	define	VERB
fumecheng-10464	364	4	here	here	ADV
fumecheng-10464	364	5	as	as	ADP
fumecheng-10464	364	6	a	a	DET
fumecheng-10464	364	7	sharp	sharp	ADJ
fumecheng-10464	364	8	resonance	resonance	NOUN
fumecheng-10464	364	9	.	.	PUNCT
fumecheng-10464	365	1	this	this	DET
fumecheng-10464	365	2	benefit	benefit	NOUN
fumecheng-10464	365	3	helps	help	VERB
fumecheng-10464	365	4	in	in	ADP
fumecheng-10464	365	5	introducing	introduce	VERB
fumecheng-10464	365	6	extra	extra	ADJ
fumecheng-10464	365	7	secular	secular	ADJ
fumecheng-10464	365	8	terms	term	NOUN
fumecheng-10464	365	9	.	.	PUNCT
fumecheng-10464	366	1	accordingly	accordingly	ADV
fumecheng-10464	366	2	,	,	PUNCT
fumecheng-10464	366	3	one	one	PRON
fumecheng-10464	366	4	may	may	AUX
fumecheng-10464	366	5	write	write	VERB
fumecheng-10464	366	6	+=	+=	PROPN
fumecheng-10464	366	7	1	1	NUM
fumecheng-10464	366	8	(	(	PUNCT
fumecheng-10464	366	9	44	44	NUM
fumecheng-10464	366	10	)	)	PUNCT
fumecheng-10464	366	11	where	where	SCONJ
fumecheng-10464	366	12	𝛿	𝛿	NOUN
fumecheng-10464	366	13	is	be	AUX
fumecheng-10464	366	14	some	some	DET
fumecheng-10464	366	15	detuning	detune	VERB
fumecheng-10464	366	16	small	small	ADJ
fumecheng-10464	366	17	parameter	parameter	NOUN
fumecheng-10464	366	18	.	.	PUNCT
fumecheng-10464	367	1	it	it	PRON
fumecheng-10464	367	2	follows	follow	VERB
fumecheng-10464	367	3	that	that	SCONJ
fumecheng-10464	367	4	the	the	DET
fumecheng-10464	367	5	governing	govern	VERB
fumecheng-10464	367	6	equation	equation	NOUN
fumecheng-10464	367	7	x1	x1	PROPN
fumecheng-10464	367	8	has	have	VERB
fumecheng-10464	367	9	an	an	DET
fumecheng-10464	367	10	extra	extra	ADJ
fumecheng-10464	367	11	secular	secular	ADJ
fumecheng-10464	367	12	term	term	NOUN
fumecheng-10464	367	13	.	.	PUNCT
fumecheng-10464	368	1	inserting	insert	VERB
fumecheng-10464	368	2	eq	eq	ADP
fumecheng-10464	368	3	.	.	PUNCT
fumecheng-10464	369	1	(	(	PUNCT
fumecheng-10464	369	2	44	44	NUM
fumecheng-10464	369	3	)	)	PUNCT
fumecheng-10464	369	4	into	into	ADP
fumecheng-10464	369	5	eq	eq	NOUN
fumecheng-10464	369	6	.	.	PUNCT
fumecheng-10464	370	1	(	(	PUNCT
fumecheng-10464	370	2	34	34	NUM
fumecheng-10464	370	3	)	)	PUNCT
fumecheng-10464	370	4	,	,	PUNCT
fumecheng-10464	370	5	one	one	PRON
fumecheng-10464	370	6	gets	get	VERB
fumecheng-10464	370	7	0	0	NUM
fumecheng-10464	370	8	01	01	NUM
fumecheng-10464	370	9	32	32	NUM
fumecheng-10464	370	10	2	2	NUM
fumecheng-10464	370	11	3	3	NUM
fumecheng-10464	370	12	0	0	NUM
fumecheng-10464	370	13	1	1	NUM
fumecheng-10464	370	14	1	1	NUM
fumecheng-10464	370	15	1	1	NUM
fumecheng-10464	370	16	(	(	PUNCT
fumecheng-10464	370	17	1	1	NUM
fumecheng-10464	370	18	)	)	PUNCT
fumecheng-10464	370	19	(	(	PUNCT
fumecheng-10464	370	20	2	2	NUM
fumecheng-10464	370	21	(	(	PUNCT
fumecheng-10464	370	22	3	3	NUM
fumecheng-10464	370	23	)	)	PUNCT
fumecheng-10464	370	24	)	)	PUNCT
fumecheng-10464	371	1	(	(	PUNCT
fumecheng-10464	371	2	)	)	PUNCT
fumecheng-10464	371	3	.	.	PUNCT
fumecheng-10464	372	1	.	.	PUNCT
fumecheng-10464	373	1	,	,	PUNCT
fumecheng-10464	373	2	2	2	NUM
fumecheng-10464	373	3	it	it	PRON
fumecheng-10464	373	4	iti	iti	INTJ
fumecheng-10464	373	5	t	t	PROPN
fumecheng-10464	374	1	d	d	X
fumecheng-10464	374	2	x	x	PUNCT
fumecheng-10464	374	3	i	i	PROPN
fumecheng-10464	374	4	d	d	PROPN
fumecheng-10464	374	5	a	a	X
fumecheng-10464	375	1	i	i	PRON
fumecheng-10464	375	2	a	a	PRON
fumecheng-10464	375	3	i	i	PRON
fumecheng-10464	376	1	a	a	DET
fumecheng-10464	376	2	a	a	DET
fumecheng-10464	376	3	fe	fe	X
fumecheng-10464	376	4	e	e	NOUN
fumecheng-10464	376	5	i	i	PRON
fumecheng-10464	376	6	a	a	X
fumecheng-10464	376	7	e	e	X
fumecheng-10464	376	8	c	c	NOUN
fumecheng-10464	376	9	c	c	PROPN
fumecheng-10464	376	10			NOUN
fumecheng-10464	376	11			NOUN
fumecheng-10464	376	12			NOUN
fumecheng-10464	376	13			NOUN
fumecheng-10464	376	14	+	+	NOUN
fumecheng-10464	376	15	=	=	SYM
fumecheng-10464	377	1	−	−	PROPN
fumecheng-10464	378	1	+	+	CCONJ
fumecheng-10464	378	2	−	−	PROPN
fumecheng-10464	379	1	+	+	CCONJ
fumecheng-10464	380	1	+	+	CCONJ
fumecheng-10464	380	2	−	−	X
fumecheng-10464	381	1	+	+	CCONJ
fumecheng-10464	381	2	+	+	CCONJ
fumecheng-10464	381	3	(	(	PUNCT
fumecheng-10464	381	4	45	45	NUM
fumecheng-10464	381	5	)	)	PUNCT
fumecheng-10464	381	6	the	the	DET
fumecheng-10464	381	7	removal	removal	NOUN
fumecheng-10464	381	8	of	of	ADP
fumecheng-10464	381	9	the	the	DET
fumecheng-10464	381	10	secular	secular	ADJ
fumecheng-10464	381	11	term	term	NOUN
fumecheng-10464	381	12	from	from	ADP
fumecheng-10464	381	13	eq	eq	PROPN
fumecheng-10464	381	14	.	.	PUNCT
fumecheng-10464	382	1	(	(	PUNCT
fumecheng-10464	382	2	45	45	NUM
fumecheng-10464	382	3	)	)	PUNCT
fumecheng-10464	382	4	requires	require	VERB
fumecheng-10464	382	5	02/)3(2	02/)3(2	PROPN
fumecheng-10464	382	6	12	12	NUM
fumecheng-10464	382	7	1	1	NUM
fumecheng-10464	382	8	=	=	ADJ
fumecheng-10464	382	9	+	+	NOUN
fumecheng-10464	382	10	+	+	ADJ
fumecheng-10464	382	11	−+−	−+−	ADJ
fumecheng-10464	382	12	ti	ti	NOUN
fumecheng-10464	382	13	feaaiaiaid	feaaiaiaid	NOUN
fumecheng-10464	382	14			PROPN
fumecheng-10464	382	15	(	(	PUNCT
fumecheng-10464	382	16	46	46	NUM
fumecheng-10464	382	17	)	)	PUNCT
fumecheng-10464	382	18	really	really	ADV
fumecheng-10464	382	19	,	,	PUNCT
fumecheng-10464	382	20	the	the	DET
fumecheng-10464	382	21	particular	particular	ADJ
fumecheng-10464	382	22	integral	integral	NOUN
fumecheng-10464	382	23	of	of	ADP
fumecheng-10464	382	24	eq	eq	PROPN
fumecheng-10464	382	25	.	.	PUNCT
fumecheng-10464	383	1	(	(	PUNCT
fumecheng-10464	383	2	45	45	NUM
fumecheng-10464	383	3	)	)	PUNCT
fumecheng-10464	383	4	is	be	AUX
fumecheng-10464	383	5	different	different	ADJ
fumecheng-10464	383	6	from	from	ADP
fumecheng-10464	383	7	the	the	DET
fumecheng-10464	383	8	previous	previous	ADJ
fumecheng-10464	383	9	corresponding	corresponding	ADJ
fumecheng-10464	383	10	equation	equation	NOUN
fumecheng-10464	383	11	as	as	SCONJ
fumecheng-10464	383	12	given	give	VERB
fumecheng-10464	383	13	in	in	ADP
fumecheng-10464	383	14	eq	eq	ADP
fumecheng-10464	383	15	.	.	PUNCT
fumecheng-10464	384	1	(	(	PUNCT
fumecheng-10464	384	2	34	34	NUM
fumecheng-10464	384	3	)	)	PUNCT
fumecheng-10464	384	4	.	.	PUNCT
fumecheng-10464	385	1	subsequently	subsequently	ADV
fumecheng-10464	385	2	,	,	PUNCT
fumecheng-10464	385	3	the	the	DET
fumecheng-10464	385	4	periodic	periodic	ADJ
fumecheng-10464	385	5	approximate	approximate	ADJ
fumecheng-10464	385	6	solution	solution	NOUN
fumecheng-10464	385	7	of	of	ADP
fumecheng-10464	385	8	the	the	DET
fumecheng-10464	385	9	firstorder	firstorder	NOUN
fumecheng-10464	385	10	will	will	AUX
fumecheng-10464	385	11	be	be	AUX
fumecheng-10464	385	12	transformed	transform	VERB
fumecheng-10464	385	13	.	.	PUNCT
fumecheng-10464	386	1	the	the	DET
fumecheng-10464	386	2	particular	particular	ADJ
fumecheng-10464	386	3	solution	solution	NOUN
fumecheng-10464	386	4	,	,	PUNCT
fumecheng-10464	386	5	in	in	ADP
fumecheng-10464	386	6	case	case	NOUN
fumecheng-10464	386	7	of	of	ADP
fumecheng-10464	386	8	the	the	DET
fumecheng-10464	386	9	harmonic	harmonic	ADJ
fumecheng-10464	386	10	resonance	resonance	NOUN
fumecheng-10464	386	11	,	,	PUNCT
fumecheng-10464	386	12	becomes	become	VERB
fumecheng-10464	386	13	..	..	PUNCT
fumecheng-10464	386	14	)	)	PUNCT
fumecheng-10464	386	15	(	(	PUNCT
fumecheng-10464	386	16	8	8	NUM
fumecheng-10464	386	17	1	1	NUM
fumecheng-10464	386	18	)	)	PUNCT
fumecheng-10464	386	19	,	,	PUNCT
fumecheng-10464	386	20	(	(	PUNCT
fumecheng-10464	386	21	033	033	NUM
fumecheng-10464	386	22	101	101	NUM
fumecheng-10464	386	23	cceaittx	cceaittx	VERB
fumecheng-10464	386	24	it	it	PRON
fumecheng-10464	387	1	+	+	PROPN
fumecheng-10464	387	2	+	+	NOUN
fumecheng-10464	387	3	=	=	SYM
fumecheng-10464	387	4			X
fumecheng-10464	387	5	(	(	PUNCT
fumecheng-10464	387	6	47	47	NUM
fumecheng-10464	387	7	)	)	PUNCT
fumecheng-10464	387	8	eq	eq	NOUN
fumecheng-10464	387	9	.	.	PUNCT
fumecheng-10464	387	10	(	(	PUNCT
fumecheng-10464	387	11	46	46	NUM
fumecheng-10464	387	12	)	)	PUNCT
fumecheng-10464	387	13	is	be	AUX
fumecheng-10464	387	14	a	a	DET
fumecheng-10464	387	15	first	first	ADJ
fumecheng-10464	387	16	-	-	PUNCT
fumecheng-10464	387	17	order	order	NOUN
fumecheng-10464	387	18	nonlinear	nonlinear	ADJ
fumecheng-10464	387	19	differential	differential	ADJ
fumecheng-10464	387	20	equation	equation	NOUN
fumecheng-10464	387	21	with	with	ADP
fumecheng-10464	387	22	complex	complex	ADJ
fumecheng-10464	387	23	coefficients	coefficient	NOUN
fumecheng-10464	387	24	.	.	PUNCT
fumecheng-10464	388	1	as	as	SCONJ
fumecheng-10464	388	2	previously	previously	ADV
fumecheng-10464	388	3	mentioned	mention	VERB
fumecheng-10464	388	4	,	,	PUNCT
fumecheng-10464	388	5	its	its	PRON
fumecheng-10464	388	6	solution	solution	NOUN
fumecheng-10464	388	7	may	may	AUX
fumecheng-10464	388	8	be	be	AUX
fumecheng-10464	388	9	considered	consider	VERB
fumecheng-10464	388	10	as	as	ADP
fumecheng-10464	388	11	:	:	PUNCT
fumecheng-10464	388	12	1	1	NUM
fumecheng-10464	388	13	)	)	PUNCT
fumecheng-10464	388	14	(	(	PUNCT
fumecheng-10464	388	15	)	)	PUNCT
fumecheng-10464	388	16	(	(	PUNCT
fumecheng-10464	388	17	11	11	NUM
fumecheng-10464	388	18	ti	ti	NOUN
fumecheng-10464	388	19	etta	etta	PROPN
fumecheng-10464	388	20	=	=	NOUN
fumecheng-10464	388	21	,	,	PUNCT
fumecheng-10464	388	22	(	(	PUNCT
fumecheng-10464	388	23	48	48	NUM
fumecheng-10464	388	24	)	)	PUNCT
fumecheng-10464	388	25	where	where	SCONJ
fumecheng-10464	388	26	𝜓	𝜓	PROPN
fumecheng-10464	388	27	(	(	PUNCT
fumecheng-10464	388	28	t1	t1	NOUN
fumecheng-10464	388	29	)	)	PUNCT
fumecheng-10464	388	30	is	be	AUX
fumecheng-10464	388	31	a	a	DET
fumecheng-10464	388	32	real	real	ADJ
fumecheng-10464	388	33	and	and	CCONJ
fumecheng-10464	388	34	time	time	NOUN
fumecheng-10464	388	35	-	-	PUNCT
fumecheng-10464	388	36	dependent	dependent	ADJ
fumecheng-10464	388	37	function	function	NOUN
fumecheng-10464	388	38	of	of	ADP
fumecheng-10464	388	39	the	the	DET
fumecheng-10464	388	40	independent	independent	ADJ
fumecheng-10464	388	41	parameter	parameter	NOUN
fumecheng-10464	388	42	t1	t1	PROPN
fumecheng-10464	388	43	.	.	PUNCT
fumecheng-10464	389	1	once	once	ADV
fumecheng-10464	389	2	more	more	ADV
fumecheng-10464	389	3	,	,	PUNCT
fumecheng-10464	389	4	as	as	ADP
fumecheng-10464	389	5	ρ→1	ρ→1	X
fumecheng-10464	389	6	,	,	PUNCT
fumecheng-10464	389	7	the	the	DET
fumecheng-10464	389	8	parameter	parameter	NOUN
fumecheng-10464	389	9	t1	t1	PROPN
fumecheng-10464	389	10	will	will	AUX
fumecheng-10464	389	11	be	be	AUX
fumecheng-10464	389	12	converted	convert	VERB
fumecheng-10464	389	13	to	to	ADP
fumecheng-10464	389	14	t.	t.	NOUN
fumecheng-10464	389	15	substituting	substituting	NOUN
fumecheng-10464	389	16	eq	eq	PROPN
fumecheng-10464	389	17	.	.	PUNCT
fumecheng-10464	390	1	(	(	PUNCT
fumecheng-10464	390	2	48	48	NUM
fumecheng-10464	390	3	)	)	PUNCT
fumecheng-10464	390	4	into	into	ADP
fumecheng-10464	390	5	eq	eq	NOUN
fumecheng-10464	390	6	.	.	PUNCT
fumecheng-10464	391	1	(	(	PUNCT
fumecheng-10464	391	2	45	45	NUM
fumecheng-10464	391	3	)	)	PUNCT
fumecheng-10464	391	4	,	,	PUNCT
fumecheng-10464	391	5	and	and	CCONJ
fumecheng-10464	391	6	then	then	ADV
fumecheng-10464	391	7	separating	separate	VERB
fumecheng-10464	391	8	the	the	DET
fumecheng-10464	391	9	real	real	ADJ
fumecheng-10464	391	10	and	and	CCONJ
fumecheng-10464	391	11	imaginary	imaginary	ADJ
fumecheng-10464	391	12	parts	part	NOUN
fumecheng-10464	391	13	,	,	PUNCT
fumecheng-10464	391	14	one	one	PRON
fumecheng-10464	391	15	gets	get	VERB
fumecheng-10464	391	16	:	:	PUNCT
fumecheng-10464	391	17	,	,	PUNCT
fumecheng-10464	391	18	22	22	NUM
fumecheng-10464	391	19	3	3	NUM
fumecheng-10464	391	20			NOUN
fumecheng-10464	391	21			NOUN
fumecheng-10464	391	22			NOUN
fumecheng-10464	391	23			NOUN
fumecheng-10464	391	24	−=	−=	NOUN
fumecheng-10464	392	1	dt	dt	X
fumecheng-10464	392	2	d	d	X
fumecheng-10464	392	3	(	(	PUNCT
fumecheng-10464	392	4	49	49	NUM
fumecheng-10464	392	5	)	)	PUNCT
fumecheng-10464	392	6	.0	.0	NUM
fumecheng-10464	392	7	2	2	NUM
fumecheng-10464	392	8	32	32	NUM
fumecheng-10464	392	9	3	3	NUM
fumecheng-10464	392	10	=	=	SYM
fumecheng-10464	392	11	+	+	ADP
fumecheng-10464	392	12	−	−	PROPN
fumecheng-10464	392	13	f	f	PROPN
fumecheng-10464	392	14			NOUN
fumecheng-10464	392	15	(	(	PUNCT
fumecheng-10464	392	16	50	50	NUM
fumecheng-10464	392	17	)	)	PUNCT
fumecheng-10464	392	18	forced	force	VERB
fumecheng-10464	392	19	nonlinear	nonlinear	ADJ
fumecheng-10464	392	20	oscillator	oscillator	NOUN
fumecheng-10464	392	21	in	in	ADP
fumecheng-10464	392	22	a	a	DET
fumecheng-10464	392	23	fractal	fractal	ADJ
fumecheng-10464	392	24	space	space	NOUN
fumecheng-10464	392	25	15	15	NUM
fumecheng-10464	392	26	the	the	DET
fumecheng-10464	392	27	combination	combination	NOUN
fumecheng-10464	392	28	of	of	ADP
fumecheng-10464	392	29	eqs	eqs	PROPN
fumecheng-10464	392	30	.	.	PUNCT
fumecheng-10464	393	1	(	(	PUNCT
fumecheng-10464	393	2	49	49	NUM
fumecheng-10464	393	3	)	)	PUNCT
fumecheng-10464	393	4	and	and	CCONJ
fumecheng-10464	393	5	(	(	PUNCT
fumecheng-10464	393	6	50	50	NUM
fumecheng-10464	393	7	)	)	PUNCT
fumecheng-10464	393	8	yields	yield	NOUN
fumecheng-10464	393	9	(	(	PUNCT
fumecheng-10464	393	10	2	2	NUM
fumecheng-10464	393	11	3	3	NUM
fumecheng-10464	393	12	)	)	PUNCT
fumecheng-10464	393	13	.	.	PUNCT
fumecheng-10464	394	1	6	6	NUM
fumecheng-10464	394	2	12	12	NUM
fumecheng-10464	394	3	d	d	NOUN
fumecheng-10464	394	4	f	f	X
fumecheng-10464	394	5	dt	dt	X
fumecheng-10464	394	6			NOUN
fumecheng-10464	394	7			NOUN
fumecheng-10464	394	8			NOUN
fumecheng-10464	394	9			NUM
fumecheng-10464	394	10			PROPN
fumecheng-10464	394	11			NOUN
fumecheng-10464	394	12			PROPN
fumecheng-10464	394	13			PROPN
fumecheng-10464	394	14	+	+	CCONJ
fumecheng-10464	394	15	−	−	PROPN
fumecheng-10464	394	16	=	=	SYM
fumecheng-10464	394	17	−	−	PROPN
fumecheng-10464	394	18	(	(	PUNCT
fumecheng-10464	394	19	51	51	NUM
fumecheng-10464	394	20	)	)	PUNCT
fumecheng-10464	394	21	eq	eq	NOUN
fumecheng-10464	394	22	.	.	PUNCT
fumecheng-10464	395	1	(	(	PUNCT
fumecheng-10464	395	2	51	51	NUM
fumecheng-10464	395	3	)	)	PUNCT
fumecheng-10464	395	4	is	be	AUX
fumecheng-10464	395	5	a	a	DET
fumecheng-10464	395	6	linear	linear	ADJ
fumecheng-10464	395	7	differential	differential	ADJ
fumecheng-10464	395	8	equation	equation	NOUN
fumecheng-10464	395	9	in	in	ADP
fumecheng-10464	395	10	the	the	DET
fumecheng-10464	395	11	function	function	NOUN
fumecheng-10464	395	12	𝜓.	𝜓.	VERB
fumecheng-10464	395	13	its	its	PRON
fumecheng-10464	395	14	solution	solution	NOUN
fumecheng-10464	395	15	may	may	AUX
fumecheng-10464	395	16	be	be	AUX
fumecheng-10464	395	17	written	write	VERB
fumecheng-10464	395	18	as	as	ADP
fumecheng-10464	395	19	,	,	PUNCT
fumecheng-10464	395	20	)	)	PUNCT
fumecheng-10464	395	21	32	32	NUM
fumecheng-10464	395	22	(	(	PUNCT
fumecheng-10464	395	23	6	6	NUM
fumecheng-10464	395	24	1	1	NUM
fumecheng-10464	395	25	32	32	NUM
fumecheng-10464	395	26	)	)	PUNCT
fumecheng-10464	396	1	(	(	PUNCT
fumecheng-10464	396	2			PROPN
fumecheng-10464	396	3			PROPN
fumecheng-10464	396	4			PROPN
fumecheng-10464	396	5			X
fumecheng-10464	396	6			NOUN
fumecheng-10464	396	7			NOUN
fumecheng-10464	396	8			VERB
fumecheng-10464	396	9			PROPN
fumecheng-10464	396	10			NOUN
fumecheng-10464	396	11			NOUN
fumecheng-10464	396	12			PROPN
fumecheng-10464	396	13			PROPN
fumecheng-10464	396	14			PROPN
fumecheng-10464	396	15			NOUN
fumecheng-10464	396	16	−+−	−+−	NOUN
fumecheng-10464	396	17	−	−	PROPN
fumecheng-10464	397	1	=	=	SYM
fumecheng-10464	397	2	texp	texp	NOUN
fumecheng-10464	397	3	f	f	PROPN
fumecheng-10464	397	4	t	t	NOUN
fumecheng-10464	397	5			PROPN
fumecheng-10464	397	6			NOUN
fumecheng-10464	397	7			NOUN
fumecheng-10464	397	8			PART
fumecheng-10464	397	9			NUM
fumecheng-10464	397	10	(	(	PUNCT
fumecheng-10464	397	11	52	52	NUM
fumecheng-10464	397	12	)	)	PUNCT
fumecheng-10464	397	13	where	where	SCONJ
fumecheng-10464	397	14	the	the	DET
fumecheng-10464	397	15	initial	initial	ADJ
fumecheng-10464	397	16	condition	condition	NOUN
fumecheng-10464	397	17	:	:	PUNCT
fumecheng-10464	397	18	𝜓	𝜓	X
fumecheng-10464	397	19	(	(	PUNCT
fumecheng-10464	397	20	0)=0	0)=0	NUM
fumecheng-10464	397	21	is	be	AUX
fumecheng-10464	397	22	used	use	VERB
fumecheng-10464	397	23	.	.	PUNCT
fumecheng-10464	398	1	it	it	PRON
fumecheng-10464	398	2	follows	follow	VERB
fumecheng-10464	398	3	that	that	SCONJ
fumecheng-10464	398	4	the	the	DET
fumecheng-10464	398	5	stability	stability	NOUN
fumecheng-10464	398	6	occurs	occur	VERB
fumecheng-10464	398	7	in	in	ADP
fumecheng-10464	398	8	such	such	DET
fumecheng-10464	398	9	a	a	DET
fumecheng-10464	398	10	way	way	NOUN
fumecheng-10464	399	1	that	that	SCONJ
fumecheng-10464	399	2	(	(	PUNCT
fumecheng-10464	399	3	2	2	NUM
fumecheng-10464	399	4	2	2	NUM
fumecheng-10464	399	5	3	3	NUM
fumecheng-10464	399	6	)	)	PUNCT
fumecheng-10464	399	7	/	/	SYM
fumecheng-10464	399	8	0,	0,	NUM
fumecheng-10464	399	9			PROPN
fumecheng-10464	399	10	−	−	PROPN
fumecheng-10464	399	11	−	−	PROPN
fumecheng-10464	399	12			PROPN
fumecheng-10464	399	13	(	(	PUNCT
fumecheng-10464	399	14	53	53	NUM
fumecheng-10464	399	15	)	)	PUNCT
fumecheng-10464	399	16	where	where	SCONJ
fumecheng-10464	399	17	eq	eq	ADJ
fumecheng-10464	399	18	.	.	PUNCT
fumecheng-10464	399	19	(	(	PUNCT
fumecheng-10464	399	20	44	44	NUM
fumecheng-10464	399	21	)	)	PUNCT
fumecheng-10464	399	22	is	be	AUX
fumecheng-10464	399	23	used	use	VERB
fumecheng-10464	399	24	.	.	PUNCT
fumecheng-10464	400	1	the	the	DET
fumecheng-10464	400	2	instability	instability	NOUN
fumecheng-10464	400	3	criterion	criterion	NOUN
fumecheng-10464	400	4	shown	show	VERB
fumecheng-10464	400	5	in	in	ADP
fumecheng-10464	400	6	the	the	DET
fumecheng-10464	400	7	inequality	inequality	NOUN
fumecheng-10464	400	8	(	(	PUNCT
fumecheng-10464	400	9	53	53	NUM
fumecheng-10464	400	10	)	)	PUNCT
fumecheng-10464	400	11	is	be	AUX
fumecheng-10464	400	12	independent	independent	ADJ
fumecheng-10464	400	13	of	of	ADP
fumecheng-10464	400	14	the	the	DET
fumecheng-10464	400	15	parameter	parameter	NOUN
fumecheng-10464	400	16	f.	f.	PROPN
fumecheng-10464	401	1	this	this	PRON
fumecheng-10464	401	2	happens	happen	VERB
fumecheng-10464	401	3	because	because	SCONJ
fumecheng-10464	401	4	the	the	DET
fumecheng-10464	401	5	parameter	parameter	NOUN
fumecheng-10464	401	6	f	f	PROPN
fumecheng-10464	401	7	lies	lie	VERB
fumecheng-10464	401	8	away	away	ADV
fumecheng-10464	401	9	from	from	ADP
fumecheng-10464	401	10	the	the	DET
fumecheng-10464	401	11	argument	argument	NOUN
fumecheng-10464	401	12	of	of	ADP
fumecheng-10464	401	13	the	the	DET
fumecheng-10464	401	14	exponential	exponential	ADJ
fumecheng-10464	401	15	function	function	NOUN
fumecheng-10464	401	16	,	,	PUNCT
fumecheng-10464	401	17	as	as	SCONJ
fumecheng-10464	401	18	seen	see	VERB
fumecheng-10464	401	19	in	in	ADP
fumecheng-10464	401	20	eq	eq	ADP
fumecheng-10464	401	21	.	.	PUNCT
fumecheng-10464	402	1	(	(	PUNCT
fumecheng-10464	402	2	52	52	NUM
fumecheng-10464	402	3	)	)	PUNCT
fumecheng-10464	402	4	.	.	PUNCT
fumecheng-10464	403	1	on	on	ADP
fumecheng-10464	403	2	the	the	DET
fumecheng-10464	403	3	other	other	ADJ
fumecheng-10464	403	4	hand	hand	NOUN
fumecheng-10464	403	5	,	,	PUNCT
fumecheng-10464	403	6	as	as	ADP
fumecheng-10464	403	7	ω=1	ω=1	X
fumecheng-10464	403	8	,	,	PUNCT
fumecheng-10464	403	9	the	the	DET
fumecheng-10464	403	10	frequency	frequency	NOUN
fumecheng-10464	403	11	of	of	ADP
fumecheng-10464	403	12	the	the	DET
fumecheng-10464	403	13	exciting	exciting	ADJ
fumecheng-10464	403	14	force	force	NOUN
fumecheng-10464	403	15	has	have	VERB
fumecheng-10464	403	16	no	no	DET
fumecheng-10464	403	17	implication	implication	NOUN
fumecheng-10464	403	18	in	in	ADP
fumecheng-10464	403	19	the	the	DET
fumecheng-10464	403	20	stability	stability	NOUN
fumecheng-10464	403	21	criterion	criterion	NOUN
fumecheng-10464	403	22	.	.	PUNCT
fumecheng-10464	404	1	this	this	PRON
fumecheng-10464	404	2	occurs	occur	VERB
fumecheng-10464	404	3	because	because	SCONJ
fumecheng-10464	404	4	the	the	DET
fumecheng-10464	404	5	natural	natural	ADJ
fumecheng-10464	404	6	frequency	frequency	NOUN
fumecheng-10464	404	7	of	of	ADP
fumecheng-10464	404	8	the	the	DET
fumecheng-10464	404	9	given	give	VERB
fumecheng-10464	404	10	dvdp	dvdp	PROPN
fumecheng-10464	404	11	is	be	AUX
fumecheng-10464	404	12	the	the	DET
fumecheng-10464	404	13	unity	unity	NOUN
fumecheng-10464	404	14	.	.	PUNCT
fumecheng-10464	405	1	in	in	ADP
fumecheng-10464	405	2	the	the	DET
fumecheng-10464	405	3	latter	latter	ADJ
fumecheng-10464	405	4	case	case	NOUN
fumecheng-10464	405	5	,	,	PUNCT
fumecheng-10464	405	6	regardless	regardless	ADV
fumecheng-10464	405	7	of	of	ADP
fumecheng-10464	405	8	the	the	DET
fumecheng-10464	405	9	sign	sign	NOUN
fumecheng-10464	405	10	of	of	ADP
fumecheng-10464	405	11	the	the	DET
fumecheng-10464	405	12	parameter	parameter	NOUN
fumecheng-10464	405	13	β	β	NOUN
fumecheng-10464	405	14	,	,	PUNCT
fumecheng-10464	405	15	the	the	DET
fumecheng-10464	405	16	stability	stability	NOUN
fumecheng-10464	405	17	criterion	criterion	NOUN
fumecheng-10464	405	18	yields	yield	NOUN
fumecheng-10464	405	19	µ>0	µ>0	PROPN
fumecheng-10464	405	20	,	,	PUNCT
fumecheng-10464	405	21	which	which	PRON
fumecheng-10464	405	22	gives	give	VERB
fumecheng-10464	405	23	the	the	DET
fumecheng-10464	405	24	same	same	ADJ
fumecheng-10464	405	25	condition	condition	NOUN
fumecheng-10464	405	26	given	give	VERB
fumecheng-10464	405	27	in	in	ADP
fumecheng-10464	405	28	the	the	DET
fumecheng-10464	405	29	non	non	ADJ
fumecheng-10464	405	30	-	-	ADJ
fumecheng-10464	405	31	resonance	resonance	NOUN
fumecheng-10464	405	32	case	case	NOUN
fumecheng-10464	405	33	.	.	PUNCT
fumecheng-10464	406	1	it	it	PRON
fumecheng-10464	406	2	is	be	AUX
fumecheng-10464	406	3	appropriate	appropriate	ADJ
fumecheng-10464	406	4	to	to	PART
fumecheng-10464	406	5	corroborate	corroborate	VERB
fumecheng-10464	406	6	this	this	DET
fumecheng-10464	406	7	stability	stability	NOUN
fumecheng-10464	406	8	criterion	criterion	NOUN
fumecheng-10464	406	9	numerically	numerically	ADV
fumecheng-10464	406	10	.	.	PUNCT
fumecheng-10464	407	1	therefore	therefore	ADV
fumecheng-10464	407	2	,	,	PUNCT
fumecheng-10464	407	3	in	in	ADP
fumecheng-10464	407	4	what	what	PRON
fumecheng-10464	407	5	follows	follow	VERB
fumecheng-10464	407	6	,	,	PUNCT
fumecheng-10464	407	7	two	two	NUM
fumecheng-10464	407	8	stability	stability	NOUN
fumecheng-10464	407	9	profiles	profile	NOUN
fumecheng-10464	407	10	are	be	AUX
fumecheng-10464	407	11	plotted	plot	VERB
fumecheng-10464	407	12	.	.	PUNCT
fumecheng-10464	408	1	in	in	ADP
fumecheng-10464	408	2	the	the	DET
fumecheng-10464	408	3	following	follow	VERB
fumecheng-10464	408	4	figures	figure	NOUN
fumecheng-10464	408	5	,	,	PUNCT
fumecheng-10464	408	6	the	the	DET
fumecheng-10464	408	7	white	white	PROPN
fumecheng-10464	408	8	areas	area	NOUN
fumecheng-10464	408	9	symbolize	symbolize	VERB
fumecheng-10464	408	10	the	the	DET
fumecheng-10464	408	11	unstable	unstable	ADJ
fumecheng-10464	408	12	regions	region	NOUN
fumecheng-10464	408	13	,	,	PUNCT
fumecheng-10464	408	14	whereas	whereas	SCONJ
fumecheng-10464	408	15	the	the	DET
fumecheng-10464	408	16	dark	dark	ADJ
fumecheng-10464	408	17	areas	area	NOUN
fumecheng-10464	408	18	stand	stand	VERB
fumecheng-10464	408	19	for	for	ADP
fumecheng-10464	408	20	the	the	DET
fumecheng-10464	408	21	stable	stable	ADJ
fumecheng-10464	408	22	regions	region	NOUN
fumecheng-10464	408	23	.	.	PUNCT
fumecheng-10464	409	1	fig	fig	NOUN
fumecheng-10464	409	2	.	.	PUNCT
fumecheng-10464	410	1	10	10	NUM
fumecheng-10464	410	2	represents	represent	VERB
fumecheng-10464	410	3	the	the	DET
fumecheng-10464	410	4	stability	stability	NOUN
fumecheng-10464	410	5	diagram	diagram	NOUN
fumecheng-10464	410	6	,	,	PUNCT
fumecheng-10464	410	7	at	at	ADP
fumecheng-10464	410	8	which	which	PRON
fumecheng-10464	410	9	the	the	DET
fumecheng-10464	410	10	parameter	parameter	NOUN
fumecheng-10464	410	11	µ	µ	PROPN
fumecheng-10464	410	12	is	be	AUX
fumecheng-10464	410	13	plotted	plot	VERB
fumecheng-10464	410	14	versus	versus	ADP
fumecheng-10464	410	15	the	the	DET
fumecheng-10464	410	16	parameter	parameter	NOUN
fumecheng-10464	410	17	ω	ω	PROPN
fumecheng-10464	410	18	,	,	PUNCT
fumecheng-10464	410	19	to	to	PART
fumecheng-10464	410	20	show	show	VERB
fumecheng-10464	410	21	the	the	DET
fumecheng-10464	410	22	influence	influence	NOUN
fumecheng-10464	410	23	of	of	ADP
fumecheng-10464	410	24	the	the	DET
fumecheng-10464	410	25	parameter	parameter	NOUN
fumecheng-10464	410	26	β	β	PROPN
fumecheng-10464	410	27	on	on	ADP
fumecheng-10464	410	28	the	the	DET
fumecheng-10464	410	29	stability	stability	NOUN
fumecheng-10464	410	30	picture	picture	NOUN
fumecheng-10464	410	31	.	.	PUNCT
fumecheng-10464	411	1	as	as	SCONJ
fumecheng-10464	411	2	seen	see	VERB
fumecheng-10464	411	3	,	,	PUNCT
fumecheng-10464	411	4	the	the	DET
fumecheng-10464	411	5	plane	plane	NOUN
fumecheng-10464	411	6	is	be	AUX
fumecheng-10464	411	7	partitioned	partition	VERB
fumecheng-10464	411	8	into	into	ADP
fumecheng-10464	411	9	white	white	ADJ
fumecheng-10464	411	10	and	and	CCONJ
fumecheng-10464	411	11	dark	dark	ADJ
fumecheng-10464	411	12	regions	region	NOUN
fumecheng-10464	411	13	.	.	PUNCT
fumecheng-10464	412	1	this	this	DET
fumecheng-10464	412	2	figure	figure	NOUN
fumecheng-10464	412	3	is	be	AUX
fumecheng-10464	412	4	interpreted	interpret	VERB
fumecheng-10464	412	5	as	as	SCONJ
fumecheng-10464	412	6	follows	follow	VERB
fumecheng-10464	412	7	:	:	PUNCT
fumecheng-10464	412	8	for	for	ADP
fumecheng-10464	412	9	positive	positive	ADJ
fumecheng-10464	412	10	values	value	NOUN
fumecheng-10464	412	11	of	of	ADP
fumecheng-10464	412	12	the	the	DET
fumecheng-10464	412	13	parameter	parameter	NOUN
fumecheng-10464	412	14	µ	µ	NOUN
fumecheng-10464	412	15	,	,	PUNCT
fumecheng-10464	412	16	the	the	DET
fumecheng-10464	412	17	increase	increase	NOUN
fumecheng-10464	412	18	of	of	ADP
fumecheng-10464	412	19	the	the	DET
fumecheng-10464	412	20	parameter	parameter	NOUN
fumecheng-10464	413	1	β	β	PROPN
fumecheng-10464	413	2	matches	match	VERB
fumecheng-10464	413	3	larger	large	ADJ
fumecheng-10464	413	4	stable	stable	ADJ
fumecheng-10464	413	5	fig	fig	NOUN
fumecheng-10464	413	6	.	.	PUNCT
fumecheng-10464	414	1	10	10	NUM
fumecheng-10464	414	2	the	the	DET
fumecheng-10464	414	3	stability	stability	NOUN
fumecheng-10464	414	4	criterion	criterion	NOUN
fumecheng-10464	414	5	as	as	SCONJ
fumecheng-10464	414	6	given	give	VERB
fumecheng-10464	414	7	in	in	ADP
fumecheng-10464	414	8	the	the	DET
fumecheng-10464	414	9	inequality	inequality	NOUN
fumecheng-10464	414	10	(	(	PUNCT
fumecheng-10464	414	11	53	53	NUM
fumecheng-10464	414	12	)	)	PUNCT
fumecheng-10464	414	13	,	,	PUNCT
fumecheng-10464	414	14	with	with	ADP
fumecheng-10464	414	15	variation	variation	NOUN
fumecheng-10464	414	16	of	of	ADP
fumecheng-10464	414	17	β	β	NOUN
fumecheng-10464	414	18	16	16	NUM
fumecheng-10464	414	19	j.-h	j.-h	NOUN
fumecheng-10464	414	20	.	.	PUNCT
fumecheng-10464	415	1	he	he	PRON
fumecheng-10464	415	2	,	,	PUNCT
fumecheng-10464	415	3	g.	g.	PROPN
fumecheng-10464	415	4	m.	m.	PROPN
fumecheng-10464	415	5	moatimid	moatimid	PROPN
fumecheng-10464	415	6	,	,	PUNCT
fumecheng-10464	415	7	m.	m.	NOUN
fumecheng-10464	415	8	h.	h.	PROPN
fumecheng-10464	415	9	zekry	zekry	PROPN
fumecheng-10464	415	10	regions	region	NOUN
fumecheng-10464	415	11	.	.	PUNCT
fumecheng-10464	416	1	on	on	ADP
fumecheng-10464	416	2	the	the	DET
fumecheng-10464	416	3	other	other	ADJ
fumecheng-10464	416	4	hand	hand	NOUN
fumecheng-10464	416	5	,	,	PUNCT
fumecheng-10464	416	6	at	at	ADP
fumecheng-10464	416	7	the	the	DET
fumecheng-10464	416	8	negative	negative	ADJ
fumecheng-10464	416	9	values	value	NOUN
fumecheng-10464	416	10	of	of	ADP
fumecheng-10464	416	11	the	the	DET
fumecheng-10464	416	12	parameter	parameter	NOUN
fumecheng-10464	416	13	µ	µ	NOUN
fumecheng-10464	416	14	,	,	PUNCT
fumecheng-10464	416	15	the	the	DET
fumecheng-10464	416	16	increase	increase	NOUN
fumecheng-10464	416	17	of	of	ADP
fumecheng-10464	416	18	the	the	DET
fumecheng-10464	416	19	parameter	parameter	NOUN
fumecheng-10464	416	20	β	β	PROPN
fumecheng-10464	416	21	meets	meet	VERB
fumecheng-10464	416	22	smaller	small	ADJ
fumecheng-10464	416	23	stable	stable	ADJ
fumecheng-10464	416	24	regions	region	NOUN
fumecheng-10464	416	25	.	.	PUNCT
fumecheng-10464	417	1	therefore	therefore	ADV
fumecheng-10464	417	2	,	,	PUNCT
fumecheng-10464	417	3	the	the	DET
fumecheng-10464	417	4	parameter	parameter	NOUN
fumecheng-10464	417	5	β	β	PROPN
fumecheng-10464	417	6	plays	play	VERB
fumecheng-10464	417	7	a	a	DET
fumecheng-10464	417	8	dual	dual	ADJ
fumecheng-10464	417	9	role	role	NOUN
fumecheng-10464	417	10	in	in	ADP
fumecheng-10464	417	11	the	the	DET
fumecheng-10464	417	12	stability	stability	NOUN
fumecheng-10464	417	13	configuration	configuration	NOUN
fumecheng-10464	417	14	.	.	PUNCT
fumecheng-10464	418	1	it	it	PRON
fumecheng-10464	418	2	should	should	AUX
fumecheng-10464	418	3	be	be	AUX
fumecheng-10464	418	4	noticed	notice	VERB
fumecheng-10464	418	5	that	that	SCONJ
fumecheng-10464	418	6	this	this	DET
fumecheng-10464	418	7	influence	influence	NOUN
fumecheng-10464	418	8	does	do	AUX
fumecheng-10464	418	9	not	not	PART
fumecheng-10464	418	10	appear	appear	VERB
fumecheng-10464	418	11	in	in	ADP
fumecheng-10464	418	12	the	the	DET
fumecheng-10464	418	13	preceding	precede	VERB
fumecheng-10464	418	14	analysis	analysis	NOUN
fumecheng-10464	418	15	.	.	PUNCT
fumecheng-10464	419	1	fig	fig	NOUN
fumecheng-10464	419	2	.	.	PUNCT
fumecheng-10464	420	1	11	11	NUM
fumecheng-10464	420	2	plots	plot	NOUN
fumecheng-10464	420	3	the	the	DET
fumecheng-10464	420	4	stability	stability	NOUN
fumecheng-10464	420	5	profile	profile	NOUN
fumecheng-10464	420	6	,	,	PUNCT
fumecheng-10464	420	7	at	at	ADP
fumecheng-10464	420	8	which	which	PRON
fumecheng-10464	420	9	the	the	DET
fumecheng-10464	420	10	parameter	parameter	NOUN
fumecheng-10464	420	11	µ	µ	PROPN
fumecheng-10464	420	12	is	be	AUX
fumecheng-10464	420	13	plotted	plot	VERB
fumecheng-10464	420	14	versus	versus	ADP
fumecheng-10464	420	15	the	the	DET
fumecheng-10464	420	16	parameter	parameter	NOUN
fumecheng-10464	420	17	β	β	PROPN
fumecheng-10464	420	18	to	to	PART
fumecheng-10464	420	19	indicate	indicate	VERB
fumecheng-10464	420	20	the	the	DET
fumecheng-10464	420	21	influence	influence	NOUN
fumecheng-10464	420	22	of	of	ADP
fumecheng-10464	420	23	the	the	DET
fumecheng-10464	420	24	parameter	parameter	PROPN
fumecheng-10464	420	25	ω	ω	PROPN
fumecheng-10464	420	26	on	on	ADP
fumecheng-10464	420	27	the	the	DET
fumecheng-10464	420	28	stability	stability	NOUN
fumecheng-10464	420	29	picture	picture	NOUN
fumecheng-10464	420	30	.	.	PUNCT
fumecheng-10464	421	1	as	as	SCONJ
fumecheng-10464	421	2	seen	see	VERB
fumecheng-10464	421	3	,	,	PUNCT
fumecheng-10464	421	4	the	the	DET
fumecheng-10464	421	5	plane	plane	NOUN
fumecheng-10464	421	6	is	be	AUX
fumecheng-10464	421	7	partitioned	partition	VERB
fumecheng-10464	421	8	into	into	ADP
fumecheng-10464	421	9	white	white	ADJ
fumecheng-10464	421	10	and	and	CCONJ
fumecheng-10464	421	11	dark	dark	ADJ
fumecheng-10464	421	12	regions	region	NOUN
fumecheng-10464	421	13	.	.	PUNCT
fumecheng-10464	422	1	this	this	DET
fumecheng-10464	422	2	figure	figure	NOUN
fumecheng-10464	422	3	illustrates	illustrate	VERB
fumecheng-10464	422	4	that	that	SCONJ
fumecheng-10464	422	5	for	for	ADP
fumecheng-10464	422	6	positive	positive	ADJ
fumecheng-10464	422	7	values	value	NOUN
fumecheng-10464	422	8	of	of	ADP
fumecheng-10464	422	9	the	the	DET
fumecheng-10464	422	10	parameter	parameter	NOUN
fumecheng-10464	422	11	µ	µ	NOUN
fumecheng-10464	422	12	,	,	PUNCT
fumecheng-10464	422	13	the	the	DET
fumecheng-10464	422	14	increase	increase	NOUN
fumecheng-10464	422	15	of	of	ADP
fumecheng-10464	422	16	the	the	DET
fumecheng-10464	422	17	parameter	parameter	NOUN
fumecheng-10464	422	18	β	β	PROPN
fumecheng-10464	422	19	meets	meet	VERB
fumecheng-10464	422	20	larger	large	ADJ
fumecheng-10464	422	21	stable	stable	ADJ
fumecheng-10464	422	22	regions	region	NOUN
fumecheng-10464	422	23	.	.	PUNCT
fumecheng-10464	423	1	on	on	ADP
fumecheng-10464	423	2	the	the	DET
fumecheng-10464	423	3	other	other	ADJ
fumecheng-10464	423	4	hand	hand	NOUN
fumecheng-10464	423	5	,	,	PUNCT
fumecheng-10464	423	6	at	at	ADP
fumecheng-10464	423	7	negative	negative	ADJ
fumecheng-10464	423	8	values	value	NOUN
fumecheng-10464	423	9	of	of	ADP
fumecheng-10464	423	10	the	the	DET
fumecheng-10464	423	11	parameter	parameter	NOUN
fumecheng-10464	423	12	µ	µ	NOUN
fumecheng-10464	423	13	,	,	PUNCT
fumecheng-10464	423	14	one	one	PRON
fumecheng-10464	423	15	finds	find	VERB
fumecheng-10464	423	16	that	that	SCONJ
fumecheng-10464	423	17	the	the	DET
fumecheng-10464	423	18	increase	increase	NOUN
fumecheng-10464	423	19	of	of	ADP
fumecheng-10464	423	20	the	the	DET
fumecheng-10464	423	21	parameter	parameter	NOUN
fumecheng-10464	423	22	β	β	PROPN
fumecheng-10464	423	23	matches	match	VERB
fumecheng-10464	423	24	smaller	small	ADJ
fumecheng-10464	423	25	stable	stable	ADJ
fumecheng-10464	423	26	regions	region	NOUN
fumecheng-10464	423	27	.	.	PUNCT
fumecheng-10464	424	1	once	once	ADV
fumecheng-10464	424	2	more	more	ADJ
fumecheng-10464	424	3	,	,	PUNCT
fumecheng-10464	424	4	the	the	DET
fumecheng-10464	424	5	parameter	parameter	PROPN
fumecheng-10464	424	6	ω	ω	PROPN
fumecheng-10464	424	7	plays	play	VERB
fumecheng-10464	424	8	a	a	DET
fumecheng-10464	424	9	dual	dual	ADJ
fumecheng-10464	424	10	role	role	NOUN
fumecheng-10464	424	11	in	in	ADP
fumecheng-10464	424	12	the	the	DET
fumecheng-10464	424	13	stability	stability	NOUN
fumecheng-10464	424	14	diagram	diagram	NOUN
fumecheng-10464	424	15	.	.	PUNCT
fumecheng-10464	425	1	this	this	PRON
fumecheng-10464	425	2	is	be	AUX
fumecheng-10464	425	3	the	the	DET
fumecheng-10464	425	4	first	first	ADJ
fumecheng-10464	425	5	mechanism	mechanism	NOUN
fumecheng-10464	425	6	for	for	ADP
fumecheng-10464	425	7	the	the	DET
fumecheng-10464	425	8	parameter	parameter	PROPN
fumecheng-10464	425	9	ω	ω	PROPN
fumecheng-10464	425	10	in	in	ADP
fumecheng-10464	425	11	the	the	DET
fumecheng-10464	425	12	entire	entire	ADJ
fumecheng-10464	425	13	analysis	analysis	NOUN
fumecheng-10464	425	14	of	of	ADP
fumecheng-10464	425	15	the	the	DET
fumecheng-10464	425	16	current	current	ADJ
fumecheng-10464	425	17	paper	paper	NOUN
fumecheng-10464	425	18	.	.	PUNCT
fumecheng-10464	426	1	fig	fig	NOUN
fumecheng-10464	426	2	.	.	PUNCT
fumecheng-10464	427	1	11	11	NUM
fumecheng-10464	428	1	the	the	DET
fumecheng-10464	428	2	stability	stability	NOUN
fumecheng-10464	428	3	criterion	criterion	NOUN
fumecheng-10464	428	4	as	as	SCONJ
fumecheng-10464	428	5	given	give	VERB
fumecheng-10464	428	6	in	in	ADP
fumecheng-10464	428	7	the	the	DET
fumecheng-10464	428	8	inequality	inequality	NOUN
fumecheng-10464	428	9	(	(	PUNCT
fumecheng-10464	428	10	53	53	NUM
fumecheng-10464	428	11	)	)	PUNCT
fumecheng-10464	428	12	,	,	PUNCT
fumecheng-10464	428	13	with	with	ADP
fumecheng-10464	428	14	variation	variation	NOUN
fumecheng-10464	428	15	of	of	ADP
fumecheng-10464	428	16	ω	ω	PROPN
fumecheng-10464	428	17	.	.	PROPN
fumecheng-10464	428	18	4	4	NUM
fumecheng-10464	428	19	.	.	X
fumecheng-10464	428	20	discussion	discussion	NOUN
fumecheng-10464	428	21	and	and	CCONJ
fumecheng-10464	428	22	concluding	conclude	VERB
fumecheng-10464	428	23	remarks	remark	NOUN
fumecheng-10464	428	24	generally	generally	ADV
fumecheng-10464	428	25	,	,	PUNCT
fumecheng-10464	428	26	a	a	DET
fumecheng-10464	428	27	conservative	conservative	ADJ
fumecheng-10464	428	28	vibration	vibration	NOUN
fumecheng-10464	428	29	system	system	NOUN
fumecheng-10464	428	30	must	must	AUX
fumecheng-10464	428	31	be	be	AUX
fumecheng-10464	428	32	free	free	ADJ
fumecheng-10464	428	33	of	of	ADP
fumecheng-10464	428	34	the	the	DET
fumecheng-10464	428	35	damping	damp	VERB
fumecheng-10464	428	36	forces	force	NOUN
fumecheng-10464	428	37	,	,	PUNCT
fumecheng-10464	428	38	and	and	CCONJ
fumecheng-10464	428	39	its	its	PRON
fumecheng-10464	428	40	amplitude	amplitude	NOUN
fumecheng-10464	428	41	will	will	AUX
fumecheng-10464	428	42	be	be	AUX
fumecheng-10464	428	43	fixed	fix	VERB
fumecheng-10464	428	44	as	as	SCONJ
fumecheng-10464	428	45	t	t	PROPN
fumecheng-10464	428	46	tends	tend	VERB
fumecheng-10464	428	47	to	to	PART
fumecheng-10464	428	48	infinity	infinity	VERB
fumecheng-10464	428	49	.	.	PUNCT
fumecheng-10464	429	1	as	as	SCONJ
fumecheng-10464	429	2	pointed	point	VERB
fumecheng-10464	429	3	out	out	ADP
fumecheng-10464	429	4	in	in	ADP
fumecheng-10464	429	5	ref	ref	NOUN
fumecheng-10464	429	6	.	.	PUNCT
fumecheng-10464	430	1	[	[	X
fumecheng-10464	430	2	44	44	NUM
fumecheng-10464	430	3	]	]	PUNCT
fumecheng-10464	430	4	,	,	PUNCT
fumecheng-10464	430	5	the	the	DET
fumecheng-10464	430	6	inertia	inertia	NOUN
fumecheng-10464	430	7	force	force	NOUN
fumecheng-10464	430	8	in	in	ADP
fumecheng-10464	430	9	a	a	DET
fumecheng-10464	430	10	fractal	fractal	ADJ
fumecheng-10464	430	11	space	space	NOUN
fumecheng-10464	430	12	can	can	AUX
fumecheng-10464	430	13	be	be	AUX
fumecheng-10464	430	14	approximately	approximately	ADV
fumecheng-10464	430	15	expressed	express	VERB
fumecheng-10464	430	16	as	as	ADP
fumecheng-10464	430	17	2	2	NUM
fumecheng-10464	430	18	2	2	NUM
fumecheng-10464	430	19	2	2	NUM
fumecheng-10464	430	20	2	2	NUM
fumecheng-10464	430	21	=	=	SYM
fumecheng-10464	431	1	+	+	ADJ
fumecheng-10464	431	2	(	(	PUNCT
fumecheng-10464	431	3	1	1	NUM
fumecheng-10464	431	4	)	)	PUNCT
fumecheng-10464	432	1	d	d	NOUN
fumecheng-10464	432	2	z	z	SYM
fumecheng-10464	433	1	d	d	NOUN
fumecheng-10464	433	2	z	z	NOUN
fumecheng-10464	433	3	dz	dz	PROPN
fumecheng-10464	434	1	p	p	NOUN
fumecheng-10464	434	2	p	p	X
fumecheng-10464	434	3	dd	dd	NOUN
fumecheng-10464	434	4	d	d	NOUN
fumecheng-10464	434	5			NOUN
fumecheng-10464	434	6			NOUN
fumecheng-10464	434	7	−	−	PROPN
fumecheng-10464	434	8	(	(	PUNCT
fumecheng-10464	434	9	54	54	NUM
fumecheng-10464	434	10	)	)	PUNCT
fumecheng-10464	434	11	where	where	SCONJ
fumecheng-10464	434	12	p	p	NOUN
fumecheng-10464	434	13	is	be	AUX
fumecheng-10464	434	14	a	a	DET
fumecheng-10464	434	15	function	function	NOUN
fumecheng-10464	434	16	of	of	ADP
fumecheng-10464	434	17	the	the	DET
fumecheng-10464	434	18	fractal	fractal	ADJ
fumecheng-10464	434	19	dimension	dimension	NOUN
fumecheng-10464	434	20	.	.	PUNCT
fumecheng-10464	435	1	in	in	ADP
fumecheng-10464	435	2	our	our	PRON
fumecheng-10464	435	3	paper	paper	NOUN
fumecheng-10464	435	4	,	,	PUNCT
fumecheng-10464	435	5	a	a	DET
fumecheng-10464	435	6	weak	weak	ADJ
fumecheng-10464	435	7	damping	damp	VERB
fumecheng-10464	435	8	effect	effect	NOUN
fumecheng-10464	435	9	is	be	AUX
fumecheng-10464	435	10	considered	consider	VERB
fumecheng-10464	435	11	.	.	PUNCT
fumecheng-10464	436	1	its	its	PRON
fumecheng-10464	436	2	amplitude	amplitude	NOUN
fumecheng-10464	436	3	changes	change	NOUN
fumecheng-10464	436	4	extremely	extremely	ADV
fumecheng-10464	436	5	slow	slow	ADJ
fumecheng-10464	436	6	,	,	PUNCT
fumecheng-10464	436	7	and	and	CCONJ
fumecheng-10464	436	8	we	we	PRON
fumecheng-10464	436	9	assume	assume	VERB
fumecheng-10464	436	10	its	its	PRON
fumecheng-10464	436	11	value	value	NOUN
fumecheng-10464	436	12	not	not	PART
fumecheng-10464	436	13	to	to	PART
fumecheng-10464	436	14	change	change	VERB
fumecheng-10464	436	15	for	for	ADP
fumecheng-10464	436	16	simplicity	simplicity	NOUN
fumecheng-10464	436	17	.	.	PUNCT
fumecheng-10464	437	1	forced	force	VERB
fumecheng-10464	437	2	nonlinear	nonlinear	ADJ
fumecheng-10464	437	3	oscillator	oscillator	NOUN
fumecheng-10464	437	4	in	in	ADP
fumecheng-10464	437	5	a	a	DET
fumecheng-10464	437	6	fractal	fractal	ADJ
fumecheng-10464	437	7	space	space	NOUN
fumecheng-10464	437	8	17	17	NUM
fumecheng-10464	437	9	by	by	ADP
fumecheng-10464	437	10	the	the	DET
fumecheng-10464	437	11	inverse	inverse	NOUN
fumecheng-10464	437	12	two	two	NUM
fumecheng-10464	437	13	-	-	PUNCT
fumecheng-10464	437	14	scale	scale	NOUN
fumecheng-10464	437	15	transform	transform	NOUN
fumecheng-10464	437	16	[	[	X
fumecheng-10464	437	17	45	45	NUM
fumecheng-10464	437	18	-	-	SYM
fumecheng-10464	437	19	47	47	NUM
fumecheng-10464	437	20	]	]	PUNCT
fumecheng-10464	437	21	,	,	PUNCT
fumecheng-10464	437	22	x	x	X
fumecheng-10464	437	23	=	=	NOUN
fumecheng-10464	437	24	z√c	z√c	NOUN
fumecheng-10464	437	25	/	/	SYM
fumecheng-10464	437	26	b	b	PROPN
fumecheng-10464	437	27	,	,	PUNCT
fumecheng-10464	437	28	t=√a	t=√a	PRON
fumecheng-10464	437	29	τα	τα	NOUN
fumecheng-10464	437	30	,	,	PUNCT
fumecheng-10464	437	31	the	the	DET
fumecheng-10464	437	32	above	above	ADJ
fumecheng-10464	437	33	results	result	NOUN
fumecheng-10464	437	34	are	be	AUX
fumecheng-10464	437	35	converted	convert	VERB
fumecheng-10464	437	36	to	to	ADP
fumecheng-10464	437	37	the	the	DET
fumecheng-10464	437	38	fractal	fractal	ADJ
fumecheng-10464	437	39	cases	case	NOUN
fumecheng-10464	437	40	.	.	PUNCT
fumecheng-10464	438	1	because	because	SCONJ
fumecheng-10464	438	2	of	of	ADP
fumecheng-10464	438	3	the	the	DET
fumecheng-10464	438	4	great	great	ADJ
fumecheng-10464	438	5	importance	importance	NOUN
fumecheng-10464	438	6	of	of	ADP
fumecheng-10464	438	7	the	the	DET
fumecheng-10464	438	8	motivation	motivation	NOUN
fumecheng-10464	438	9	of	of	ADP
fumecheng-10464	438	10	the	the	DET
fumecheng-10464	438	11	dvdp	dvdp	ADJ
fumecheng-10464	438	12	in	in	ADP
fumecheng-10464	438	13	extensive	extensive	ADJ
fumecheng-10464	438	14	applications	application	NOUN
fumecheng-10464	438	15	in	in	ADP
fumecheng-10464	438	16	several	several	ADJ
fumecheng-10464	438	17	areas	area	NOUN
fumecheng-10464	438	18	in	in	ADP
fumecheng-10464	438	19	the	the	DET
fumecheng-10464	438	20	sciences	science	NOUN
fumecheng-10464	438	21	,	,	PUNCT
fumecheng-10464	438	22	many	many	ADJ
fumecheng-10464	438	23	researchers	researcher	NOUN
fumecheng-10464	438	24	have	have	AUX
fumecheng-10464	438	25	examined	examine	VERB
fumecheng-10464	438	26	this	this	DET
fumecheng-10464	438	27	problem	problem	NOUN
fumecheng-10464	438	28	.	.	PUNCT
fumecheng-10464	439	1	really	really	ADV
fumecheng-10464	439	2	,	,	PUNCT
fumecheng-10464	439	3	the	the	DET
fumecheng-10464	439	4	dvdp	dvdp	PROPN
fumecheng-10464	439	5	is	be	AUX
fumecheng-10464	439	6	one	one	NUM
fumecheng-10464	439	7	of	of	ADP
fumecheng-10464	439	8	the	the	DET
fumecheng-10464	439	9	significant	significant	ADJ
fumecheng-10464	439	10	mathematical	mathematical	ADJ
fumecheng-10464	439	11	models	model	NOUN
fumecheng-10464	439	12	for	for	ADP
fumecheng-10464	439	13	demonstrating	demonstrate	VERB
fumecheng-10464	439	14	a	a	DET
fumecheng-10464	439	15	dynamical	dynamical	ADJ
fumecheng-10464	439	16	system	system	NOUN
fumecheng-10464	439	17	having	have	VERB
fumecheng-10464	439	18	a	a	DET
fumecheng-10464	439	19	single	single	ADJ
fumecheng-10464	439	20	unstable	unstable	ADJ
fumecheng-10464	439	21	fixed	fix	VERB
fumecheng-10464	439	22	point	point	NOUN
fumecheng-10464	439	23	and	and	CCONJ
fumecheng-10464	439	24	a	a	DET
fumecheng-10464	439	25	single	single	ADJ
fumecheng-10464	439	26	stable	stable	ADJ
fumecheng-10464	439	27	limit	limit	NOUN
fumecheng-10464	439	28	cycle	cycle	NOUN
fumecheng-10464	439	29	.	.	PUNCT
fumecheng-10464	440	1	the	the	DET
fumecheng-10464	440	2	forced	force	VERB
fumecheng-10464	440	3	dvdp	dvdp	NOUN
fumecheng-10464	440	4	does	do	AUX
fumecheng-10464	440	5	not	not	PART
fumecheng-10464	440	6	have	have	VERB
fumecheng-10464	440	7	global	global	ADJ
fumecheng-10464	440	8	analytical	analytical	ADJ
fumecheng-10464	440	9	first	first	ADJ
fumecheng-10464	440	10	integrals	integral	NOUN
fumecheng-10464	440	11	.	.	PUNCT
fumecheng-10464	441	1	this	this	DET
fumecheng-10464	441	2	classical	classical	ADJ
fumecheng-10464	441	3	technique	technique	NOUN
fumecheng-10464	441	4	of	of	ADP
fumecheng-10464	441	5	he	he	NOUN
fumecheng-10464	441	6	-	-	PUNCT
fumecheng-10464	441	7	laplace	laplace	NOUN
fumecheng-10464	441	8	does	do	AUX
fumecheng-10464	441	9	not	not	PART
fumecheng-10464	441	10	have	have	VERB
fumecheng-10464	441	11	any	any	DET
fumecheng-10464	441	12	authority	authority	NOUN
fumecheng-10464	441	13	to	to	PART
fumecheng-10464	441	14	avoid	avoid	VERB
fumecheng-10464	441	15	the	the	DET
fumecheng-10464	441	16	presence	presence	NOUN
fumecheng-10464	441	17	of	of	ADP
fumecheng-10464	441	18	the	the	DET
fumecheng-10464	441	19	secular	secular	ADJ
fumecheng-10464	441	20	terms	term	NOUN
fumecheng-10464	441	21	that	that	PRON
fumecheng-10464	441	22	have	have	AUX
fumecheng-10464	441	23	been	be	AUX
fumecheng-10464	441	24	assimilated	assimilate	VERB
fumecheng-10464	441	25	during	during	ADP
fumecheng-10464	441	26	obtaining	obtain	VERB
fumecheng-10464	441	27	the	the	DET
fumecheng-10464	441	28	approximate	approximate	ADJ
fumecheng-10464	441	29	solution	solution	NOUN
fumecheng-10464	441	30	.	.	PUNCT
fumecheng-10464	442	1	accordingly	accordingly	ADV
fumecheng-10464	442	2	,	,	PUNCT
fumecheng-10464	442	3	the	the	DET
fumecheng-10464	442	4	resulting	result	VERB
fumecheng-10464	442	5	approximate	approximate	ADJ
fumecheng-10464	442	6	solution	solution	NOUN
fumecheng-10464	442	7	has	have	VERB
fumecheng-10464	442	8	an	an	DET
fumecheng-10464	442	9	increased	increase	VERB
fumecheng-10464	442	10	amplitude	amplitude	NOUN
fumecheng-10464	442	11	with	with	ADP
fumecheng-10464	442	12	the	the	DET
fumecheng-10464	442	13	increase	increase	NOUN
fumecheng-10464	442	14	of	of	ADP
fumecheng-10464	442	15	time	time	NOUN
fumecheng-10464	442	16	.	.	PUNCT
fumecheng-10464	443	1	on	on	ADP
fumecheng-10464	443	2	the	the	DET
fumecheng-10464	443	3	other	other	ADJ
fumecheng-10464	443	4	hand	hand	NOUN
fumecheng-10464	443	5	,	,	PUNCT
fumecheng-10464	443	6	the	the	DET
fumecheng-10464	443	7	bounded	bounded	ADJ
fumecheng-10464	443	8	solution	solution	NOUN
fumecheng-10464	443	9	is	be	AUX
fumecheng-10464	443	10	accomplished	accomplish	VERB
fumecheng-10464	443	11	by	by	ADP
fumecheng-10464	443	12	means	mean	NOUN
fumecheng-10464	443	13	of	of	ADP
fumecheng-10464	443	14	nonlinear	nonlinear	ADJ
fumecheng-10464	443	15	frequency	frequency	NOUN
fumecheng-10464	443	16	analysis	analysis	NOUN
fumecheng-10464	443	17	.	.	PUNCT
fumecheng-10464	444	1	actually	actually	ADV
fumecheng-10464	444	2	,	,	PUNCT
fumecheng-10464	444	3	this	this	DET
fumecheng-10464	444	4	approach	approach	NOUN
fumecheng-10464	444	5	is	be	AUX
fumecheng-10464	444	6	easy	easy	ADJ
fumecheng-10464	444	7	,	,	PUNCT
fumecheng-10464	444	8	straightforward	straightforward	ADJ
fumecheng-10464	444	9	,	,	PUNCT
fumecheng-10464	444	10	powerful	powerful	ADJ
fumecheng-10464	444	11	,	,	PUNCT
fumecheng-10464	444	12	and	and	CCONJ
fumecheng-10464	444	13	promising	promise	VERB
fumecheng-10464	444	14	.	.	PUNCT
fumecheng-10464	445	1	it	it	PRON
fumecheng-10464	445	2	may	may	AUX
fumecheng-10464	445	3	be	be	AUX
fumecheng-10464	445	4	applied	apply	VERB
fumecheng-10464	445	5	to	to	PART
fumecheng-10464	445	6	analyze	analyze	VERB
fumecheng-10464	445	7	different	different	ADJ
fumecheng-10464	445	8	types	type	NOUN
fumecheng-10464	445	9	of	of	ADP
fumecheng-10464	445	10	highly	highly	ADV
fumecheng-10464	445	11	nonlinear	nonlinear	ADJ
fumecheng-10464	445	12	problems	problem	NOUN
fumecheng-10464	445	13	.	.	PUNCT
fumecheng-10464	446	1	through	through	ADP
fumecheng-10464	446	2	this	this	DET
fumecheng-10464	446	3	method	method	NOUN
fumecheng-10464	446	4	,	,	PUNCT
fumecheng-10464	446	5	a	a	DET
fumecheng-10464	446	6	dispersion	dispersion	NOUN
fumecheng-10464	446	7	relation	relation	NOUN
fumecheng-10464	446	8	that	that	PRON
fumecheng-10464	446	9	guarantees	guarantee	VERB
fumecheng-10464	446	10	the	the	DET
fumecheng-10464	446	11	periodic	periodic	ADJ
fumecheng-10464	446	12	nature	nature	NOUN
fumecheng-10464	446	13	of	of	ADP
fumecheng-10464	446	14	the	the	DET
fumecheng-10464	446	15	solution	solution	NOUN
fumecheng-10464	446	16	is	be	AUX
fumecheng-10464	446	17	reached	reach	VERB
fumecheng-10464	446	18	.	.	PUNCT
fumecheng-10464	447	1	once	once	ADV
fumecheng-10464	447	2	more	more	ADJ
fumecheng-10464	447	3	,	,	PUNCT
fumecheng-10464	447	4	the	the	DET
fumecheng-10464	447	5	hpm	hpm	NOUN
fumecheng-10464	447	6	is	be	AUX
fumecheng-10464	447	7	utilized	utilize	VERB
fumecheng-10464	447	8	to	to	PART
fumecheng-10464	447	9	realize	realize	VERB
fumecheng-10464	447	10	an	an	DET
fumecheng-10464	447	11	approximate	approximate	ADJ
fumecheng-10464	447	12	solution	solution	NOUN
fumecheng-10464	447	13	of	of	ADP
fumecheng-10464	447	14	this	this	DET
fumecheng-10464	447	15	characteristic	characteristic	ADJ
fumecheng-10464	447	16	equation	equation	NOUN
fumecheng-10464	447	17	.	.	PUNCT
fumecheng-10464	448	1	simultaneously	simultaneously	ADV
fumecheng-10464	448	2	,	,	PUNCT
fumecheng-10464	448	3	stability	stability	NOUN
fumecheng-10464	448	4	restrictions	restriction	NOUN
fumecheng-10464	448	5	are	be	AUX
fumecheng-10464	448	6	addressed	address	VERB
fumecheng-10464	448	7	.	.	PUNCT
fumecheng-10464	449	1	the	the	DET
fumecheng-10464	449	2	periodic	periodic	ADJ
fumecheng-10464	449	3	solution	solution	NOUN
fumecheng-10464	449	4	,	,	PUNCT
fumecheng-10464	449	5	in	in	ADP
fumecheng-10464	449	6	light	light	NOUN
fumecheng-10464	449	7	of	of	ADP
fumecheng-10464	449	8	the	the	DET
fumecheng-10464	449	9	second	second	ADJ
fumecheng-10464	449	10	method	method	NOUN
fumecheng-10464	449	11	,	,	PUNCT
fumecheng-10464	449	12	is	be	AUX
fumecheng-10464	449	13	graphed	graph	VERB
fumecheng-10464	449	14	.	.	PUNCT
fumecheng-10464	450	1	by	by	ADP
fumecheng-10464	450	2	means	mean	NOUN
fumecheng-10464	450	3	of	of	ADP
fumecheng-10464	450	4	the	the	DET
fumecheng-10464	450	5	linearized	linearize	VERB
fumecheng-10464	450	6	stability	stability	NOUN
fumecheng-10464	450	7	analysis	analysis	NOUN
fumecheng-10464	450	8	,	,	PUNCT
fumecheng-10464	450	9	the	the	DET
fumecheng-10464	450	10	stability	stability	NOUN
fumecheng-10464	450	11	criterion	criterion	NOUN
fumecheng-10464	450	12	of	of	ADP
fumecheng-10464	450	13	the	the	DET
fumecheng-10464	450	14	autonomous	autonomous	ADJ
fumecheng-10464	450	15	system	system	NOUN
fumecheng-10464	450	16	is	be	AUX
fumecheng-10464	450	17	carried	carry	VERB
fumecheng-10464	450	18	out	out	ADP
fumecheng-10464	450	19	.	.	PUNCT
fumecheng-10464	451	1	finally	finally	ADV
fumecheng-10464	451	2	,	,	PUNCT
fumecheng-10464	451	3	the	the	DET
fumecheng-10464	451	4	multiple	multiple	ADJ
fumecheng-10464	451	5	time	time	NOUN
fumecheng-10464	451	6	scales	scale	VERB
fumecheng-10464	451	7	together	together	ADV
fumecheng-10464	451	8	with	with	ADP
fumecheng-10464	451	9	the	the	DET
fumecheng-10464	451	10	homotopy	homotopy	NOUN
fumecheng-10464	451	11	concept	concept	NOUN
fumecheng-10464	451	12	are	be	AUX
fumecheng-10464	451	13	used	use	VERB
fumecheng-10464	451	14	to	to	PART
fumecheng-10464	451	15	govern	govern	VERB
fumecheng-10464	451	16	those	those	DET
fumecheng-10464	451	17	stability	stability	NOUN
fumecheng-10464	451	18	criteria	criterion	NOUN
fumecheng-10464	451	19	of	of	ADP
fumecheng-10464	451	20	the	the	DET
fumecheng-10464	451	21	whole	whole	ADJ
fumecheng-10464	451	22	system	system	NOUN
fumecheng-10464	451	23	.	.	PUNCT
fumecheng-10464	452	1	the	the	DET
fumecheng-10464	452	2	latter	latter	ADJ
fumecheng-10464	452	3	analyses	analysis	NOUN
fumecheng-10464	452	4	include	include	VERB
fumecheng-10464	452	5	the	the	DET
fumecheng-10464	452	6	resonance	resonance	NOUN
fumecheng-10464	452	7	as	as	ADV
fumecheng-10464	452	8	well	well	ADV
fumecheng-10464	452	9	as	as	ADP
fumecheng-10464	452	10	the	the	DET
fumecheng-10464	452	11	non	non	ADJ
fumecheng-10464	452	12	-	-	ADJ
fumecheng-10464	452	13	resonance	resonance	ADJ
fumecheng-10464	452	14	cases	case	NOUN
fumecheng-10464	452	15	.	.	PUNCT
fumecheng-10464	453	1	it	it	PRON
fumecheng-10464	453	2	is	be	AUX
fumecheng-10464	453	3	concluded	conclude	VERB
fumecheng-10464	453	4	that	that	SCONJ
fumecheng-10464	453	5	the	the	DET
fumecheng-10464	453	6	multiple	multiple	ADJ
fumecheng-10464	453	7	scales	scale	NOUN
fumecheng-10464	453	8	method	method	NOUN
fumecheng-10464	453	9	is	be	AUX
fumecheng-10464	453	10	one	one	NUM
fumecheng-10464	453	11	the	the	DET
fumecheng-10464	453	12	most	most	ADV
fumecheng-10464	453	13	powerful	powerful	ADJ
fumecheng-10464	453	14	mathematical	mathematical	ADJ
fumecheng-10464	453	15	tool	tool	NOUN
fumecheng-10464	453	16	in	in	ADP
fumecheng-10464	453	17	analyzing	analyze	VERB
fumecheng-10464	453	18	the	the	DET
fumecheng-10464	453	19	nonlinear	nonlinear	ADJ
fumecheng-10464	453	20	oscillation	oscillation	NOUN
fumecheng-10464	453	21	system	system	NOUN
fumecheng-10464	453	22	that	that	PRON
fumecheng-10464	453	23	arises	arise	VERB
fumecheng-10464	453	24	in	in	ADP
fumecheng-10464	453	25	physical	physical	ADJ
fumecheng-10464	453	26	applications	application	NOUN
fumecheng-10464	453	27	and	and	CCONJ
fumecheng-10464	453	28	engineering	engineering	NOUN
fumecheng-10464	453	29	.	.	PUNCT
fumecheng-10464	454	1	overall	overall	ADV
fumecheng-10464	454	2	,	,	PUNCT
fumecheng-10464	454	3	the	the	DET
fumecheng-10464	454	4	concluding	concluding	NOUN
fumecheng-10464	454	5	remarks	remark	NOUN
fumecheng-10464	454	6	of	of	ADP
fumecheng-10464	454	7	the	the	DET
fumecheng-10464	454	8	present	present	ADJ
fumecheng-10464	454	9	work	work	NOUN
fumecheng-10464	454	10	may	may	AUX
fumecheng-10464	454	11	be	be	AUX
fumecheng-10464	454	12	summarized	summarize	VERB
fumecheng-10464	454	13	as	as	SCONJ
fumecheng-10464	454	14	follows	follow	VERB
fumecheng-10464	454	15	:	:	PUNCT
fumecheng-10464	454	16	▪	▪	NOUN
fumecheng-10464	454	17	from	from	ADP
fumecheng-10464	454	18	the	the	DET
fumecheng-10464	454	19	mathematical	mathematical	ADJ
fumecheng-10464	454	20	analysis	analysis	NOUN
fumecheng-10464	454	21	of	of	ADP
fumecheng-10464	454	22	the	the	DET
fumecheng-10464	454	23	nonlinear	nonlinear	ADJ
fumecheng-10464	454	24	expanded	expand	VERB
fumecheng-10464	454	25	frequency	frequency	NOUN
fumecheng-10464	454	26	,	,	PUNCT
fumecheng-10464	454	27	one	one	PRON
fumecheng-10464	454	28	finds	find	VERB
fumecheng-10464	454	29	▪	▪	NOUN
fumecheng-10464	454	30	to	to	PART
fumecheng-10464	454	31	maintain	maintain	VERB
fumecheng-10464	454	32	the	the	DET
fumecheng-10464	454	33	presence	presence	NOUN
fumecheng-10464	454	34	of	of	ADP
fumecheng-10464	454	35	the	the	DET
fumecheng-10464	454	36	cubic	cubic	ADJ
fumecheng-10464	454	37	stiffness	stiffness	NOUN
fumecheng-10464	454	38	parameter	parameter	PROPN
fumecheng-10464	454	39	µ	µ	NOUN
fumecheng-10464	454	40	in	in	ADP
fumecheng-10464	454	41	the	the	DET
fumecheng-10464	454	42	stability	stability	NOUN
fumecheng-10464	454	43	criterion	criterion	NOUN
fumecheng-10464	454	44	,	,	PUNCT
fumecheng-10464	454	45	a	a	DET
fumecheng-10464	454	46	modification	modification	NOUN
fumecheng-10464	454	47	of	of	ADP
fumecheng-10464	454	48	the	the	DET
fumecheng-10464	454	49	initial	initial	ADJ
fumecheng-10464	454	50	conditions	condition	NOUN
fumecheng-10464	454	51	has	have	AUX
fumecheng-10464	454	52	been	be	AUX
fumecheng-10464	454	53	made	make	VERB
fumecheng-10464	454	54	.	.	PUNCT
fumecheng-10464	455	1	▪	▪	NOUN
fumecheng-10464	455	2	the	the	DET
fumecheng-10464	455	3	criterion	criterion	NOUN
fumecheng-10464	455	4	of	of	ADP
fumecheng-10464	455	5	the	the	DET
fumecheng-10464	455	6	analytical	analytical	ADJ
fumecheng-10464	455	7	bounded	bound	VERB
fumecheng-10464	455	8	approximate	approximate	ADJ
fumecheng-10464	455	9	solution	solution	NOUN
fumecheng-10464	455	10	is	be	AUX
fumecheng-10464	455	11	given	give	VERB
fumecheng-10464	455	12	as	as	ADP
fumecheng-10464	455	13	36β−µ2>0	36β−µ2>0	NUM
fumecheng-10464	455	14	.	.	PUNCT
fumecheng-10464	455	15	▪	▪	NOUN
fumecheng-10464	455	16	in	in	ADP
fumecheng-10464	455	17	accordance	accordance	NOUN
fumecheng-10464	455	18	with	with	ADP
fumecheng-10464	455	19	the	the	DET
fumecheng-10464	455	20	multiple	multiple	ADJ
fumecheng-10464	455	21	scales	scale	NOUN
fumecheng-10464	455	22	method	method	NOUN
fumecheng-10464	455	23	,	,	PUNCT
fumecheng-10464	455	24	the	the	DET
fumecheng-10464	455	25	following	follow	VERB
fumecheng-10464	455	26	outcomes	outcome	NOUN
fumecheng-10464	455	27	are	be	AUX
fumecheng-10464	455	28	reached	reach	VERB
fumecheng-10464	455	29	:	:	PUNCT
fumecheng-10464	455	30	▪	▪	X
fumecheng-10464	455	31	the	the	DET
fumecheng-10464	455	32	stability	stability	NOUN
fumecheng-10464	455	33	criterion	criterion	NOUN
fumecheng-10464	455	34	in	in	ADP
fumecheng-10464	455	35	the	the	DET
fumecheng-10464	455	36	non	non	ADJ
fumecheng-10464	455	37	-	-	ADJ
fumecheng-10464	455	38	resonance	resonance	NOUN
fumecheng-10464	455	39	case	case	NOUN
fumecheng-10464	455	40	,	,	PUNCT
fumecheng-10464	455	41	regardless	regardless	ADV
fumecheng-10464	455	42	of	of	ADP
fumecheng-10464	455	43	the	the	DET
fumecheng-10464	455	44	sign	sign	NOUN
fumecheng-10464	455	45	of	of	ADP
fumecheng-10464	455	46	the	the	DET
fumecheng-10464	455	47	parameter	parameter	NOUN
fumecheng-10464	455	48	β	β	PROPN
fumecheng-10464	455	49	,	,	PUNCT
fumecheng-10464	455	50	requires	require	VERB
fumecheng-10464	455	51	that	that	SCONJ
fumecheng-10464	455	52	µ>0	µ>0	NOUN
fumecheng-10464	455	53	.	.	PUNCT
fumecheng-10464	455	54	▪	▪	NOUN
fumecheng-10464	455	55	the	the	DET
fumecheng-10464	455	56	stability	stability	NOUN
fumecheng-10464	455	57	criterion	criterion	NOUN
fumecheng-10464	455	58	,	,	PUNCT
fumecheng-10464	455	59	in	in	ADP
fumecheng-10464	455	60	the	the	DET
fumecheng-10464	455	61	resonance	resonance	NOUN
fumecheng-10464	455	62	case	case	NOUN
fumecheng-10464	455	63	,	,	PUNCT
fumecheng-10464	455	64	needs	need	VERB
fumecheng-10464	455	65	µ(2ω−2−3β	µ(2ω−2−3β	NOUN
fumecheng-10464	455	66	)	)	PUNCT
fumecheng-10464	455	67	β	β	X
fumecheng-10464	455	68	<	<	X
fumecheng-10464	455	69	0	0	NUM
fumecheng-10464	455	70	.	.	PUNCT
fumecheng-10464	455	71	▪	▪	NOUN
fumecheng-10464	455	72	because	because	SCONJ
fumecheng-10464	455	73	the	the	DET
fumecheng-10464	455	74	natural	natural	ADJ
fumecheng-10464	455	75	frequency	frequency	NOUN
fumecheng-10464	455	76	of	of	ADP
fumecheng-10464	455	77	the	the	DET
fumecheng-10464	455	78	considered	consider	VERB
fumecheng-10464	455	79	system	system	NOUN
fumecheng-10464	455	80	is	be	AUX
fumecheng-10464	455	81	the	the	DET
fumecheng-10464	455	82	unity	unity	NOUN
fumecheng-10464	455	83	,	,	PUNCT
fumecheng-10464	455	84	the	the	DET
fumecheng-10464	455	85	parameter	parameter	PROPN
fumecheng-10464	455	86	ω	ω	PROPN
fumecheng-10464	455	87	has	have	VERB
fumecheng-10464	455	88	no	no	DET
fumecheng-10464	455	89	implication	implication	NOUN
fumecheng-10464	455	90	on	on	ADP
fumecheng-10464	455	91	the	the	DET
fumecheng-10464	455	92	stability	stability	NOUN
fumecheng-10464	455	93	configuration	configuration	NOUN
fumecheng-10464	455	94	.	.	PUNCT
fumecheng-10464	456	1	▪	▪	X
fumecheng-10464	456	2	the	the	DET
fumecheng-10464	456	3	numerical	numerical	ADJ
fumecheng-10464	456	4	calculations	calculation	NOUN
fumecheng-10464	456	5	of	of	ADP
fumecheng-10464	456	6	the	the	DET
fumecheng-10464	456	7	previous	previous	ADJ
fumecheng-10464	456	8	stability	stability	NOUN
fumecheng-10464	456	9	criterion	criterion	NOUN
fumecheng-10464	456	10	show	show	VERB
fumecheng-10464	456	11	a	a	DET
fumecheng-10464	456	12	dual	dual	ADJ
fumecheng-10464	456	13	role	role	NOUN
fumecheng-10464	456	14	of	of	ADP
fumecheng-10464	456	15	both	both	CCONJ
fumecheng-10464	456	16	the	the	DET
fumecheng-10464	456	17	parameters	parameter	NOUN
fumecheng-10464	456	18	β	β	X
fumecheng-10464	456	19	and	and	CCONJ
fumecheng-10464	456	20	ω	ω	X
fumecheng-10464	456	21	.	.	PUNCT
fumecheng-10464	457	1	these	these	DET
fumecheng-10464	457	2	mechanisms	mechanism	NOUN
fumecheng-10464	457	3	depend	depend	VERB
fumecheng-10464	457	4	mainly	mainly	ADV
fumecheng-10464	457	5	on	on	ADP
fumecheng-10464	457	6	the	the	DET
fumecheng-10464	457	7	sign	sign	NOUN
fumecheng-10464	457	8	of	of	ADP
fumecheng-10464	457	9	the	the	DET
fumecheng-10464	457	10	parameter	parameter	NOUN
fumecheng-10464	457	11	µ.	µ.	NOUN
fumecheng-10464	457	12	▪	▪	ADV
fumecheng-10464	457	13	unfortunately	unfortunately	ADV
fumecheng-10464	457	14	,	,	PUNCT
fumecheng-10464	457	15	through	through	ADP
fumecheng-10464	457	16	the	the	DET
fumecheng-10464	457	17	multiple	multiple	ADJ
fumecheng-10464	457	18	time	time	NOUN
fumecheng-10464	457	19	scale	scale	NOUN
fumecheng-10464	457	20	method	method	NOUN
fumecheng-10464	457	21	,	,	PUNCT
fumecheng-10464	457	22	the	the	DET
fumecheng-10464	457	23	stability	stability	NOUN
fumecheng-10464	457	24	criteria	criterion	NOUN
fumecheng-10464	457	25	are	be	AUX
fumecheng-10464	457	26	independent	independent	ADJ
fumecheng-10464	457	27	of	of	ADP
fumecheng-10464	457	28	the	the	DET
fumecheng-10464	457	29	influence	influence	NOUN
fumecheng-10464	457	30	of	of	ADP
fumecheng-10464	457	31	the	the	DET
fumecheng-10464	457	32	parameter	parameter	NOUN
fumecheng-10464	457	33	f.	f.	PROPN
fumecheng-10464	457	34	18	18	NUM
fumecheng-10464	457	35	j.-h	j.-h	NOUN
fumecheng-10464	457	36	.	.	PUNCT
fumecheng-10464	458	1	he	he	PRON
fumecheng-10464	458	2	,	,	PUNCT
fumecheng-10464	458	3	g.	g.	PROPN
fumecheng-10464	458	4	m.	m.	PROPN
fumecheng-10464	458	5	moatimid	moatimid	PROPN
fumecheng-10464	458	6	,	,	PUNCT
fumecheng-10464	458	7	m.	m.	PROPN
fumecheng-10464	458	8	h.	h.	PROPN
fumecheng-10464	458	9	zekry	zekry	PROPN
fumecheng-10464	458	10	references	reference	NOUN
fumecheng-10464	458	11	1	1	NUM
fumecheng-10464	458	12	.	.	PUNCT
fumecheng-10464	459	1	zuo	zuo	NOUN
fumecheng-10464	459	2	,	,	PUNCT
fumecheng-10464	459	3	y.-t	y.-t	NOUN
fumecheng-10464	459	4	.	.	PUNCT
fumecheng-10464	459	5	,	,	PUNCT
fumecheng-10464	459	6	2021	2021	NUM
fumecheng-10464	459	7	,	,	PUNCT
fumecheng-10464	459	8	a	a	DET
fumecheng-10464	459	9	gecko	gecko	NOUN
fumecheng-10464	459	10	-	-	PUNCT
fumecheng-10464	459	11	like	like	ADJ
fumecheng-10464	459	12	fractal	fractal	ADJ
fumecheng-10464	459	13	receptor	receptor	NOUN
fumecheng-10464	459	14	of	of	ADP
fumecheng-10464	459	15	a	a	DET
fumecheng-10464	459	16	three	three	NUM
fumecheng-10464	459	17	-	-	PUNCT
fumecheng-10464	459	18	dimensional	dimensional	ADJ
fumecheng-10464	459	19	printing	printing	NOUN
fumecheng-10464	459	20	technology	technology	NOUN
fumecheng-10464	459	21	:	:	PUNCT
fumecheng-10464	459	22	a	a	DET
fumecheng-10464	459	23	fractal	fractal	ADJ
fumecheng-10464	459	24	oscillator	oscillator	NOUN
fumecheng-10464	459	25	,	,	PUNCT
fumecheng-10464	459	26	journal	journal	NOUN
fumecheng-10464	459	27	of	of	ADP
fumecheng-10464	459	28	mathematical	mathematical	ADJ
fumecheng-10464	459	29	chemistry	chemistry	NOUN
fumecheng-10464	459	30	,	,	PUNCT
fumecheng-10464	459	31	59(4	59(4	NUM
fumecheng-10464	459	32	)	)	PUNCT
fumecheng-10464	459	33	,	,	PUNCT
fumecheng-10464	459	34	pp	pp	PROPN
fumecheng-10464	459	35	.	.	PUNCT
fumecheng-10464	460	1	1	1	NUM
fumecheng-10464	460	2	-	-	SYM
fumecheng-10464	460	3	10	10	NUM
fumecheng-10464	460	4	.	.	PUNCT
fumecheng-10464	461	1	2	2	NUM
fumecheng-10464	461	2	.	.	X
fumecheng-10464	461	3	elias	elias	PROPN
fumecheng-10464	461	4	-	-	PUNCT
fumecheng-10464	461	5	zuniga	zuniga	PROPN
fumecheng-10464	461	6	,	,	PUNCT
fumecheng-10464	461	7	a.	a.	NOUN
fumecheng-10464	461	8	,	,	PUNCT
fumecheng-10464	461	9	palacios	palacio	NOUN
fumecheng-10464	461	10	-	-	PUNCT
fumecheng-10464	461	11	pineda	pineda	PROPN
fumecheng-10464	461	12	,	,	PUNCT
fumecheng-10464	461	13	l.m	l.m	PROPN
fumecheng-10464	461	14	.	.	PROPN
fumecheng-10464	461	15	,	,	PUNCT
fumecheng-10464	461	16	jimenez	jimenez	PROPN
fumecheng-10464	461	17	-	-	PUNCT
fumecheng-10464	461	18	cedeno	cedeno	PROPN
fumecheng-10464	461	19	,	,	PUNCT
fumecheng-10464	461	20	i.h	i.h	PROPN
fumecheng-10464	461	21	.	.	PROPN
fumecheng-10464	461	22	,	,	PUNCT
fumecheng-10464	461	23	2021	2021	NUM
fumecheng-10464	461	24	,	,	PUNCT
fumecheng-10464	461	25	equivalent	equivalent	ADJ
fumecheng-10464	461	26	power	power	NOUN
fumecheng-10464	461	27	-	-	PUNCT
fumecheng-10464	461	28	form	form	NOUN
fumecheng-10464	461	29	representation	representation	NOUN
fumecheng-10464	461	30	of	of	ADP
fumecheng-10464	461	31	the	the	DET
fumecheng-10464	461	32	fractal	fractal	ADJ
fumecheng-10464	461	33	toda	toda	PROPN
fumecheng-10464	461	34	oscillator	oscillator	PROPN
fumecheng-10464	461	35	,	,	PUNCT
fumecheng-10464	461	36	fractals	fractal	NOUN
fumecheng-10464	461	37	,	,	PUNCT
fumecheng-10464	461	38	29(1	29(1	NUM
fumecheng-10464	461	39	)	)	PUNCT
fumecheng-10464	461	40	,	,	PUNCT
fumecheng-10464	461	41	2150019	2150019	NUM
fumecheng-10464	461	42	.	.	PUNCT
fumecheng-10464	462	1	3	3	X
fumecheng-10464	462	2	.	.	X
fumecheng-10464	462	3	tian	tian	PROPN
fumecheng-10464	462	4	,	,	PUNCT
fumecheng-10464	462	5	d.	d.	PROPN
fumecheng-10464	462	6	,	,	PUNCT
fumecheng-10464	462	7	ain	ain	PROPN
fumecheng-10464	462	8	,	,	PUNCT
fumecheng-10464	462	9	q.t	q.t	PROPN
fumecheng-10464	462	10	.	.	PROPN
fumecheng-10464	462	11	,	,	PUNCT
fumecheng-10464	462	12	anjum	anjum	PROPN
fumecheng-10464	462	13	,	,	PUNCT
fumecheng-10464	462	14	n.	n.	PROPN
fumecheng-10464	462	15	,	,	PUNCT
fumecheng-10464	462	16	he	he	PRON
fumecheng-10464	462	17	,	,	PUNCT
fumecheng-10464	462	18	c	c	X
fumecheng-10464	462	19	-	-	PUNCT
fumecheng-10464	462	20	h	h	NOUN
fumecheng-10464	462	21	,	,	PUNCT
fumecheng-10464	462	22	cheng	cheng	PROPN
fumecheng-10464	462	23	,	,	PUNCT
fumecheng-10464	462	24	b.	b.	PROPN
fumecheng-10464	462	25	,	,	PUNCT
fumecheng-10464	462	26	2020	2020	NUM
fumecheng-10464	462	27	,	,	PUNCT
fumecheng-10464	462	28	fractal	fractal	ADJ
fumecheng-10464	462	29	n	n	CCONJ
fumecheng-10464	462	30	/	/	SYM
fumecheng-10464	462	31	mems	mem	NOUN
fumecheng-10464	462	32	:	:	PUNCT
fumecheng-10464	462	33	from	from	ADP
fumecheng-10464	462	34	the	the	DET
fumecheng-10464	462	35	pull	pull	NOUN
fumecheng-10464	462	36	-	-	PUNCT
fumecheng-10464	462	37	in	in	ADP
fumecheng-10464	462	38	instability	instability	NOUN
fumecheng-10464	462	39	to	to	PART
fumecheng-10464	462	40	pull	pull	VERB
fumecheng-10464	462	41	-	-	PUNCT
fumecheng-10464	462	42	in	in	ADP
fumecheng-10464	462	43	stability	stability	NOUN
fumecheng-10464	462	44	,	,	PUNCT
fumecheng-10464	462	45	fractals	fractal	NOUN
fumecheng-10464	462	46	,	,	PUNCT
fumecheng-10464	462	47	29(2	29(2	NUM
fumecheng-10464	462	48	)	)	PUNCT
fumecheng-10464	462	49	,	,	PUNCT
fumecheng-10464	462	50	2150030	2150030	NUM
fumecheng-10464	462	51	.	.	PUNCT
fumecheng-10464	463	1	4	4	X
fumecheng-10464	463	2	.	.	X
fumecheng-10464	463	3	tian	tian	PROPN
fumecheng-10464	463	4	,	,	PUNCT
fumecheng-10464	463	5	d.	d.	PROPN
fumecheng-10464	463	6	,	,	PUNCT
fumecheng-10464	463	7	he	he	PRON
fumecheng-10464	463	8	,	,	PUNCT
fumecheng-10464	463	9	c.h	c.h	PROPN
fumecheng-10464	463	10	.	.	PROPN
fumecheng-10464	463	11	,	,	PUNCT
fumecheng-10464	463	12	2021	2021	NUM
fumecheng-10464	463	13	,	,	PUNCT
fumecheng-10464	463	14	a	a	DET
fumecheng-10464	463	15	fractal	fractal	ADJ
fumecheng-10464	463	16	micro	micro	ADJ
fumecheng-10464	463	17	-	-	ADJ
fumecheng-10464	463	18	electromechanical	electromechanical	ADJ
fumecheng-10464	463	19	system	system	NOUN
fumecheng-10464	463	20	and	and	CCONJ
fumecheng-10464	463	21	its	its	PRON
fumecheng-10464	463	22	pull	pull	NOUN
fumecheng-10464	463	23	-	-	PUNCT
fumecheng-10464	463	24	in	in	ADP
fumecheng-10464	463	25	stability	stability	NOUN
fumecheng-10464	463	26	,	,	PUNCT
fumecheng-10464	463	27	journal	journal	NOUN
fumecheng-10464	463	28	of	of	ADP
fumecheng-10464	463	29	low	low	ADJ
fumecheng-10464	463	30	frequency	frequency	NOUN
fumecheng-10464	463	31	noise	noise	NOUN
fumecheng-10464	463	32	,	,	PUNCT
fumecheng-10464	463	33	vibration	vibration	NOUN
fumecheng-10464	463	34	and	and	CCONJ
fumecheng-10464	463	35	active	active	ADJ
fumecheng-10464	463	36	control	control	NOUN
fumecheng-10464	463	37	,	,	PUNCT
fumecheng-10464	463	38	40(3	40(3	NUM
fumecheng-10464	463	39	)	)	PUNCT
fumecheng-10464	463	40	,	,	PUNCT
fumecheng-10464	463	41	pp	pp	ADP
fumecheng-10464	463	42	.	.	PUNCT
fumecheng-10464	464	1	1380	1380	NUM
fumecheng-10464	464	2	-	-	SYM
fumecheng-10464	464	3	1386	1386	NUM
fumecheng-10464	464	4	.	.	PUNCT
fumecheng-10464	465	1	5	5	NUM
fumecheng-10464	465	2	.	.	X
fumecheng-10464	465	3	he	he	PRON
fumecheng-10464	465	4	,	,	PUNCT
fumecheng-10464	465	5	j.h	j.h	PROPN
fumecheng-10464	465	6	.	.	PROPN
fumecheng-10464	465	7	,	,	PUNCT
fumecheng-10464	465	8	na	na	PROPN
fumecheng-10464	465	9	,	,	PUNCT
fumecheng-10464	465	10	q.	q.	PROPN
fumecheng-10464	465	11	,	,	PUNCT
fumecheng-10464	465	12	chun	chun	PROPN
fumecheng-10464	465	13	-	-	PUNCT
fumecheng-10464	465	14	hui	hui	PROPN
fumecheng-10464	465	15	,	,	PUNCT
fumecheng-10464	465	16	h.	h.	PROPN
fumecheng-10464	465	17	,	,	PUNCT
fumecheng-10464	465	18	khaled	khaled	PROPN
fumecheng-10464	465	19	,	,	PUNCT
fumecheng-10464	465	20	g.	g.	PROPN
fumecheng-10464	465	21	,	,	PUNCT
fumecheng-10464	465	22	2022	2022	NUM
fumecheng-10464	465	23	,	,	PUNCT
fumecheng-10464	465	24	fast	fast	ADJ
fumecheng-10464	465	25	identification	identification	NOUN
fumecheng-10464	465	26	of	of	ADP
fumecheng-10464	465	27	the	the	DET
fumecheng-10464	465	28	pull	pull	NOUN
fumecheng-10464	465	29	-	-	PUNCT
fumecheng-10464	465	30	in	in	ADP
fumecheng-10464	465	31	voltage	voltage	NOUN
fumecheng-10464	465	32	of	of	ADP
fumecheng-10464	465	33	a	a	DET
fumecheng-10464	465	34	nano	nano	NOUN
fumecheng-10464	465	35	/	/	SYM
fumecheng-10464	465	36	micro	micro	ADJ
fumecheng-10464	465	37	-	-	ADJ
fumecheng-10464	465	38	electromechanical	electromechanical	ADJ
fumecheng-10464	465	39	system	system	NOUN
fumecheng-10464	465	40	,	,	PUNCT
fumecheng-10464	465	41	journal	journal	NOUN
fumecheng-10464	465	42	of	of	ADP
fumecheng-10464	465	43	low	low	ADJ
fumecheng-10464	465	44	frequency	frequency	NOUN
fumecheng-10464	465	45	noise	noise	NOUN
fumecheng-10464	465	46	,	,	PUNCT
fumecheng-10464	465	47	vibration	vibration	NOUN
fumecheng-10464	465	48	and	and	CCONJ
fumecheng-10464	465	49	active	active	ADJ
fumecheng-10464	465	50	control	control	NOUN
fumecheng-10464	465	51	,	,	PUNCT
fumecheng-10464	465	52	doi:10.1177/14613484211068252	doi:10.1177/14613484211068252	VERB
fumecheng-10464	465	53	6	6	NUM
fumecheng-10464	465	54	.	.	PUNCT
fumecheng-10464	466	1	liu	liu	PROPN
fumecheng-10464	466	2	,	,	PUNCT
fumecheng-10464	466	3	c.	c.	PROPN
fumecheng-10464	466	4	x.	x.	PROPN
fumecheng-10464	466	5	,	,	PUNCT
fumecheng-10464	466	6	2021	2021	NUM
fumecheng-10464	466	7	,	,	PUNCT
fumecheng-10464	466	8	periodic	periodic	ADJ
fumecheng-10464	466	9	solution	solution	NOUN
fumecheng-10464	466	10	of	of	ADP
fumecheng-10464	466	11	fractal	fractal	ADJ
fumecheng-10464	466	12	phi-4	phi-4	PRON
fumecheng-10464	466	13	equation	equation	NOUN
fumecheng-10464	466	14	,	,	PUNCT
fumecheng-10464	466	15	thermal	thermal	ADJ
fumecheng-10464	466	16	science	science	NOUN
fumecheng-10464	466	17	,	,	PUNCT
fumecheng-10464	466	18	25(2b	25(2b	NUM
fumecheng-10464	466	19	)	)	PUNCT
fumecheng-10464	466	20	,	,	PUNCT
fumecheng-10464	466	21	pp	pp	ADP
fumecheng-10464	466	22	.	.	PUNCT
fumecheng-10464	466	23	1345	1345	NUM
fumecheng-10464	466	24	-	-	SYM
fumecheng-10464	466	25	1350	1350	NUM
fumecheng-10464	466	26	.	.	PUNCT
fumecheng-10464	467	1	7	7	X
fumecheng-10464	467	2	.	.	X
fumecheng-10464	467	3	wang	wang	PROPN
fumecheng-10464	467	4	,	,	PUNCT
fumecheng-10464	467	5	k.l	k.l	PROPN
fumecheng-10464	467	6	.	.	PROPN
fumecheng-10464	467	7	,	,	PUNCT
fumecheng-10464	467	8	2021	2021	NUM
fumecheng-10464	467	9	,	,	PUNCT
fumecheng-10464	467	10	he	he	PRON
fumecheng-10464	467	11	's	's	PART
fumecheng-10464	467	12	frequency	frequency	NOUN
fumecheng-10464	467	13	formulation	formulation	NOUN
fumecheng-10464	467	14	for	for	ADP
fumecheng-10464	467	15	fractal	fractal	ADJ
fumecheng-10464	467	16	nonlinear	nonlinear	ADJ
fumecheng-10464	467	17	oscillator	oscillator	NOUN
fumecheng-10464	467	18	arising	arise	VERB
fumecheng-10464	467	19	in	in	ADP
fumecheng-10464	467	20	a	a	DET
fumecheng-10464	467	21	microgravity	microgravity	NOUN
fumecheng-10464	467	22	space	space	NOUN
fumecheng-10464	467	23	,	,	PUNCT
fumecheng-10464	467	24	numerical	numerical	ADJ
fumecheng-10464	467	25	methods	method	NOUN
fumecheng-10464	467	26	for	for	ADP
fumecheng-10464	467	27	partial	partial	ADJ
fumecheng-10464	467	28	differential	differential	NOUN
fumecheng-10464	467	29	equations	equation	NOUN
fumecheng-10464	467	30	,	,	PUNCT
fumecheng-10464	467	31	37(2	37(2	PRON
fumecheng-10464	467	32	)	)	PUNCT
fumecheng-10464	467	33	,	,	PUNCT
fumecheng-10464	467	34	pp	pp	ADJ
fumecheng-10464	467	35	.	.	PUNCT
fumecheng-10464	468	1	1374	1374	NUM
fumecheng-10464	468	2	-	-	SYM
fumecheng-10464	468	3	1384	1384	NUM
fumecheng-10464	468	4	.	.	PUNCT
fumecheng-10464	469	1	8	8	NUM
fumecheng-10464	469	2	.	.	X
fumecheng-10464	470	1	wang	wang	PROPN
fumecheng-10464	470	2	,	,	PUNCT
fumecheng-10464	470	3	k.l	k.l	PROPN
fumecheng-10464	470	4	.	.	PROPN
fumecheng-10464	470	5	,	,	PUNCT
fumecheng-10464	470	6	wei	wei	PROPN
fumecheng-10464	470	7	c.	c.	PROPN
fumecheng-10464	470	8	f.	f.	PROPN
fumecheng-10464	470	9	,	,	PUNCT
fumecheng-10464	470	10	2020	2020	NUM
fumecheng-10464	470	11	,	,	PUNCT
fumecheng-10464	470	12	a	a	DET
fumecheng-10464	470	13	powerful	powerful	ADJ
fumecheng-10464	470	14	and	and	CCONJ
fumecheng-10464	470	15	simple	simple	ADJ
fumecheng-10464	470	16	frequency	frequency	NOUN
fumecheng-10464	470	17	formula	formula	NOUN
fumecheng-10464	470	18	to	to	PART
fumecheng-10464	470	19	nonlinear	nonlinear	ADJ
fumecheng-10464	470	20	fractal	fractal	ADJ
fumecheng-10464	470	21	oscillators	oscillator	NOUN
fumecheng-10464	470	22	,	,	PUNCT
fumecheng-10464	470	23	journal	journal	NOUN
fumecheng-10464	470	24	of	of	ADP
fumecheng-10464	470	25	low	low	ADJ
fumecheng-10464	470	26	frequency	frequency	NOUN
fumecheng-10464	470	27	noise	noise	NOUN
fumecheng-10464	470	28	,	,	PUNCT
fumecheng-10464	470	29	vibration	vibration	NOUN
fumecheng-10464	470	30	and	and	CCONJ
fumecheng-10464	470	31	active	active	ADJ
fumecheng-10464	470	32	control	control	NOUN
fumecheng-10464	470	33	,	,	PUNCT
fumecheng-10464	470	34	40(3	40(3	NUM
fumecheng-10464	470	35	)	)	PUNCT
fumecheng-10464	470	36	,	,	PUNCT
fumecheng-10464	470	37	pp	pp	ADP
fumecheng-10464	470	38	.	.	PUNCT
fumecheng-10464	470	39	1373	1373	NUM
fumecheng-10464	470	40	-	-	SYM
fumecheng-10464	470	41	1379	1379	NUM
fumecheng-10464	470	42	.	.	PUNCT
fumecheng-10464	471	1	9	9	NUM
fumecheng-10464	471	2	.	.	X
fumecheng-10464	471	3	elias	elias	PROPN
fumecheng-10464	471	4	-	-	PUNCT
fumecheng-10464	471	5	zuniga	zuniga	PROPN
fumecheng-10464	471	6	,	,	PUNCT
fumecheng-10464	471	7	a.	a.	PROPN
fumecheng-10464	471	8	,	,	PUNCT
fumecheng-10464	471	9	martinez	martinez	PROPN
fumecheng-10464	471	10	-	-	PUNCT
fumecheng-10464	471	11	romero	romero	PROPN
fumecheng-10464	471	12	,	,	PUNCT
fumecheng-10464	471	13	o.	o.	PROPN
fumecheng-10464	471	14	,	,	PUNCT
fumecheng-10464	471	15	trejo	trejo	PROPN
fumecheng-10464	471	16	,	,	PUNCT
fumecheng-10464	471	17	d.o	d.o	PROPN
fumecheng-10464	471	18	.	.	PROPN
fumecheng-10464	471	19	,	,	PUNCT
fumecheng-10464	471	20	palacios	palacio	NOUN
fumecheng-10464	471	21	-	-	PUNCT
fumecheng-10464	471	22	pineda	pineda	PROPN
fumecheng-10464	471	23	,	,	PUNCT
fumecheng-10464	471	24	l.m	l.m	PROPN
fumecheng-10464	471	25	.	.	PROPN
fumecheng-10464	471	26	,	,	PUNCT
fumecheng-10464	471	27	2021	2021	NUM
fumecheng-10464	471	28	,	,	PUNCT
fumecheng-10464	471	29	an	an	DET
fumecheng-10464	471	30	efficient	efficient	ADJ
fumecheng-10464	471	31	ancient	ancient	ADJ
fumecheng-10464	471	32	chinese	chinese	ADJ
fumecheng-10464	471	33	algorithm	algorithm	NOUN
fumecheng-10464	471	34	to	to	PART
fumecheng-10464	471	35	investigate	investigate	VERB
fumecheng-10464	471	36	the	the	DET
fumecheng-10464	471	37	dynamics	dynamic	NOUN
fumecheng-10464	471	38	response	response	NOUN
fumecheng-10464	471	39	of	of	ADP
fumecheng-10464	471	40	a	a	DET
fumecheng-10464	471	41	fractal	fractal	ADJ
fumecheng-10464	471	42	microgravity	microgravity	NOUN
fumecheng-10464	471	43	forced	force	VERB
fumecheng-10464	471	44	oscillator	oscillator	NOUN
fumecheng-10464	471	45	,	,	PUNCT
fumecheng-10464	471	46	accepted	accept	VERB
fumecheng-10464	471	47	in	in	ADP
fumecheng-10464	471	48	fractals	fractal	NOUN
fumecheng-10464	471	49	.	.	PUNCT
fumecheng-10464	472	1	10	10	NUM
fumecheng-10464	472	2	.	.	PUNCT
fumecheng-10464	473	1	he	he	PRON
fumecheng-10464	473	2	,	,	PUNCT
fumecheng-10464	473	3	c.h	c.h	PROPN
fumecheng-10464	473	4	.	.	PROPN
fumecheng-10464	473	5	,	,	PUNCT
fumecheng-10464	473	6	liu	liu	PROPN
fumecheng-10464	473	7	,	,	PUNCT
fumecheng-10464	473	8	c.	c.	PROPN
fumecheng-10464	473	9	,	,	PUNCT
fumecheng-10464	473	10	gepreel	gepreel	PROPN
fumecheng-10464	473	11	k.	k.	PROPN
fumecheng-10464	473	12	a.	a.	PROPN
fumecheng-10464	473	13	,	,	PUNCT
fumecheng-10464	473	14	2021	2021	NUM
fumecheng-10464	473	15	,	,	PUNCT
fumecheng-10464	473	16	low	low	ADJ
fumecheng-10464	473	17	frequency	frequency	NOUN
fumecheng-10464	473	18	property	property	NOUN
fumecheng-10464	473	19	of	of	ADP
fumecheng-10464	473	20	a	a	DET
fumecheng-10464	473	21	fractal	fractal	ADJ
fumecheng-10464	473	22	vibration	vibration	NOUN
fumecheng-10464	473	23	model	model	NOUN
fumecheng-10464	473	24	for	for	ADP
fumecheng-10464	473	25	a	a	DET
fumecheng-10464	473	26	concrete	concrete	ADJ
fumecheng-10464	473	27	beam	beam	NOUN
fumecheng-10464	473	28	,	,	PUNCT
fumecheng-10464	473	29	accepted	accept	VERB
fumecheng-10464	473	30	in	in	ADP
fumecheng-10464	473	31	fractals	fractal	NOUN
fumecheng-10464	473	32	.	.	PUNCT
fumecheng-10464	474	1	11	11	NUM
fumecheng-10464	474	2	.	.	PUNCT
fumecheng-10464	475	1	he	he	PRON
fumecheng-10464	475	2	,	,	PUNCT
fumecheng-10464	475	3	c.h	c.h	PROPN
fumecheng-10464	475	4	.	.	PROPN
fumecheng-10464	475	5	,	,	PUNCT
fumecheng-10464	475	6	liu	liu	PROPN
fumecheng-10464	475	7	.	.	PUNCT
fumecheng-10464	475	8	c.	c.	PROPN
fumecheng-10464	475	9	,	,	PUNCT
fumecheng-10464	475	10	2022	2022	NUM
fumecheng-10464	475	11	,	,	PUNCT
fumecheng-10464	475	12	a	a	DET
fumecheng-10464	475	13	modified	modify	VERB
fumecheng-10464	475	14	frequency	frequency	NOUN
fumecheng-10464	475	15	-	-	PUNCT
fumecheng-10464	475	16	amplitude	amplitude	NOUN
fumecheng-10464	475	17	formulation	formulation	NOUN
fumecheng-10464	475	18	for	for	ADP
fumecheng-10464	475	19	fractal	fractal	ADJ
fumecheng-10464	475	20	vibration	vibration	NOUN
fumecheng-10464	475	21	systems	system	NOUN
fumecheng-10464	475	22	,	,	PUNCT
fumecheng-10464	475	23	fractals	fractal	NOUN
fumecheng-10464	475	24	,	,	PUNCT
fumecheng-10464	475	25	doi	doi	NOUN
fumecheng-10464	475	26	:	:	PUNCT
fumecheng-10464	475	27	10.1142	10.1142	NUM
fumecheng-10464	475	28	/	/	SYM
fumecheng-10464	475	29	s0218348x22500463	s0218348x22500463	ADJ
fumecheng-10464	475	30	12	12	NUM
fumecheng-10464	475	31	.	.	PUNCT
fumecheng-10464	476	1	he	he	PRON
fumecheng-10464	476	2	,	,	PUNCT
fumecheng-10464	476	3	c.h	c.h	PROPN
fumecheng-10464	476	4	.	.	PROPN
fumecheng-10464	476	5	,	,	PUNCT
fumecheng-10464	476	6	liu	liu	PROPN
fumecheng-10464	476	7	,	,	PUNCT
fumecheng-10464	476	8	c.	c.	PROPN
fumecheng-10464	476	9	,	,	PUNCT
fumecheng-10464	476	10	he	he	PRON
fumecheng-10464	476	11	,	,	PUNCT
fumecheng-10464	476	12	j.	j.	PROPN
fumecheng-10464	476	13	h.	h.	PROPN
fumecheng-10464	476	14	,	,	PUNCT
fumecheng-10464	476	15	shirazi	shirazi	PROPN
fumecheng-10464	476	16	,	,	PUNCT
fumecheng-10464	476	17	a.	a.	PROPN
fumecheng-10464	476	18	h.	h.	PROPN
fumecheng-10464	476	19	,	,	PUNCT
fumecheng-10464	476	20	mohammad	mohammad	PROPN
fumecheng-10464	476	21	-	-	PUNCT
fumecheng-10464	476	22	sedighi	sedighi	PROPN
fumecheng-10464	476	23	,	,	PUNCT
fumecheng-10464	476	24	h.	h.	PROPN
fumecheng-10464	476	25	,	,	PUNCT
fumecheng-10464	476	26	2021	2021	NUM
fumecheng-10464	476	27	,	,	PUNCT
fumecheng-10464	476	28	passive	passive	ADJ
fumecheng-10464	476	29	atmospheric	atmospheric	ADJ
fumecheng-10464	476	30	water	water	NOUN
fumecheng-10464	476	31	harvesting	harvesting	NOUN
fumecheng-10464	476	32	utilizing	utilize	VERB
fumecheng-10464	476	33	an	an	DET
fumecheng-10464	476	34	ancient	ancient	ADJ
fumecheng-10464	476	35	chinese	chinese	ADJ
fumecheng-10464	476	36	ink	ink	NOUN
fumecheng-10464	476	37	slab	slab	NOUN
fumecheng-10464	476	38	and	and	CCONJ
fumecheng-10464	476	39	its	its	PRON
fumecheng-10464	476	40	possible	possible	ADJ
fumecheng-10464	476	41	applications	application	NOUN
fumecheng-10464	476	42	in	in	ADP
fumecheng-10464	476	43	modern	modern	ADJ
fumecheng-10464	476	44	architecture	architecture	NOUN
fumecheng-10464	476	45	,	,	PUNCT
fumecheng-10464	476	46	facta	facta	PROPN
fumecheng-10464	476	47	universitatis	universitatis	PROPN
fumecheng-10464	476	48	-	-	PUNCT
fumecheng-10464	476	49	series	series	NOUN
fumecheng-10464	476	50	mechanical	mechanical	ADJ
fumecheng-10464	476	51	engineering	engineering	NOUN
fumecheng-10464	476	52	,	,	PUNCT
fumecheng-10464	476	53	19(2	19(2	NUM
fumecheng-10464	476	54	)	)	PUNCT
fumecheng-10464	476	55	,	,	PUNCT
fumecheng-10464	476	56	pp	pp	PROPN
fumecheng-10464	476	57	.	.	PUNCT
fumecheng-10464	477	1	229	229	NUM
fumecheng-10464	477	2	-	-	SYM
fumecheng-10464	477	3	239	239	NUM
fumecheng-10464	477	4	.	.	PUNCT
fumecheng-10464	478	1	13	13	NUM
fumecheng-10464	478	2	.	.	PUNCT
fumecheng-10464	479	1	feng	feng	PROPN
fumecheng-10464	479	2	,	,	PUNCT
fumecheng-10464	479	3	g.q	g.q	PROPN
fumecheng-10464	479	4	.	.	PROPN
fumecheng-10464	479	5	,	,	PUNCT
fumecheng-10464	479	6	2021	2021	NUM
fumecheng-10464	479	7	,	,	PUNCT
fumecheng-10464	479	8	he	he	PRON
fumecheng-10464	479	9	’s	’	VERB
fumecheng-10464	479	10	frequency	frequency	NOUN
fumecheng-10464	479	11	formula	formula	NOUN
fumecheng-10464	479	12	to	to	ADP
fumecheng-10464	479	13	fractal	fractal	ADJ
fumecheng-10464	479	14	undamped	undampe	VERB
fumecheng-10464	479	15	duffing	duffing	NOUN
fumecheng-10464	479	16	equation	equation	NOUN
fumecheng-10464	479	17	,	,	PUNCT
fumecheng-10464	479	18	journal	journal	NOUN
fumecheng-10464	479	19	of	of	ADP
fumecheng-10464	479	20	low	low	ADJ
fumecheng-10464	479	21	frequency	frequency	NOUN
fumecheng-10464	479	22	noise	noise	NOUN
fumecheng-10464	479	23	,	,	PUNCT
fumecheng-10464	479	24	vibration	vibration	NOUN
fumecheng-10464	479	25	and	and	CCONJ
fumecheng-10464	479	26	active	active	ADJ
fumecheng-10464	479	27	control	control	NOUN
fumecheng-10464	479	28	,	,	PUNCT
fumecheng-10464	479	29	40(4	40(4	NUM
fumecheng-10464	479	30	)	)	PUNCT
fumecheng-10464	479	31	,	,	PUNCT
fumecheng-10464	479	32	pp	pp	ADP
fumecheng-10464	479	33	.	.	PUNCT
fumecheng-10464	480	1	1671	1671	NUM
fumecheng-10464	480	2	-	-	SYM
fumecheng-10464	480	3	1676	1676	NUM
fumecheng-10464	480	4	.	.	PUNCT
fumecheng-10464	481	1	14	14	NUM
fumecheng-10464	481	2	.	.	PUNCT
fumecheng-10464	482	1	elías	elías	PROPN
fumecheng-10464	482	2	-	-	PUNCT
fumecheng-10464	482	3	zúñiga	zúñiga	PROPN
fumecheng-10464	482	4	,	,	PUNCT
fumecheng-10464	482	5	a.	a.	NOUN
fumecheng-10464	482	6	,	,	PUNCT
fumecheng-10464	482	7	palacios	palacio	NOUN
fumecheng-10464	482	8	-	-	PUNCT
fumecheng-10464	482	9	pineda	pineda	PROPN
fumecheng-10464	482	10	,	,	PUNCT
fumecheng-10464	482	11	l.m	l.m	PROPN
fumecheng-10464	482	12	.	.	PROPN
fumecheng-10464	482	13	,	,	PUNCT
fumecheng-10464	482	14	jiménez	jiménez	PROPN
fumecheng-10464	482	15	-	-	PUNCT
fumecheng-10464	482	16	cedeño	cedeño	PROPN
fumecheng-10464	482	17	,	,	PUNCT
fumecheng-10464	482	18	i.h	i.h	PROPN
fumecheng-10464	482	19	.	.	PROPN
fumecheng-10464	482	20	,	,	PUNCT
fumecheng-10464	482	21	martínez	martínez	PROPN
fumecheng-10464	482	22	-	-	PUNCT
fumecheng-10464	482	23	romero	romero	PROPN
fumecheng-10464	482	24	,	,	PUNCT
fumecheng-10464	482	25	olvera	olvera	NOUN
fumecheng-10464	482	26	-	-	PUNCT
fumecheng-10464	482	27	terjo	terjo	PROPN
fumecheng-10464	482	28	,	,	PUNCT
fumecheng-10464	482	29	d.	d.	NOUN
fumecheng-10464	482	30	,	,	PUNCT
fumecheng-10464	482	31	2021	2021	NUM
fumecheng-10464	482	32	,	,	PUNCT
fumecheng-10464	482	33	analytical	analytical	ADJ
fumecheng-10464	482	34	solution	solution	NOUN
fumecheng-10464	482	35	of	of	ADP
fumecheng-10464	482	36	the	the	DET
fumecheng-10464	482	37	fractal	fractal	ADJ
fumecheng-10464	482	38	cubi	cubi	PROPN
fumecheng-10464	482	39	-	-	ADJ
fumecheng-10464	482	40	quintic	quintic	ADJ
fumecheng-10464	482	41	duffing	duffing	NOUN
fumecheng-10464	482	42	equation	equation	NOUN
fumecheng-10464	482	43	,	,	PUNCT
fumecheng-10464	482	44	fractals	fractal	NOUN
fumecheng-10464	482	45	,	,	PUNCT
fumecheng-10464	482	46	29(4	29(4	NOUN
fumecheng-10464	482	47	)	)	PUNCT
fumecheng-10464	482	48	,	,	PUNCT
fumecheng-10464	482	49	2150080	2150080	NUM
fumecheng-10464	482	50	.	.	PUNCT
fumecheng-10464	483	1	15	15	NUM
fumecheng-10464	483	2	.	.	PUNCT
fumecheng-10464	483	3	elias	elias	PROPN
fumecheng-10464	483	4	-	-	PUNCT
fumecheng-10464	483	5	zuniga	zuniga	PROPN
fumecheng-10464	483	6	,	,	PUNCT
fumecheng-10464	483	7	a.	a.	NOUN
fumecheng-10464	483	8	,	,	PUNCT
fumecheng-10464	483	9	palacios	palacio	NOUN
fumecheng-10464	483	10	-	-	PUNCT
fumecheng-10464	483	11	pineda	pineda	PROPN
fumecheng-10464	483	12	,	,	PUNCT
fumecheng-10464	483	13	l.m	l.m	PROPN
fumecheng-10464	483	14	.	.	PROPN
fumecheng-10464	483	15	,	,	PUNCT
fumecheng-10464	483	16	martinez	martinez	PROPN
fumecheng-10464	483	17	-	-	PUNCT
fumecheng-10464	483	18	romero	romero	PROPN
fumecheng-10464	483	19	,	,	PUNCT
fumecheng-10464	483	20	o.	o.	PROPN
fumecheng-10464	483	21	,	,	PUNCT
fumecheng-10464	483	22	and	and	CCONJ
fumecheng-10464	483	23	trejo	trejo	PROPN
fumecheng-10464	483	24	,	,	PUNCT
fumecheng-10464	483	25	d.o	d.o	PROPN
fumecheng-10464	483	26	.	.	PROPN
fumecheng-10464	483	27	,	,	PUNCT
fumecheng-10464	483	28	2021	2021	NUM
fumecheng-10464	483	29	,	,	PUNCT
fumecheng-10464	483	30	dynamics	dynamic	NOUN
fumecheng-10464	483	31	response	response	NOUN
fumecheng-10464	483	32	of	of	ADP
fumecheng-10464	483	33	the	the	DET
fumecheng-10464	483	34	forced	force	VERB
fumecheng-10464	483	35	fangzhu	fangzhu	NOUN
fumecheng-10464	483	36	devices	device	NOUN
fumecheng-10464	483	37	for	for	ADP
fumecheng-10464	483	38	water	water	NOUN
fumecheng-10464	483	39	collection	collection	NOUN
fumecheng-10464	483	40	from	from	ADP
fumecheng-10464	483	41	air	air	NOUN
fumecheng-10464	483	42	,	,	PUNCT
fumecheng-10464	483	43	accepted	accept	VERB
fumecheng-10464	483	44	in	in	ADP
fumecheng-10464	483	45	fractals	fractal	NOUN
fumecheng-10464	483	46	.	.	PUNCT
fumecheng-10464	484	1	16	16	NUM
fumecheng-10464	484	2	.	.	PUNCT
fumecheng-10464	485	1	he	he	PRON
fumecheng-10464	485	2	,	,	PUNCT
fumecheng-10464	485	3	j.h	j.h	PROPN
fumecheng-10464	485	4	.	.	PROPN
fumecheng-10464	485	5	,	,	PUNCT
fumecheng-10464	485	6	el	el	PROPN
fumecheng-10464	485	7	-	-	PUNCT
fumecheng-10464	485	8	dib	dib	PROPN
fumecheng-10464	485	9	,	,	PUNCT
fumecheng-10464	485	10	y.o	y.o	PROPN
fumecheng-10464	485	11	.	.	PROPN
fumecheng-10464	485	12	,	,	PUNCT
fumecheng-10464	485	13	2021	2021	NUM
fumecheng-10464	485	14	,	,	PUNCT
fumecheng-10464	485	15	a	a	DET
fumecheng-10464	485	16	tutorial	tutorial	ADJ
fumecheng-10464	485	17	introduction	introduction	NOUN
fumecheng-10464	485	18	to	to	ADP
fumecheng-10464	485	19	the	the	DET
fumecheng-10464	485	20	two	two	NUM
fumecheng-10464	485	21	-	-	PUNCT
fumecheng-10464	485	22	scale	scale	NOUN
fumecheng-10464	485	23	fractal	fractal	ADJ
fumecheng-10464	485	24	calculus	calculus	NOUN
fumecheng-10464	485	25	and	and	CCONJ
fumecheng-10464	485	26	its	its	PRON
fumecheng-10464	485	27	application	application	NOUN
fumecheng-10464	485	28	to	to	ADP
fumecheng-10464	485	29	the	the	DET
fumecheng-10464	485	30	fractal	fractal	ADJ
fumecheng-10464	485	31	zhiber	zhiber	NOUN
fumecheng-10464	485	32	-	-	PUNCT
fumecheng-10464	485	33	shabat	shabat	PROPN
fumecheng-10464	485	34	oscillator	oscillator	NOUN
fumecheng-10464	485	35	,	,	PUNCT
fumecheng-10464	485	36	fractals	fractal	NOUN
fumecheng-10464	485	37	,	,	PUNCT
fumecheng-10464	485	38	doi	doi	NOUN
fumecheng-10464	485	39	:	:	PUNCT
fumecheng-10464	485	40	10.1142	10.1142	NUM
fumecheng-10464	485	41	/	/	SYM
fumecheng-10464	485	42	s0218348x21502686	s0218348x21502686	ADJ
fumecheng-10464	485	43	.	.	PUNCT
fumecheng-10464	485	44	17	17	NUM
fumecheng-10464	485	45	.	.	PUNCT
fumecheng-10464	486	1	he	he	PRON
fumecheng-10464	486	2	,	,	PUNCT
fumecheng-10464	486	3	c.h	c.h	PROPN
fumecheng-10464	486	4	.	.	PROPN
fumecheng-10464	486	5	,	,	PUNCT
fumecheng-10464	486	6	liu	liu	PROPN
fumecheng-10464	486	7	,	,	PUNCT
fumecheng-10464	486	8	s.h	s.h	PROPN
fumecheng-10464	486	9	.	.	PROPN
fumecheng-10464	486	10	,	,	PUNCT
fumecheng-10464	486	11	liu	liu	PROPN
fumecheng-10464	486	12	,	,	PUNCT
fumecheng-10464	486	13	c.	c.	PROPN
fumecheng-10464	486	14	,	,	PUNCT
fumecheng-10464	486	15	mohammad	mohammad	PROPN
fumecheng-10464	486	16	-	-	PUNCT
fumecheng-10464	486	17	sedighi	sedighi	PROPN
fumecheng-10464	486	18	,	,	PUNCT
fumecheng-10464	486	19	h.	h.	PROPN
fumecheng-10464	486	20	,	,	PUNCT
fumecheng-10464	486	21	2021	2021	NUM
fumecheng-10464	486	22	,	,	PUNCT
fumecheng-10464	486	23	a	a	DET
fumecheng-10464	486	24	novel	novel	ADJ
fumecheng-10464	486	25	bond	bond	NOUN
fumecheng-10464	486	26	stress	stress	NOUN
fumecheng-10464	486	27	-	-	PUNCT
fumecheng-10464	486	28	slip	slip	NOUN
fumecheng-10464	486	29	model	model	NOUN
fumecheng-10464	486	30	for	for	ADP
fumecheng-10464	486	31	3	3	NUM
fumecheng-10464	486	32	-	-	SYM
fumecheng-10464	486	33	d	d	ADJ
fumecheng-10464	486	34	printed	print	VERB
fumecheng-10464	486	35	concretes	concrete	NOUN
fumecheng-10464	486	36	,	,	PUNCT
fumecheng-10464	486	37	discrete	discrete	ADJ
fumecheng-10464	486	38	and	and	CCONJ
fumecheng-10464	486	39	continuous	continuous	ADJ
fumecheng-10464	486	40	dynamical	dynamical	ADJ
fumecheng-10464	486	41	systems	system	NOUN
fumecheng-10464	486	42	s	s	PROPN
fumecheng-10464	486	43	,	,	PUNCT
fumecheng-10464	486	44	doi	doi	NOUN
fumecheng-10464	486	45	:	:	PUNCT
fumecheng-10464	486	46	10.3934	10.3934	NUM
fumecheng-10464	486	47	/	/	SYM
fumecheng-10464	486	48	dcdss.2021161	dcdss.2021161	ADJ
fumecheng-10464	486	49	18	18	NUM
fumecheng-10464	486	50	.	.	PUNCT
fumecheng-10464	487	1	wang	wang	PROPN
fumecheng-10464	487	2	,	,	PUNCT
fumecheng-10464	487	3	k.l	k.l	PROPN
fumecheng-10464	487	4	.	.	PROPN
fumecheng-10464	487	5	,	,	PUNCT
fumecheng-10464	487	6	2022	2022	NUM
fumecheng-10464	487	7	,	,	PUNCT
fumecheng-10464	487	8	exact	exact	ADJ
fumecheng-10464	487	9	solitary	solitary	ADJ
fumecheng-10464	487	10	wave	wave	NOUN
fumecheng-10464	487	11	solution	solution	NOUN
fumecheng-10464	487	12	for	for	ADP
fumecheng-10464	487	13	fractal	fractal	ADJ
fumecheng-10464	487	14	shallow	shallow	ADJ
fumecheng-10464	487	15	water	water	NOUN
fumecheng-10464	487	16	wave	wave	NOUN
fumecheng-10464	487	17	model	model	NOUN
fumecheng-10464	487	18	by	by	ADP
fumecheng-10464	487	19	he	he	PRON
fumecheng-10464	487	20	’s	’	VERB
fumecheng-10464	487	21	variational	variational	ADJ
fumecheng-10464	487	22	method	method	NOUN
fumecheng-10464	487	23	,	,	PUNCT
fumecheng-10464	487	24	modern	modern	ADJ
fumecheng-10464	487	25	physics	physics	NOUN
fumecheng-10464	487	26	letters	letter	NOUN
fumecheng-10464	487	27	b	b	NOUN
fumecheng-10464	487	28	,	,	PUNCT
fumecheng-10464	487	29	2150602	2150602	NUM
fumecheng-10464	487	30	,	,	PUNCT
fumecheng-10464	487	31	doi	doi	NOUN
fumecheng-10464	487	32	:	:	PUNCT
fumecheng-10464	487	33	10.1142	10.1142	NUM
fumecheng-10464	487	34	/	/	SYM
fumecheng-10464	487	35	s0217984921506028	s0217984921506028	NOUN
fumecheng-10464	487	36	.	.	PUNCT
fumecheng-10464	488	1	19	19	NUM
fumecheng-10464	488	2	.	.	X
fumecheng-10464	489	1	wang	wang	PROPN
fumecheng-10464	489	2	,	,	PUNCT
fumecheng-10464	489	3	k.l	k.l	PROPN
fumecheng-10464	489	4	.	.	PROPN
fumecheng-10464	489	5	,	,	PUNCT
fumecheng-10464	489	6	2022	2022	NUM
fumecheng-10464	489	7	,	,	PUNCT
fumecheng-10464	489	8	solitary	solitary	ADJ
fumecheng-10464	489	9	wave	wave	NOUN
fumecheng-10464	489	10	solution	solution	NOUN
fumecheng-10464	489	11	of	of	ADP
fumecheng-10464	489	12	nonlinear	nonlinear	ADJ
fumecheng-10464	489	13	bogoyavlenskii	bogoyavlenskii	ADJ
fumecheng-10464	489	14	system	system	NOUN
fumecheng-10464	489	15	by	by	ADP
fumecheng-10464	489	16	variational	variational	ADJ
fumecheng-10464	489	17	analysis	analysis	NOUN
fumecheng-10464	489	18	method	method	NOUN
fumecheng-10464	489	19	,	,	PUNCT
fumecheng-10464	489	20	international	international	ADJ
fumecheng-10464	489	21	journal	journal	NOUN
fumecheng-10464	489	22	of	of	ADP
fumecheng-10464	489	23	modern	modern	ADJ
fumecheng-10464	489	24	physics	physics	PROPN
fumecheng-10464	489	25	b	b	PROPN
fumecheng-10464	489	26	,	,	PUNCT
fumecheng-10464	489	27	doi	doi	NOUN
fumecheng-10464	489	28	:	:	PUNCT
fumecheng-10464	489	29	10.1142	10.1142	NUM
fumecheng-10464	489	30	/	/	SYM
fumecheng-10464	489	31	s0217979222500151	s0217979222500151	NOUN
fumecheng-10464	489	32	.	.	PUNCT
fumecheng-10464	490	1	20	20	NUM
fumecheng-10464	490	2	.	.	PUNCT
fumecheng-10464	491	1	zuo	zuo	PROPN
fumecheng-10464	491	2	,	,	PUNCT
fumecheng-10464	491	3	y.t	y.t	PROPN
fumecheng-10464	491	4	.	.	PROPN
fumecheng-10464	491	5	,	,	PUNCT
fumecheng-10464	491	6	2021	2021	NUM
fumecheng-10464	491	7	,	,	PUNCT
fumecheng-10464	491	8	effect	effect	NOUN
fumecheng-10464	491	9	of	of	ADP
fumecheng-10464	491	10	sic	sic	ADJ
fumecheng-10464	491	11	particles	particle	NOUN
fumecheng-10464	491	12	on	on	ADP
fumecheng-10464	491	13	viscosity	viscosity	NOUN
fumecheng-10464	491	14	of	of	ADP
fumecheng-10464	491	15	3d	3d	PROPN
fumecheng-10464	491	16	print	print	NOUN
fumecheng-10464	491	17	paste	paste	NOUN
fumecheng-10464	491	18	:	:	PUNCT
fumecheng-10464	491	19	a	a	DET
fumecheng-10464	491	20	fractal	fractal	ADJ
fumecheng-10464	491	21	rheological	rheological	ADJ
fumecheng-10464	491	22	model	model	NOUN
fumecheng-10464	491	23	and	and	CCONJ
fumecheng-10464	491	24	experimental	experimental	ADJ
fumecheng-10464	491	25	verification	verification	NOUN
fumecheng-10464	491	26	,	,	PUNCT
fumecheng-10464	491	27	thermal	thermal	ADJ
fumecheng-10464	491	28	science	science	NOUN
fumecheng-10464	491	29	,	,	PUNCT
fumecheng-10464	491	30	25(3	25(3	NUM
fumecheng-10464	491	31	)	)	PUNCT
fumecheng-10464	491	32	,	,	PUNCT
fumecheng-10464	491	33	pp	pp	ADJ
fumecheng-10464	491	34	.	.	PUNCT
fumecheng-10464	492	1	2403	2403	NUM
fumecheng-10464	492	2	-	-	SYM
fumecheng-10464	492	3	2407	2407	NUM
fumecheng-10464	492	4	.	.	PUNCT
fumecheng-10464	493	1	21	21	NUM
fumecheng-10464	493	2	.	.	PUNCT
fumecheng-10464	494	1	zuo	zuo	PROPN
fumecheng-10464	494	2	,	,	PUNCT
fumecheng-10464	494	3	y.t	y.t	PROPN
fumecheng-10464	494	4	.	.	PROPN
fumecheng-10464	494	5	,	,	PUNCT
fumecheng-10464	494	6	liu	liu	PROPN
fumecheng-10464	494	7	,	,	PUNCT
fumecheng-10464	494	8	h.j	h.j	PROPN
fumecheng-10464	494	9	.	.	PROPN
fumecheng-10464	494	10	,	,	PUNCT
fumecheng-10464	494	11	2021	2021	NUM
fumecheng-10464	494	12	,	,	PUNCT
fumecheng-10464	494	13	a	a	DET
fumecheng-10464	494	14	fractal	fractal	ADJ
fumecheng-10464	494	15	rheological	rheological	ADJ
fumecheng-10464	494	16	model	model	NOUN
fumecheng-10464	494	17	for	for	ADP
fumecheng-10464	494	18	sic	sic	ADJ
fumecheng-10464	494	19	paste	paste	NOUN
fumecheng-10464	494	20	using	use	VERB
fumecheng-10464	494	21	a	a	DET
fumecheng-10464	494	22	fractal	fractal	ADJ
fumecheng-10464	494	23	derivative	derivative	NOUN
fumecheng-10464	494	24	,	,	PUNCT
fumecheng-10464	494	25	journal	journal	NOUN
fumecheng-10464	494	26	of	of	ADP
fumecheng-10464	494	27	applied	applied	ADJ
fumecheng-10464	494	28	and	and	CCONJ
fumecheng-10464	494	29	computational	computational	ADJ
fumecheng-10464	494	30	mechanics	mechanic	NOUN
fumecheng-10464	494	31	,	,	PUNCT
fumecheng-10464	494	32	7	7	NUM
fumecheng-10464	494	33	,	,	PUNCT
fumecheng-10464	494	34	pp	pp	ADJ
fumecheng-10464	494	35	.	.	PUNCT
fumecheng-10464	495	1	13	13	NUM
fumecheng-10464	495	2	-	-	SYM
fumecheng-10464	495	3	18	18	NUM
fumecheng-10464	495	4	.	.	PUNCT
fumecheng-10464	496	1	22	22	NUM
fumecheng-10464	496	2	.	.	PUNCT
fumecheng-10464	497	1	zuo	zuo	NOUN
fumecheng-10464	497	2	,	,	PUNCT
fumecheng-10464	497	3	y.-t	y.-t	NOUN
fumecheng-10464	497	4	.	.	PUNCT
fumecheng-10464	497	5	,	,	PUNCT
fumecheng-10464	497	6	liu	liu	PROPN
fumecheng-10464	497	7	,	,	PUNCT
fumecheng-10464	497	8	h.-j	h.-j	PROPN
fumecheng-10464	497	9	.	.	PROPN
fumecheng-10464	497	10	,	,	PUNCT
fumecheng-10464	497	11	2021	2021	NUM
fumecheng-10464	497	12	,	,	PUNCT
fumecheng-10464	497	13	fractal	fractal	ADJ
fumecheng-10464	497	14	approach	approach	NOUN
fumecheng-10464	497	15	to	to	ADP
fumecheng-10464	497	16	mechanical	mechanical	ADJ
fumecheng-10464	497	17	and	and	CCONJ
fumecheng-10464	497	18	electrical	electrical	ADJ
fumecheng-10464	497	19	properties	property	NOUN
fumecheng-10464	497	20	of	of	ADP
fumecheng-10464	497	21	graphene	graphene	NOUN
fumecheng-10464	497	22	/	/	SYM
fumecheng-10464	497	23	sic	sic	ADJ
fumecheng-10464	497	24	composites	composite	NOUN
fumecheng-10464	497	25	,	,	PUNCT
fumecheng-10464	497	26	facta	facta	PROPN
fumecheng-10464	497	27	universitatis	universitatis	PROPN
fumecheng-10464	497	28	-	-	PUNCT
fumecheng-10464	497	29	series	series	NOUN
fumecheng-10464	497	30	mechanical	mechanical	ADJ
fumecheng-10464	497	31	engineering	engineering	NOUN
fumecheng-10464	497	32	,	,	PUNCT
fumecheng-10464	497	33	19(2	19(2	NUM
fumecheng-10464	497	34	)	)	PUNCT
fumecheng-10464	497	35	,	,	PUNCT
fumecheng-10464	497	36	pp	pp	PROPN
fumecheng-10464	497	37	.	.	PUNCT
fumecheng-10464	498	1	271	271	NUM
fumecheng-10464	498	2	-	-	SYM
fumecheng-10464	498	3	284	284	NUM
fumecheng-10464	498	4	.	.	PUNCT
fumecheng-10464	499	1	23	23	NUM
fumecheng-10464	499	2	.	.	PUNCT
fumecheng-10464	500	1	li	li	PROPN
fumecheng-10464	500	2	,	,	PUNCT
fumecheng-10464	500	3	x.j	x.j	PROPN
fumecheng-10464	500	4	.	.	PROPN
fumecheng-10464	500	5	,	,	PUNCT
fumecheng-10464	500	6	liu	liu	PROPN
fumecheng-10464	500	7	,	,	PUNCT
fumecheng-10464	500	8	z.	z.	PROPN
fumecheng-10464	500	9	,	,	PUNCT
fumecheng-10464	500	10	he	he	PRON
fumecheng-10464	500	11	,	,	PUNCT
fumecheng-10464	500	12	j.h	j.h	PROPN
fumecheng-10464	500	13	.	.	PROPN
fumecheng-10464	500	14	,	,	PUNCT
fumecheng-10464	500	15	2020	2020	NUM
fumecheng-10464	500	16	,	,	PUNCT
fumecheng-10464	500	17	a	a	DET
fumecheng-10464	500	18	fractal	fractal	ADJ
fumecheng-10464	500	19	two	two	NUM
fumecheng-10464	500	20	-	-	PUNCT
fumecheng-10464	500	21	phase	phase	NOUN
fumecheng-10464	500	22	flow	flow	NOUN
fumecheng-10464	500	23	model	model	NOUN
fumecheng-10464	500	24	for	for	ADP
fumecheng-10464	500	25	the	the	DET
fumecheng-10464	500	26	fiber	fiber	NOUN
fumecheng-10464	500	27	motion	motion	NOUN
fumecheng-10464	500	28	in	in	ADP
fumecheng-10464	500	29	a	a	DET
fumecheng-10464	500	30	polymer	polymer	NOUN
fumecheng-10464	500	31	filling	filling	NOUN
fumecheng-10464	500	32	process	process	NOUN
fumecheng-10464	500	33	,	,	PUNCT
fumecheng-10464	500	34	fractals	fractal	NOUN
fumecheng-10464	500	35	,	,	PUNCT
fumecheng-10464	500	36	28(4	28(4	NUM
fumecheng-10464	500	37	)	)	PUNCT
fumecheng-10464	500	38	,	,	PUNCT
fumecheng-10464	500	39	2050093	2050093	NUM
fumecheng-10464	500	40	.	.	PUNCT
fumecheng-10464	501	1	24	24	NUM
fumecheng-10464	501	2	.	.	PUNCT
fumecheng-10464	501	3	kang	kang	PROPN
fumecheng-10464	501	4	-	-	PUNCT
fumecheng-10464	501	5	le	le	X
fumecheng-10464	501	6	wang	wang	PROPN
fumecheng-10464	501	7	,	,	PUNCT
fumecheng-10464	501	8	2022	2022	NUM
fumecheng-10464	501	9	,	,	PUNCT
fumecheng-10464	501	10	new	new	ADJ
fumecheng-10464	501	11	variational	variational	ADJ
fumecheng-10464	501	12	theory	theory	NOUN
fumecheng-10464	501	13	for	for	ADP
fumecheng-10464	501	14	coupled	couple	VERB
fumecheng-10464	501	15	nonlinear	nonlinear	ADJ
fumecheng-10464	501	16	fractal	fractal	PROPN
fumecheng-10464	501	17	schrodinger	schrodinger	PROPN
fumecheng-10464	501	18	system	system	PROPN
fumecheng-10464	501	19	,	,	PUNCT
fumecheng-10464	501	20	international	international	ADJ
fumecheng-10464	501	21	journal	journal	NOUN
fumecheng-10464	501	22	of	of	ADP
fumecheng-10464	501	23	numerical	numerical	ADJ
fumecheng-10464	501	24	methods	method	NOUN
fumecheng-10464	501	25	for	for	ADP
fumecheng-10464	501	26	heat	heat	NOUN
fumecheng-10464	501	27	and	and	CCONJ
fumecheng-10464	501	28	fluid	fluid	ADJ
fumecheng-10464	501	29	flow	flow	NOUN
fumecheng-10464	501	30	,	,	PUNCT
fumecheng-10464	501	31	32(2	32(2	NUM
fumecheng-10464	501	32	)	)	PUNCT
fumecheng-10464	501	33	,	,	PUNCT
fumecheng-10464	501	34	pp	pp	ADP
fumecheng-10464	501	35	.	.	PUNCT
fumecheng-10464	502	1	589	589	NUM
fumecheng-10464	502	2	-	-	SYM
fumecheng-10464	502	3	597	597	NUM
fumecheng-10464	502	4	.	.	X
fumecheng-10464	503	1	25	25	NUM
fumecheng-10464	503	2	.	.	PUNCT
fumecheng-10464	504	1	liu	liu	PROPN
fumecheng-10464	504	2	,	,	PUNCT
fumecheng-10464	504	3	x.y	x.y	PROPN
fumecheng-10464	504	4	.	.	PROPN
fumecheng-10464	504	5	,	,	PUNCT
fumecheng-10464	504	6	liu	liu	PROPN
fumecheng-10464	504	7	,	,	PUNCT
fumecheng-10464	504	8	y.p	y.p	PROPN
fumecheng-10464	504	9	.	.	PROPN
fumecheng-10464	504	10	,	,	PUNCT
fumecheng-10464	504	11	wu	wu	PROPN
fumecheng-10464	504	12	,	,	PUNCT
fumecheng-10464	504	13	z.w	z.w	PROPN
fumecheng-10464	504	14	.	.	PROPN
fumecheng-10464	504	15	,	,	PUNCT
fumecheng-10464	504	16	2021	2021	NUM
fumecheng-10464	504	17	,	,	PUNCT
fumecheng-10464	504	18	fractal	fractal	ADJ
fumecheng-10464	504	19	calculus	calculus	NOUN
fumecheng-10464	504	20	for	for	ADP
fumecheng-10464	504	21	modeling	model	VERB
fumecheng-10464	504	22	electrochemical	electrochemical	ADJ
fumecheng-10464	504	23	capacitors	capacitor	NOUN
fumecheng-10464	504	24	under	under	ADP
fumecheng-10464	504	25	dynamical	dynamical	ADJ
fumecheng-10464	504	26	cycling	cycling	NOUN
fumecheng-10464	504	27	,	,	PUNCT
fumecheng-10464	504	28	thermal	thermal	ADJ
fumecheng-10464	504	29	science	science	NOUN
fumecheng-10464	504	30	,	,	PUNCT
fumecheng-10464	504	31	25	25	NUM
fumecheng-10464	504	32	(	(	PUNCT
fumecheng-10464	504	33	2	2	NUM
fumecheng-10464	504	34	)	)	PUNCT
fumecheng-10464	504	35	,	,	PUNCT
fumecheng-10464	504	36	pp	pp	ADP
fumecheng-10464	504	37	.	.	PUNCT
fumecheng-10464	505	1	1317	1317	NUM
fumecheng-10464	505	2	-	-	SYM
fumecheng-10464	505	3	1320	1320	NUM
fumecheng-10464	505	4	.	.	PUNCT
fumecheng-10464	506	1	26	26	NUM
fumecheng-10464	506	2	.	.	PUNCT
fumecheng-10464	506	3	alghassab	alghassab	ADJ
fumecheng-10464	506	4	,	,	PUNCT
fumecheng-10464	506	5	m.	m.	NOUN
fumecheng-10464	506	6	,	,	PUNCT
fumecheng-10464	506	7	mahmoud	mahmoud	PROPN
fumecheng-10464	506	8	,	,	PUNCT
fumecheng-10464	506	9	a.	a.	NOUN
fumecheng-10464	506	10	,	,	PUNCT
fumecheng-10464	506	11	zohdy	zohdy	PROPN
fumecheng-10464	506	12	,	,	PUNCT
fumecheng-10464	506	13	m.z	m.z	PROPN
fumecheng-10464	506	14	.	.	PROPN
fumecheng-10464	506	15	,	,	PUNCT
fumecheng-10464	506	16	2017	2017	NUM
fumecheng-10464	506	17	,	,	PUNCT
fumecheng-10464	506	18	nonlinear	nonlinear	ADJ
fumecheng-10464	506	19	control	control	NOUN
fumecheng-10464	506	20	of	of	ADP
fumecheng-10464	506	21	chaotic	chaotic	ADJ
fumecheng-10464	506	22	forced	force	VERB
fumecheng-10464	506	23	duffing	duffing	NOUN
fumecheng-10464	506	24	and	and	CCONJ
fumecheng-10464	506	25	van	van	PROPN
fumecheng-10464	506	26	der	der	ADJ
fumecheng-10464	506	27	pol	pol	PROPN
fumecheng-10464	506	28	oscillators	oscillator	NOUN
fumecheng-10464	506	29	,	,	PUNCT
fumecheng-10464	506	30	international	international	ADJ
fumecheng-10464	506	31	journal	journal	NOUN
fumecheng-10464	506	32	of	of	ADP
fumecheng-10464	506	33	modern	modern	ADJ
fumecheng-10464	506	34	nonlinear	nonlinear	ADJ
fumecheng-10464	506	35	theory	theory	NOUN
fumecheng-10464	506	36	and	and	CCONJ
fumecheng-10464	506	37	application	application	NOUN
fumecheng-10464	506	38	,	,	PUNCT
fumecheng-10464	506	39	6(1	6(1	NUM
fumecheng-10464	506	40	)	)	PUNCT
fumecheng-10464	506	41	,	,	PUNCT
fumecheng-10464	506	42	pp	pp	ADP
fumecheng-10464	506	43	.	.	PUNCT
fumecheng-10464	507	1	26	26	NUM
fumecheng-10464	507	2	-	-	SYM
fumecheng-10464	507	3	37	37	NUM
fumecheng-10464	507	4	.	.	PUNCT
fumecheng-10464	508	1	27	27	NUM
fumecheng-10464	508	2	.	.	PUNCT
fumecheng-10464	509	1	zhihong	zhihong	PROPN
fumecheng-10464	509	2	,	,	PUNCT
fumecheng-10464	509	3	z.	z.	PROPN
fumecheng-10464	509	4	,	,	PUNCT
fumecheng-10464	509	5	shaopu	shaopu	PROPN
fumecheng-10464	509	6	,	,	PUNCT
fumecheng-10464	509	7	y.	y.	NOUN
fumecheng-10464	509	8	,	,	PUNCT
fumecheng-10464	509	9	2015	2015	NUM
fumecheng-10464	509	10	,	,	PUNCT
fumecheng-10464	509	11	application	application	NOUN
fumecheng-10464	509	12	of	of	ADP
fumecheng-10464	509	13	van	van	PROPN
fumecheng-10464	509	14	der	der	PROPN
fumecheng-10464	509	15	pol	pol	PROPN
fumecheng-10464	509	16	–	–	PUNCT
fumecheng-10464	509	17	duffing	duffe	VERB
fumecheng-10464	509	18	oscillator	oscillator	NOUN
fumecheng-10464	509	19	in	in	ADP
fumecheng-10464	509	20	weak	weak	ADJ
fumecheng-10464	509	21	signal	signal	NOUN
fumecheng-10464	509	22	detection	detection	NOUN
fumecheng-10464	509	23	,	,	PUNCT
fumecheng-10464	509	24	computers	computer	NOUN
fumecheng-10464	509	25	&	&	CCONJ
fumecheng-10464	509	26	electrical	electrical	ADJ
fumecheng-10464	509	27	engineering	engineering	NOUN
fumecheng-10464	509	28	,	,	PUNCT
fumecheng-10464	509	29	41	41	NUM
fumecheng-10464	509	30	,	,	PUNCT
fumecheng-10464	509	31	pp	pp	ADJ
fumecheng-10464	509	32	.	.	PUNCT
fumecheng-10464	510	1	1	1	NUM
fumecheng-10464	510	2	-	-	SYM
fumecheng-10464	510	3	8	8	NUM
fumecheng-10464	510	4	.	.	PUNCT
fumecheng-10464	511	1	https://www.worldscientific.com/worldscinet/fractals	https://www.worldscientific.com/worldscinet/fractal	NOUN
fumecheng-10464	511	2	https://www.worldscientific.com/toc/fractals/29/01	https://www.worldscientific.com/toc/fractals/29/01	NOUN
fumecheng-10464	511	3	https://doi.org/10.1142/s0218348x22500463	https://doi.org/10.1142/s0218348x22500463	NOUN
fumecheng-10464	511	4	https://www.worldscientific.com/toc/fractals/29/04	https://www.worldscientific.com/toc/fractals/29/04	X
fumecheng-10464	511	5	https://www.sciencedirect.com/science/journal/00457906	https://www.sciencedirect.com/science/journal/00457906	NUM
fumecheng-10464	511	6	forced	force	VERB
fumecheng-10464	511	7	nonlinear	nonlinear	ADJ
fumecheng-10464	511	8	oscillator	oscillator	NOUN
fumecheng-10464	511	9	in	in	ADP
fumecheng-10464	511	10	a	a	DET
fumecheng-10464	511	11	fractal	fractal	ADJ
fumecheng-10464	511	12	space	space	NOUN
fumecheng-10464	511	13	19	19	NUM
fumecheng-10464	511	14	28	28	NUM
fumecheng-10464	511	15	.	.	PUNCT
fumecheng-10464	512	1	gao	gao	PROPN
fumecheng-10464	512	2	,	,	PUNCT
fumecheng-10464	512	3	g.	g.	PROPN
fumecheng-10464	512	4	,	,	PUNCT
fumecheng-10464	512	5	feng	feng	PROPN
fumecheng-10464	512	6	,	,	PUNCT
fumecheng-10464	512	7	z.	z.	PROPN
fumecheng-10464	512	8	,	,	PUNCT
fumecheng-10464	512	9	2010	2010	NUM
fumecheng-10464	512	10	,	,	PUNCT
fumecheng-10464	512	11	first	first	ADV
fumecheng-10464	512	12	integral	integral	ADJ
fumecheng-10464	512	13	for	for	ADP
fumecheng-10464	512	14	the	the	DET
fumecheng-10464	512	15	duffing	duffing	PROPN
fumecheng-10464	512	16	van	van	PROPN
fumecheng-10464	512	17	der	der	ADJ
fumecheng-10464	512	18	pol	pol	PROPN
fumecheng-10464	512	19	type	type	NOUN
fumecheng-10464	512	20	oscillator	oscillator	NOUN
fumecheng-10464	512	21	,	,	PUNCT
fumecheng-10464	512	22	uab	uab	PROPN
fumecheng-10464	512	23	conference	conference	NOUN
fumecheng-10464	512	24	on	on	ADP
fumecheng-10464	512	25	differential	differential	ADJ
fumecheng-10464	512	26	equations	equation	NOUN
fumecheng-10464	512	27	and	and	CCONJ
fumecheng-10464	512	28	computational	computational	ADJ
fumecheng-10464	512	29	simulations	simulation	NOUN
fumecheng-10464	512	30	,	,	PUNCT
fumecheng-10464	512	31	electronic	electronic	ADJ
fumecheng-10464	512	32	journal	journal	NOUN
fumecheng-10464	512	33	of	of	ADP
fumecheng-10464	512	34	differential	differential	ADJ
fumecheng-10464	512	35	equations	equation	NOUN
fumecheng-10464	512	36	,	,	PUNCT
fumecheng-10464	512	37	pp	pp	ADV
fumecheng-10464	512	38	.	.	PUNCT
fumecheng-10464	513	1	123–133	123–133	NUM
fumecheng-10464	513	2	.	.	PUNCT
fumecheng-10464	514	1	29	29	NUM
fumecheng-10464	514	2	.	.	PUNCT
fumecheng-10464	514	3	motsa	motsa	PROPN
fumecheng-10464	514	4	,	,	PUNCT
fumecheng-10464	514	5	s.s	s.s	PROPN
fumecheng-10464	514	6	.	.	PROPN
fumecheng-10464	514	7	,	,	PUNCT
fumecheng-10464	514	8	sibanda	sibanda	NOUN
fumecheng-10464	514	9	,	,	PUNCT
fumecheng-10464	514	10	p.	p.	NOUN
fumecheng-10464	514	11	,	,	PUNCT
fumecheng-10464	514	12	2012	2012	NUM
fumecheng-10464	514	13	,	,	PUNCT
fumecheng-10464	514	14	a	a	DET
fumecheng-10464	514	15	note	note	NOUN
fumecheng-10464	514	16	on	on	ADP
fumecheng-10464	514	17	the	the	DET
fumecheng-10464	514	18	solutions	solution	NOUN
fumecheng-10464	514	19	of	of	ADP
fumecheng-10464	514	20	the	the	DET
fumecheng-10464	514	21	van	van	PROPN
fumecheng-10464	514	22	der	der	ADJ
fumecheng-10464	514	23	pol	pol	NOUN
fumecheng-10464	514	24	and	and	CCONJ
fumecheng-10464	514	25	duffing	duffe	VERB
fumecheng-10464	514	26	equations	equation	NOUN
fumecheng-10464	514	27	using	use	VERB
fumecheng-10464	514	28	a	a	DET
fumecheng-10464	514	29	linearization	linearization	NOUN
fumecheng-10464	514	30	method	method	NOUN
fumecheng-10464	514	31	,	,	PUNCT
fumecheng-10464	514	32	mathematical	mathematical	ADJ
fumecheng-10464	514	33	problems	problem	NOUN
fumecheng-10464	514	34	in	in	ADP
fumecheng-10464	514	35	engineering	engineering	NOUN
fumecheng-10464	514	36	,	,	PUNCT
fumecheng-10464	514	37	2012	2012	NUM
fumecheng-10464	514	38	,	,	PUNCT
fumecheng-10464	514	39	693453	693453	NUM
fumecheng-10464	514	40	.	.	PUNCT
fumecheng-10464	515	1	30	30	NUM
fumecheng-10464	515	2	.	.	PUNCT
fumecheng-10464	515	3	cui	cui	PROPN
fumecheng-10464	515	4	,	,	PUNCT
fumecheng-10464	515	5	j.	j.	PROPN
fumecheng-10464	515	6	,	,	PUNCT
fumecheng-10464	515	7	liang	liang	PROPN
fumecheng-10464	515	8	,	,	PUNCT
fumecheng-10464	515	9	j.	j.	PROPN
fumecheng-10464	515	10	,	,	PUNCT
fumecheng-10464	515	11	lin	lin	PROPN
fumecheng-10464	515	12	,	,	PUNCT
fumecheng-10464	515	13	z.	z.	PROPN
fumecheng-10464	515	14	,	,	PUNCT
fumecheng-10464	515	15	2016	2016	NUM
fumecheng-10464	515	16	,	,	PUNCT
fumecheng-10464	515	17	stability	stability	NOUN
fumecheng-10464	515	18	analysis	analysis	NOUN
fumecheng-10464	515	19	for	for	ADP
fumecheng-10464	515	20	periodic	periodic	ADJ
fumecheng-10464	515	21	solutions	solution	NOUN
fumecheng-10464	515	22	of	of	ADP
fumecheng-10464	515	23	the	the	DET
fumecheng-10464	515	24	van	van	PROPN
fumecheng-10464	515	25	der	der	PROPN
fumecheng-10464	515	26	pol	pol	PROPN
fumecheng-10464	515	27	-	-	PUNCT
fumecheng-10464	515	28	duffing	duffing	NOUN
fumecheng-10464	515	29	forced	force	VERB
fumecheng-10464	515	30	oscillator	oscillator	NOUN
fumecheng-10464	515	31	,	,	PUNCT
fumecheng-10464	515	32	physica	physica	PROPN
fumecheng-10464	515	33	scripta	scripta	PROPN
fumecheng-10464	515	34	,	,	PUNCT
fumecheng-10464	515	35	91	91	NUM
fumecheng-10464	515	36	,	,	PUNCT
fumecheng-10464	515	37	015201	015201	NUM
fumecheng-10464	515	38	.	.	PUNCT
fumecheng-10464	516	1	31	31	NUM
fumecheng-10464	516	2	.	.	PUNCT
fumecheng-10464	517	1	moatimid	moatimid	PROPN
fumecheng-10464	517	2	,	,	PUNCT
fumecheng-10464	517	3	g.m	g.m	PROPN
fumecheng-10464	517	4	.	.	PROPN
fumecheng-10464	517	5	,	,	PUNCT
fumecheng-10464	517	6	2020	2020	NUM
fumecheng-10464	517	7	,	,	PUNCT
fumecheng-10464	517	8	stability	stability	NOUN
fumecheng-10464	517	9	analysis	analysis	NOUN
fumecheng-10464	517	10	of	of	ADP
fumecheng-10464	517	11	a	a	DET
fumecheng-10464	517	12	parametric	parametric	ADJ
fumecheng-10464	517	13	duffing	duffing	NOUN
fumecheng-10464	517	14	oscillator	oscillator	NOUN
fumecheng-10464	517	15	,	,	PUNCT
fumecheng-10464	517	16	journal	journal	NOUN
fumecheng-10464	517	17	of	of	ADP
fumecheng-10464	517	18	engineering	engineering	NOUN
fumecheng-10464	517	19	mechanics	mechanic	NOUN
fumecheng-10464	517	20	,	,	PUNCT
fumecheng-10464	517	21	146(5	146(5	NUM
fumecheng-10464	517	22	)	)	PUNCT
fumecheng-10464	517	23	,	,	PUNCT
fumecheng-10464	517	24	05020001	05020001	NUM
fumecheng-10464	517	25	.	.	PUNCT
fumecheng-10464	518	1	32	32	NUM
fumecheng-10464	518	2	.	.	PUNCT
fumecheng-10464	519	1	wei	wei	PROPN
fumecheng-10464	519	2	,	,	PUNCT
fumecheng-10464	519	3	x.	x.	PROPN
fumecheng-10464	519	4	,	,	PUNCT
fumecheng-10464	519	5	xiang	xiang	PROPN
fumecheng-10464	519	6	-	-	PUNCT
fumecheng-10464	519	7	dong	dong	PROPN
fumecheng-10464	519	8	,	,	PUNCT
fumecheng-10464	519	9	w.	w.	PROPN
fumecheng-10464	519	10	,	,	PUNCT
fumecheng-10464	519	11	guang	guang	PROPN
fumecheng-10464	519	12	,	,	PUNCT
fumecheng-10464	519	13	m.	m.	NOUN
fumecheng-10464	519	14	,	,	PUNCT
fumecheng-10464	519	15	tong	tong	PROPN
fumecheng-10464	519	16	,	,	PUNCT
fumecheng-10464	519	17	f.	f.	PROPN
fumecheng-10464	519	18	,	,	PUNCT
fumecheng-10464	519	19	2002	2002	NUM
fumecheng-10464	519	20	,	,	PUNCT
fumecheng-10464	519	21	principal	principal	ADJ
fumecheng-10464	519	22	response	response	NOUN
fumecheng-10464	519	23	of	of	ADP
fumecheng-10464	519	24	van	van	PROPN
fumecheng-10464	519	25	der	der	PROPN
fumecheng-10464	519	26	pol	pol	PROPN
fumecheng-10464	519	27	-	-	PUNCT
fumecheng-10464	519	28	duffing	duffe	VERB
fumecheng-10464	519	29	oscillator	oscillator	NOUN
fumecheng-10464	519	30	under	under	ADP
fumecheng-10464	519	31	combined	combine	VERB
fumecheng-10464	519	32	deterministic	deterministic	ADJ
fumecheng-10464	519	33	and	and	CCONJ
fumecheng-10464	519	34	random	random	ADJ
fumecheng-10464	519	35	parametric	parametric	ADJ
fumecheng-10464	519	36	excitation	excitation	NOUN
fumecheng-10464	519	37	,	,	PUNCT
fumecheng-10464	519	38	applied	apply	VERB
fumecheng-10464	519	39	mathematics	mathematic	NOUN
fumecheng-10464	519	40	and	and	CCONJ
fumecheng-10464	519	41	mechanics	mechanic	NOUN
fumecheng-10464	519	42	,	,	PUNCT
fumecheng-10464	519	43	23	23	NUM
fumecheng-10464	519	44	,	,	PUNCT
fumecheng-10464	519	45	pp	pp	ADJ
fumecheng-10464	519	46	.	.	PUNCT
fumecheng-10464	519	47	299	299	NUM
fumecheng-10464	519	48	-	-	SYM
fumecheng-10464	519	49	310	310	NUM
fumecheng-10464	519	50	.	.	NOUN
fumecheng-10464	519	51	33	33	NUM
fumecheng-10464	519	52	.	.	PUNCT
fumecheng-10464	520	1	dao	dao	PROPN
fumecheng-10464	520	2	,	,	PUNCT
fumecheng-10464	520	3	n.v	n.v	PROPN
fumecheng-10464	520	4	.	.	PROPN
fumecheng-10464	520	5	,	,	PUNCT
fumecheng-10464	520	6	dinh	dinh	PROPN
fumecheng-10464	520	7	,	,	PUNCT
fumecheng-10464	520	8	n.v	n.v	PROPN
fumecheng-10464	520	9	.	.	PROPN
fumecheng-10464	520	10	,	,	PUNCT
fumecheng-10464	520	11	chi	chi	PROPN
fumecheng-10464	520	12	,	,	PUNCT
fumecheng-10464	520	13	t.	t.	PROPN
fumecheng-10464	520	14	k.	k.	PROPN
fumecheng-10464	520	15	,	,	PUNCT
fumecheng-10464	520	16	2007	2007	NUM
fumecheng-10464	520	17	,	,	PUNCT
fumecheng-10464	520	18	van	van	PROPN
fumecheng-10464	520	19	der	der	PROPN
fumecheng-10464	520	20	pol	pol	PROPN
fumecheng-10464	520	21	oscillator	oscillator	NOUN
fumecheng-10464	520	22	under	under	ADP
fumecheng-10464	520	23	parametric	parametric	ADJ
fumecheng-10464	520	24	and	and	CCONJ
fumecheng-10464	520	25	forced	force	VERB
fumecheng-10464	520	26	excitation	excitation	NOUN
fumecheng-10464	520	27	,	,	PUNCT
fumecheng-10464	520	28	ukrainian	ukrainian	ADJ
fumecheng-10464	520	29	mathematical	mathematical	ADJ
fumecheng-10464	520	30	journal	journal	NOUN
fumecheng-10464	520	31	,	,	PUNCT
fumecheng-10464	520	32	59(2	59(2	NUM
fumecheng-10464	520	33	)	)	PUNCT
fumecheng-10464	520	34	,	,	PUNCT
fumecheng-10464	520	35	pp	pp	ADP
fumecheng-10464	520	36	.	.	PUNCT
fumecheng-10464	521	1	215	215	NUM
fumecheng-10464	521	2	-	-	SYM
fumecheng-10464	521	3	228	228	NUM
fumecheng-10464	521	4	.	.	PUNCT
fumecheng-10464	522	1	34	34	NUM
fumecheng-10464	522	2	.	.	PUNCT
fumecheng-10464	523	1	han	han	PROPN
fumecheng-10464	523	2	,	,	PUNCT
fumecheng-10464	523	3	x.	x.	PROPN
fumecheng-10464	523	4	,	,	PUNCT
fumecheng-10464	523	5	bi	bi	PROPN
fumecheng-10464	523	6	,	,	PUNCT
fumecheng-10464	523	7	q.	q.	PROPN
fumecheng-10464	523	8	,	,	PUNCT
fumecheng-10464	523	9	chun	chun	PROPN
fumecheng-10464	523	10	,	,	PUNCT
fumecheng-10464	523	11	z.	z.	PROPN
fumecheng-10464	523	12	,	,	PUNCT
fumecheng-10464	523	13	yue	yue	PROPN
fumecheng-10464	523	14	,	,	PUNCT
fumecheng-10464	523	15	y.	y.	PROPN
fumecheng-10464	523	16	,	,	PUNCT
fumecheng-10464	523	17	2014	2014	NUM
fumecheng-10464	523	18	,	,	PUNCT
fumecheng-10464	523	19	study	study	NOUN
fumecheng-10464	523	20	of	of	ADP
fumecheng-10464	523	21	mixed	mixed	ADJ
fumecheng-10464	523	22	-	-	PUNCT
fumecheng-10464	523	23	mode	mode	NOUN
fumecheng-10464	523	24	oscillations	oscillation	NOUN
fumecheng-10464	523	25	in	in	ADP
fumecheng-10464	523	26	parametrically	parametrically	ADV
fumecheng-10464	523	27	excited	excite	VERB
fumecheng-10464	523	28	van	van	PROPN
fumecheng-10464	523	29	der	der	PROPN
fumecheng-10464	523	30	pol	pol	PROPN
fumecheng-10464	523	31	,	,	PUNCT
fumecheng-10464	523	32	nonlinear	nonlinear	ADJ
fumecheng-10464	523	33	dynamics	dynamic	NOUN
fumecheng-10464	523	34	,	,	PUNCT
fumecheng-10464	523	35	77(4	77(4	NUM
fumecheng-10464	523	36	)	)	PUNCT
fumecheng-10464	523	37	,	,	PUNCT
fumecheng-10464	523	38	pp	pp	PROPN
fumecheng-10464	523	39	.	.	PUNCT
fumecheng-10464	523	40	1285	1285	NUM
fumecheng-10464	523	41	-	-	SYM
fumecheng-10464	523	42	1296	1296	NUM
fumecheng-10464	523	43	.	.	PUNCT
fumecheng-10464	524	1	35	35	NUM
fumecheng-10464	524	2	.	.	PUNCT
fumecheng-10464	525	1	kovacic	kovacic	PROPN
fumecheng-10464	525	2	,	,	PUNCT
fumecheng-10464	525	3	i.	i.	PROPN
fumecheng-10464	525	4	,	,	PUNCT
fumecheng-10464	525	5	2013	2013	NUM
fumecheng-10464	525	6	,	,	PUNCT
fumecheng-10464	525	7	harmonically	harmonically	ADV
fumecheng-10464	525	8	excited	excite	VERB
fumecheng-10464	525	9	generalized	generalize	VERB
fumecheng-10464	525	10	van	van	PROPN
fumecheng-10464	525	11	der	der	ADJ
fumecheng-10464	525	12	pol	pol	PROPN
fumecheng-10464	525	13	oscillators	oscillator	NOUN
fumecheng-10464	525	14	:	:	PUNCT
fumecheng-10464	525	15	entertainment	entertainment	NOUN
fumecheng-10464	525	16	phenomenon	phenomenon	NOUN
fumecheng-10464	525	17	,	,	PUNCT
fumecheng-10464	525	18	meccanica	meccanica	PROPN
fumecheng-10464	525	19	,	,	PUNCT
fumecheng-10464	525	20	48	48	NUM
fumecheng-10464	525	21	,	,	PUNCT
fumecheng-10464	525	22	pp	pp	ADJ
fumecheng-10464	525	23	.	.	PUNCT
fumecheng-10464	526	1	2415	2415	NUM
fumecheng-10464	526	2	-	-	SYM
fumecheng-10464	526	3	2425	2425	NUM
fumecheng-10464	526	4	.	.	PUNCT
fumecheng-10464	527	1	36	36	NUM
fumecheng-10464	527	2	.	.	PUNCT
fumecheng-10464	527	3	shen	shen	PROPN
fumecheng-10464	527	4	,	,	PUNCT
fumecheng-10464	527	5	y.	y.	PROPN
fumecheng-10464	527	6	,	,	PUNCT
fumecheng-10464	527	7	li	li	PROPN
fumecheng-10464	527	8	,	,	PUNCT
fumecheng-10464	527	9	h.	h.	PROPN
fumecheng-10464	527	10	,	,	PUNCT
fumecheng-10464	527	11	yang	yang	PROPN
fumecheng-10464	527	12	,	,	PUNCT
fumecheng-10464	527	13	s.	s.	PROPN
fumecheng-10464	527	14	,	,	PUNCT
fumecheng-10464	527	15	peng	peng	PROPN
fumecheng-10464	527	16	,	,	PUNCT
fumecheng-10464	527	17	m.	m.	NOUN
fumecheng-10464	527	18	,	,	PUNCT
fumecheng-10464	527	19	han	han	PROPN
fumecheng-10464	527	20	,	,	PUNCT
fumecheng-10464	527	21	y.	y.	PROPN
fumecheng-10464	527	22	,	,	PUNCT
fumecheng-10464	527	23	2020	2020	NUM
fumecheng-10464	527	24	,	,	PUNCT
fumecheng-10464	527	25	primary	primary	ADJ
fumecheng-10464	527	26	and	and	CCONJ
fumecheng-10464	527	27	subharmonic	subharmonic	ADJ
fumecheng-10464	527	28	simultaneous	simultaneous	ADJ
fumecheng-10464	527	29	resonance	resonance	NOUN
fumecheng-10464	527	30	of	of	ADP
fumecheng-10464	527	31	fractional	fractional	ADJ
fumecheng-10464	527	32	-	-	PUNCT
fumecheng-10464	527	33	order	order	NOUN
fumecheng-10464	527	34	duffing	duffing	NOUN
fumecheng-10464	527	35	oscillator	oscillator	NOUN
fumecheng-10464	527	36	,	,	PUNCT
fumecheng-10464	527	37	nonlinear	nonlinear	ADJ
fumecheng-10464	527	38	dynamics	dynamic	NOUN
fumecheng-10464	527	39	,	,	PUNCT
fumecheng-10464	527	40	102	102	NUM
fumecheng-10464	527	41	,	,	PUNCT
fumecheng-10464	527	42	pp	pp	ADJ
fumecheng-10464	527	43	.	.	PUNCT
fumecheng-10464	527	44	1485	1485	NUM
fumecheng-10464	527	45	-	-	SYM
fumecheng-10464	527	46	1497	1497	NUM
fumecheng-10464	527	47	.	.	PUNCT
fumecheng-10464	528	1	37	37	NUM
fumecheng-10464	528	2	.	.	PUNCT
fumecheng-10464	528	3	wu	wu	PROPN
fumecheng-10464	528	4	,	,	PUNCT
fumecheng-10464	528	5	h.	h.	PROPN
fumecheng-10464	528	6	,	,	PUNCT
fumecheng-10464	528	7	zeng	zeng	PROPN
fumecheng-10464	528	8	,	,	PUNCT
fumecheng-10464	528	9	x.	x.	PROPN
fumecheng-10464	528	10	,	,	PUNCT
fumecheng-10464	528	11	liu	liu	PROPN
fumecheng-10464	528	12	,	,	PUNCT
fumecheng-10464	528	13	y.	y.	PROPN
fumecheng-10464	528	14	,	,	PUNCT
fumecheng-10464	528	15	lai	lai	PROPN
fumecheng-10464	528	16	,	,	PUNCT
fumecheng-10464	528	17	j.	j.	PROPN
fumecheng-10464	528	18	,	,	PUNCT
fumecheng-10464	528	19	2021	2021	NUM
fumecheng-10464	528	20	,	,	PUNCT
fumecheng-10464	528	21	analysis	analysis	NOUN
fumecheng-10464	528	22	of	of	ADP
fumecheng-10464	528	23	harmonically	harmonically	ADV
fumecheng-10464	528	24	forced	force	VERB
fumecheng-10464	528	25	duffing	duffing	NOUN
fumecheng-10464	528	26	oscillator	oscillator	NOUN
fumecheng-10464	528	27	with	with	ADP
fumecheng-10464	528	28	time	time	NOUN
fumecheng-10464	528	29	delay	delay	NOUN
fumecheng-10464	528	30	state	state	NOUN
fumecheng-10464	528	31	feedback	feedback	NOUN
fumecheng-10464	528	32	by	by	ADP
fumecheng-10464	528	33	incremental	incremental	ADJ
fumecheng-10464	528	34	harmonic	harmonic	ADJ
fumecheng-10464	528	35	balance	balance	NOUN
fumecheng-10464	528	36	method	method	NOUN
fumecheng-10464	528	37	,	,	PUNCT
fumecheng-10464	528	38	journal	journal	NOUN
fumecheng-10464	528	39	of	of	ADP
fumecheng-10464	528	40	vibration	vibration	NOUN
fumecheng-10464	528	41	engineering	engineering	NOUN
fumecheng-10464	528	42	&	&	CCONJ
fumecheng-10464	528	43	technologies	technology	NOUN
fumecheng-10464	528	44	,	,	PUNCT
fumecheng-10464	528	45	9	9	NUM
fumecheng-10464	528	46	,	,	PUNCT
fumecheng-10464	528	47	pp	pp	ADJ
fumecheng-10464	528	48	.	.	PUNCT
fumecheng-10464	529	1	1239	1239	NUM
fumecheng-10464	529	2	-	-	SYM
fumecheng-10464	529	3	1251	1251	NUM
fumecheng-10464	529	4	.	.	PUNCT
fumecheng-10464	530	1	38	38	NUM
fumecheng-10464	530	2	.	.	PUNCT
fumecheng-10464	531	1	he	he	PRON
fumecheng-10464	531	2	,	,	PUNCT
fumecheng-10464	531	3	j.‐h	j.‐h	PROPN
fumecheng-10464	531	4	.	.	PROPN
fumecheng-10464	531	5	,	,	PUNCT
fumecheng-10464	531	6	el‐dib	el‐dib	X
fumecheng-10464	531	7	,	,	PUNCT
fumecheng-10464	531	8	y.o	y.o	PROPN
fumecheng-10464	531	9	.	.	PROPN
fumecheng-10464	531	10	,	,	PUNCT
fumecheng-10464	531	11	mady	mady	PROPN
fumecheng-10464	531	12	,	,	PUNCT
fumecheng-10464	531	13	a.a	a.a	PROPN
fumecheng-10464	531	14	.	.	PROPN
fumecheng-10464	531	15	,	,	PUNCT
fumecheng-10464	531	16	2021	2021	NUM
fumecheng-10464	531	17	,	,	PUNCT
fumecheng-10464	531	18	homotopy	homotopy	VERB
fumecheng-10464	531	19	perturbation	perturbation	NOUN
fumecheng-10464	531	20	method	method	NOUN
fumecheng-10464	531	21	for	for	ADP
fumecheng-10464	531	22	the	the	DET
fumecheng-10464	531	23	fractal	fractal	ADJ
fumecheng-10464	531	24	toda	toda	PROPN
fumecheng-10464	531	25	oscillator	oscillator	PROPN
fumecheng-10464	531	26	,	,	PUNCT
fumecheng-10464	531	27	fractal	fractal	ADJ
fumecheng-10464	531	28	fractional	fractional	ADJ
fumecheng-10464	531	29	,	,	PUNCT
fumecheng-10464	531	30	5(3	5(3	NUM
fumecheng-10464	531	31	)	)	PUNCT
fumecheng-10464	531	32	,	,	PUNCT
fumecheng-10464	531	33	pp	pp	ADJ
fumecheng-10464	531	34	.	.	PUNCT
fumecheng-10464	532	1	1	1	NUM
fumecheng-10464	532	2	-	-	SYM
fumecheng-10464	532	3	8	8	NUM
fumecheng-10464	532	4	.	.	NOUN
fumecheng-10464	532	5	39	39	NUM
fumecheng-10464	532	6	.	.	PUNCT
fumecheng-10464	532	7	gómez	gómez	NOUN
fumecheng-10464	532	8	-	-	PUNCT
fumecheng-10464	532	9	aguilar	aguilar	PROPN
fumecheng-10464	532	10	,	,	PUNCT
fumecheng-10464	532	11	j.f	j.f	PROPN
fumecheng-10464	532	12	.	.	PROPN
fumecheng-10464	532	13	,	,	PUNCT
fumecheng-10464	532	14	yépez	yépez	NOUN
fumecheng-10464	532	15	-	-	PUNCT
fumecheng-10464	532	16	martínez	martínez	PROPN
fumecheng-10464	532	17	,	,	PUNCT
fumecheng-10464	532	18	h.	h.	PROPN
fumecheng-10464	532	19	,	,	PUNCT
fumecheng-10464	532	20	calderón	calderón	NOUN
fumecheng-10464	532	21	-	-	PUNCT
fumecheng-10464	532	22	ramón	ramón	NOUN
fumecheng-10464	532	23	,	,	PUNCT
fumecheng-10464	532	24	c.	c.	NOUN
fumecheng-10464	532	25	,	,	PUNCT
fumecheng-10464	532	26	cruz	cruz	NOUN
fumecheng-10464	532	27	-	-	PUNCT
fumecheng-10464	532	28	orduña	orduña	PROPN
fumecheng-10464	532	29	,	,	PUNCT
fumecheng-10464	532	30	i.	i.	NOUN
fumecheng-10464	532	31	,	,	PUNCT
fumecheng-10464	532	32	escobar	escobar	PROPN
fumecheng-10464	532	33	-	-	PUNCT
fumecheng-10464	532	34	jiménez	jiménez	PROPN
fumecheng-10464	532	35	,	,	PUNCT
fumecheng-10464	532	36	r.f	r.f	PROPN
fumecheng-10464	532	37	.	.	PROPN
fumecheng-10464	532	38	,	,	PUNCT
fumecheng-10464	532	39	olivares	olivare	NOUN
fumecheng-10464	532	40	-	-	PUNCT
fumecheng-10464	532	41	peregrino	peregrino	PROPN
fumecheng-10464	532	42	,	,	PUNCT
fumecheng-10464	532	43	v.	v.	PROPN
fumecheng-10464	532	44	h.	h.	PROPN
fumecheng-10464	532	45	,	,	PUNCT
fumecheng-10464	532	46	2015	2015	NUM
fumecheng-10464	532	47	,	,	PUNCT
fumecheng-10464	532	48	modeling	modeling	NOUN
fumecheng-10464	532	49	of	of	ADP
fumecheng-10464	532	50	a	a	DET
fumecheng-10464	532	51	mass	mass	ADJ
fumecheng-10464	532	52	-	-	PUNCT
fumecheng-10464	532	53	spring	spring	NOUN
fumecheng-10464	532	54	-	-	PUNCT
fumecheng-10464	532	55	damper	damper	NOUN
fumecheng-10464	532	56	system	system	NOUN
fumecheng-10464	532	57	by	by	ADP
fumecheng-10464	532	58	fractional	fractional	ADJ
fumecheng-10464	532	59	derivatives	derivative	NOUN
fumecheng-10464	532	60	with	with	ADP
fumecheng-10464	532	61	and	and	CCONJ
fumecheng-10464	532	62	without	without	ADP
fumecheng-10464	532	63	a	a	DET
fumecheng-10464	532	64	singular	singular	ADJ
fumecheng-10464	532	65	kernel	kernel	NOUN
fumecheng-10464	532	66	,	,	PUNCT
fumecheng-10464	532	67	entropy	entropy	PROPN
fumecheng-10464	532	68	,	,	PUNCT
fumecheng-10464	532	69	17	17	NUM
fumecheng-10464	532	70	,	,	PUNCT
fumecheng-10464	532	71	pp	pp	ADJ
fumecheng-10464	532	72	.	.	PUNCT
fumecheng-10464	533	1	6289	6289	NUM
fumecheng-10464	533	2	-	-	SYM
fumecheng-10464	533	3	6303	6303	NUM
fumecheng-10464	533	4	.	.	PUNCT
fumecheng-10464	534	1	40	40	NUM
fumecheng-10464	534	2	.	.	X
fumecheng-10464	535	1	yang	yang	PROPN
fumecheng-10464	535	2	,	,	PUNCT
fumecheng-10464	535	3	c	c	PROPN
fumecheng-10464	535	4	-	-	PUNCT
fumecheng-10464	535	5	y.	y.	PROPN
fumecheng-10464	535	6	,	,	PUNCT
fumecheng-10464	535	7	zhang	zhang	PROPN
fumecheng-10464	535	8	,	,	PUNCT
fumecheng-10464	535	9	y	y	PROPN
fumecheng-10464	535	10	-	-	PUNCT
fumecheng-10464	535	11	d.	d.	PROPN
fumecheng-10464	535	12	,	,	PUNCT
fumecheng-10464	535	13	yang	yang	PROPN
fumecheng-10464	535	14	,	,	PUNCT
fumecheng-10464	535	15	x	x	PROPN
fumecheng-10464	535	16	-	-	PUNCT
fumecheng-10464	535	17	j.	j.	PROPN
fumecheng-10464	535	18	,	,	PUNCT
fumecheng-10464	535	19	2016	2016	NUM
fumecheng-10464	535	20	,	,	PUNCT
fumecheng-10464	535	21	exact	exact	ADJ
fumecheng-10464	535	22	solutions	solution	NOUN
fumecheng-10464	535	23	for	for	ADP
fumecheng-10464	535	24	the	the	DET
fumecheng-10464	535	25	differential	differential	ADJ
fumecheng-10464	535	26	equations	equation	NOUN
fumecheng-10464	535	27	in	in	ADP
fumecheng-10464	535	28	fractal	fractal	ADJ
fumecheng-10464	535	29	heat	heat	NOUN
fumecheng-10464	535	30	transfer	transfer	NOUN
fumecheng-10464	535	31	,	,	PUNCT
fumecheng-10464	535	32	thermal	thermal	ADJ
fumecheng-10464	535	33	science	science	NOUN
fumecheng-10464	535	34	,	,	PUNCT
fumecheng-10464	535	35	20(3	20(3	NOUN
fumecheng-10464	535	36	)	)	PUNCT
fumecheng-10464	535	37	,	,	PUNCT
fumecheng-10464	535	38	pp	pp	ADJ
fumecheng-10464	535	39	.	.	PUNCT
fumecheng-10464	536	1	747	747	NUM
fumecheng-10464	536	2	-	-	SYM
fumecheng-10464	536	3	750	750	NUM
fumecheng-10464	536	4	.	.	PUNCT
fumecheng-10464	537	1	41	41	NUM
fumecheng-10464	537	2	.	.	PUNCT
fumecheng-10464	538	1	elías	elías	PROPN
fumecheng-10464	538	2	-	-	PUNCT
fumecheng-10464	538	3	zúñiga	zúñiga	PROPN
fumecheng-10464	538	4	,	,	PUNCT
fumecheng-10464	538	5	a.	a.	NOUN
fumecheng-10464	538	6	,	,	PUNCT
fumecheng-10464	538	7	martínez	martínez	PROPN
fumecheng-10464	538	8	-	-	PUNCT
fumecheng-10464	538	9	romero	romero	PROPN
fumecheng-10464	538	10	,	,	PUNCT
fumecheng-10464	538	11	o.	o.	PROPN
fumecheng-10464	538	12	,	,	PUNCT
fumecheng-10464	538	13	trejo	trejo	PROPN
fumecheng-10464	538	14	,	,	PUNCT
fumecheng-10464	538	15	d.o	d.o	PROPN
fumecheng-10464	538	16	.	.	PROPN
fumecheng-10464	538	17	palacios	palacios	PROPN
fumecheng-10464	538	18	-	-	PUNCT
fumecheng-10464	538	19	pineda	pineda	PROPN
fumecheng-10464	538	20	,	,	PUNCT
fumecheng-10464	538	21	l.m	l.m	PROPN
fumecheng-10464	538	22	.	.	PROPN
fumecheng-10464	538	23	,	,	PUNCT
fumecheng-10464	538	24	2021	2021	NUM
fumecheng-10464	538	25	,	,	PUNCT
fumecheng-10464	538	26	exact	exact	ADJ
fumecheng-10464	538	27	steady	steady	ADJ
fumecheng-10464	538	28	-	-	PUNCT
fumecheng-10464	538	29	state	state	NOUN
fumecheng-10464	538	30	solution	solution	NOUN
fumecheng-10464	538	31	of	of	ADP
fumecheng-10464	538	32	fractals	fractal	NOUN
fumecheng-10464	538	33	damped	damp	VERB
fumecheng-10464	538	34	,	,	PUNCT
fumecheng-10464	538	35	and	and	CCONJ
fumecheng-10464	538	36	forced	force	VERB
fumecheng-10464	538	37	systems	system	NOUN
fumecheng-10464	538	38	,	,	PUNCT
fumecheng-10464	538	39	results	result	NOUN
fumecheng-10464	538	40	in	in	ADP
fumecheng-10464	538	41	physics	physics	NOUN
fumecheng-10464	538	42	,	,	PUNCT
fumecheng-10464	538	43	28	28	NUM
fumecheng-10464	538	44	,	,	PUNCT
fumecheng-10464	538	45	104580	104580	NUM
fumecheng-10464	538	46	.	.	PUNCT
fumecheng-10464	539	1	42	42	NUM
fumecheng-10464	539	2	.	.	PUNCT
fumecheng-10464	540	1	ghaleb	ghaleb	PROPN
fumecheng-10464	540	2	,	,	PUNCT
fumecheng-10464	540	3	a.f	a.f	PROPN
fumecheng-10464	540	4	.	.	PROPN
fumecheng-10464	540	5	,	,	PUNCT
fumecheng-10464	540	6	abou	abou	PROPN
fumecheng-10464	540	7	-	-	PUNCT
fumecheng-10464	540	8	dina	dina	PROPN
fumecheng-10464	540	9	,	,	PUNCT
fumecheng-10464	540	10	m.s	m.s	PROPN
fumecheng-10464	540	11	.	.	PROPN
fumecheng-10464	540	12	,	,	PUNCT
fumecheng-10464	540	13	moatimid	moatimid	PROPN
fumecheng-10464	540	14	,	,	PUNCT
fumecheng-10464	540	15	g.m	g.m	PROPN
fumecheng-10464	540	16	.	.	PROPN
fumecheng-10464	540	17	,	,	PUNCT
fumecheng-10464	540	18	zekry	zekry	PROPN
fumecheng-10464	540	19	,	,	PUNCT
fumecheng-10464	540	20	m.h	m.h	PROPN
fumecheng-10464	540	21	.	.	PROPN
fumecheng-10464	540	22	,	,	PUNCT
fumecheng-10464	540	23	2021	2021	NUM
fumecheng-10464	540	24	,	,	PUNCT
fumecheng-10464	540	25	analytic	analytic	ADJ
fumecheng-10464	540	26	approximate	approximate	ADJ
fumecheng-10464	540	27	solutions	solution	NOUN
fumecheng-10464	540	28	of	of	ADP
fumecheng-10464	540	29	the	the	DET
fumecheng-10464	540	30	cubic	cubic	ADJ
fumecheng-10464	540	31	–	–	PUNCT
fumecheng-10464	540	32	quintic	quintic	ADJ
fumecheng-10464	540	33	duffing	duffing	NOUN
fumecheng-10464	540	34	–	–	PUNCT
fumecheng-10464	540	35	van	van	PROPN
fumecheng-10464	540	36	der	der	ADJ
fumecheng-10464	540	37	pol	pol	NOUN
fumecheng-10464	540	38	equation	equation	NOUN
fumecheng-10464	540	39	with	with	ADP
fumecheng-10464	540	40	two	two	NUM
fumecheng-10464	540	41	-	-	PUNCT
fumecheng-10464	540	42	external	external	ADJ
fumecheng-10464	540	43	periodic	periodic	ADJ
fumecheng-10464	540	44	forcing	force	VERB
fumecheng-10464	540	45	terms	term	NOUN
fumecheng-10464	540	46	:	:	PUNCT
fumecheng-10464	540	47	stability	stability	NOUN
fumecheng-10464	540	48	analysis	analysis	NOUN
fumecheng-10464	540	49	,	,	PUNCT
fumecheng-10464	540	50	mathematics	mathematic	NOUN
fumecheng-10464	540	51	and	and	CCONJ
fumecheng-10464	540	52	computers	computer	NOUN
fumecheng-10464	540	53	in	in	ADP
fumecheng-10464	540	54	simulation	simulation	NOUN
fumecheng-10464	540	55	,	,	PUNCT
fumecheng-10464	540	56	180	180	NUM
fumecheng-10464	540	57	,	,	PUNCT
fumecheng-10464	540	58	pp	pp	ADJ
fumecheng-10464	540	59	.	.	PUNCT
fumecheng-10464	541	1	129–151	129–151	NUM
fumecheng-10464	541	2	.	.	X
fumecheng-10464	542	1	43	43	NUM
fumecheng-10464	542	2	.	.	PUNCT
fumecheng-10464	543	1	nayfeh	nayfeh	PROPN
fumecheng-10464	543	2	,	,	PUNCT
fumecheng-10464	543	3	a.h	a.h	PROPN
fumecheng-10464	543	4	.	.	PROPN
fumecheng-10464	543	5	,	,	PUNCT
fumecheng-10464	543	6	1973	1973	NUM
fumecheng-10464	543	7	,	,	PUNCT
fumecheng-10464	543	8	perturbation	perturbation	NOUN
fumecheng-10464	543	9	methods	method	NOUN
fumecheng-10464	543	10	,	,	PUNCT
fumecheng-10464	543	11	john	john	PROPN
fumecheng-10464	543	12	wiley	wiley	PROPN
fumecheng-10464	543	13	-	-	PUNCT
fumecheng-10464	543	14	interscience	interscience	PROPN
fumecheng-10464	543	15	,	,	PUNCT
fumecheng-10464	543	16	new	new	PROPN
fumecheng-10464	543	17	york	york	PROPN
fumecheng-10464	543	18	,	,	PUNCT
fumecheng-10464	543	19	425	425	NUM
fumecheng-10464	543	20	p.	p.	NOUN
fumecheng-10464	543	21	44	44	NUM
fumecheng-10464	543	22	.	.	PUNCT
fumecheng-10464	544	1	he	he	PRON
fumecheng-10464	544	2	,	,	PUNCT
fumecheng-10464	544	3	c.h	c.h	PROPN
fumecheng-10464	544	4	.	.	PROPN
fumecheng-10464	544	5	,	,	PUNCT
fumecheng-10464	544	6	liu	liu	PROPN
fumecheng-10464	544	7	,	,	PUNCT
fumecheng-10464	544	8	c.	c.	PROPN
fumecheng-10464	544	9	,	,	PUNCT
fumecheng-10464	544	10	he	he	PRON
fumecheng-10464	544	11	,	,	PUNCT
fumecheng-10464	544	12	j.h	j.h	PROPN
fumecheng-10464	544	13	.	.	PROPN
fumecheng-10464	544	14	,	,	PUNCT
fumecheng-10464	544	15	mohammad	mohammad	PROPN
fumecheng-10464	544	16	-	-	PUNCT
fumecheng-10464	544	17	sedighi	sedighi	PROPN
fumecheng-10464	544	18	,	,	PUNCT
fumecheng-10464	544	19	h.	h.	PROPN
fumecheng-10464	544	20	,	,	PUNCT
fumecheng-10464	544	21	shokri	shokri	PROPN
fumecheng-10464	544	22	,	,	PUNCT
fumecheng-10464	544	23	a.	a.	NOUN
fumecheng-10464	544	24	,	,	PUNCT
fumecheng-10464	544	25	gepreel	gepreel	PROPN
fumecheng-10464	544	26	k.a	k.a	PROPN
fumecheng-10464	544	27	.	.	PROPN
fumecheng-10464	544	28	,	,	PUNCT
fumecheng-10464	544	29	2021	2021	NUM
fumecheng-10464	544	30	,	,	PUNCT
fumecheng-10464	544	31	a	a	DET
fumecheng-10464	544	32	fractal	fractal	ADJ
fumecheng-10464	544	33	model	model	NOUN
fumecheng-10464	544	34	for	for	ADP
fumecheng-10464	544	35	the	the	DET
fumecheng-10464	544	36	internal	internal	ADJ
fumecheng-10464	544	37	temperature	temperature	NOUN
fumecheng-10464	544	38	response	response	NOUN
fumecheng-10464	544	39	of	of	ADP
fumecheng-10464	544	40	a	a	DET
fumecheng-10464	544	41	porous	porous	ADJ
fumecheng-10464	544	42	concrete	concrete	NOUN
fumecheng-10464	544	43	,	,	PUNCT
fumecheng-10464	544	44	applied	apply	VERB
fumecheng-10464	544	45	and	and	CCONJ
fumecheng-10464	544	46	computational	computational	ADJ
fumecheng-10464	544	47	mathematics	mathematic	NOUN
fumecheng-10464	544	48	,	,	PUNCT
fumecheng-10464	544	49	20	20	NUM
fumecheng-10464	544	50	,	,	PUNCT
fumecheng-10464	544	51	pp	pp	ADJ
fumecheng-10464	544	52	.	.	PUNCT
fumecheng-10464	545	1	1871	1871	NUM
fumecheng-10464	545	2	-	-	SYM
fumecheng-10464	545	3	1875	1875	NUM
fumecheng-10464	545	4	.	.	PUNCT
fumecheng-10464	546	1	45	45	NUM
fumecheng-10464	546	2	.	.	PUNCT
fumecheng-10464	547	1	liu	liu	PROPN
fumecheng-10464	547	2	,	,	PUNCT
fumecheng-10464	547	3	x.y	x.y	PROPN
fumecheng-10464	547	4	.	.	PROPN
fumecheng-10464	547	5	,	,	PUNCT
fumecheng-10464	547	6	liu	liu	PROPN
fumecheng-10464	547	7	,	,	PUNCT
fumecheng-10464	547	8	y.p	y.p	PROPN
fumecheng-10464	547	9	.	.	PROPN
fumecheng-10464	547	10	,	,	PUNCT
fumecheng-10464	547	11	wu	wu	PROPN
fumecheng-10464	547	12	,	,	PUNCT
fumecheng-10464	547	13	z.w	z.w	PROPN
fumecheng-10464	547	14	.	.	PROPN
fumecheng-10464	547	15	,	,	PUNCT
fumecheng-10464	547	16	2021	2021	NUM
fumecheng-10464	547	17	,	,	PUNCT
fumecheng-10464	547	18	optimization	optimization	NOUN
fumecheng-10464	547	19	of	of	ADP
fumecheng-10464	547	20	a	a	DET
fumecheng-10464	547	21	fractal	fractal	ADJ
fumecheng-10464	547	22	electrode	electrode	NOUN
fumecheng-10464	547	23	-	-	PUNCT
fumecheng-10464	547	24	level	level	NOUN
fumecheng-10464	547	25	charge	charge	NOUN
fumecheng-10464	547	26	transport	transport	NOUN
fumecheng-10464	547	27	model	model	NOUN
fumecheng-10464	547	28	,	,	PUNCT
fumecheng-10464	547	29	thermal	thermal	ADJ
fumecheng-10464	547	30	science	science	NOUN
fumecheng-10464	547	31	,	,	PUNCT
fumecheng-10464	547	32	25(3	25(3	NUM
fumecheng-10464	547	33	)	)	PUNCT
fumecheng-10464	547	34	,	,	PUNCT
fumecheng-10464	547	35	pp	pp	ADP
fumecheng-10464	547	36	.	.	PUNCT
fumecheng-10464	547	37	2213	2213	NUM
fumecheng-10464	547	38	-	-	SYM
fumecheng-10464	547	39	2220	2220	NUM
fumecheng-10464	547	40	.	.	PUNCT
fumecheng-10464	547	41	46	46	NUM
fumecheng-10464	547	42	.	.	PUNCT
fumecheng-10464	548	1	liu	liu	PROPN
fumecheng-10464	548	2	,	,	PUNCT
fumecheng-10464	548	3	y.p	y.p	PROPN
fumecheng-10464	548	4	.	.	PROPN
fumecheng-10464	548	5	,	,	PUNCT
fumecheng-10464	548	6	wang	wang	PROPN
fumecheng-10464	548	7	,	,	PUNCT
fumecheng-10464	548	8	c.c	c.c	PROPN
fumecheng-10464	548	9	.	.	PROPN
fumecheng-10464	548	10	,	,	PUNCT
fumecheng-10464	548	11	li	li	PROPN
fumecheng-10464	548	12	,	,	PUNCT
fumecheng-10464	548	13	s.j	s.j	PROPN
fumecheng-10464	548	14	.	.	PROPN
fumecheng-10464	548	15	,	,	PUNCT
fumecheng-10464	548	16	2021	2021	NUM
fumecheng-10464	548	17	,	,	PUNCT
fumecheng-10464	548	18	a	a	DET
fumecheng-10464	548	19	fractal	fractal	ADJ
fumecheng-10464	548	20	langmuir	langmuir	X
fumecheng-10464	548	21	kinetic	kinetic	NOUN
fumecheng-10464	548	22	equation	equation	NOUN
fumecheng-10464	548	23	and	and	CCONJ
fumecheng-10464	548	24	its	its	PRON
fumecheng-10464	548	25	solution	solution	NOUN
fumecheng-10464	548	26	structure	structure	NOUN
fumecheng-10464	548	27	,	,	PUNCT
fumecheng-10464	548	28	thermal	thermal	ADJ
fumecheng-10464	548	29	science	science	NOUN
fumecheng-10464	548	30	,	,	PUNCT
fumecheng-10464	548	31	25(2	25(2	NUM
fumecheng-10464	548	32	)	)	PUNCT
fumecheng-10464	548	33	,	,	PUNCT
fumecheng-10464	548	34	pp	pp	ADJ
fumecheng-10464	548	35	.	.	PUNCT
fumecheng-10464	548	36	1351	1351	NUM
fumecheng-10464	548	37	-	-	SYM
fumecheng-10464	548	38	1354	1354	NUM
fumecheng-10464	548	39	.	.	PUNCT
fumecheng-10464	549	1	47	47	NUM
fumecheng-10464	549	2	.	.	PUNCT
fumecheng-10464	550	1	wang	wang	PROPN
fumecheng-10464	550	2	,	,	PUNCT
fumecheng-10464	550	3	k.j	k.j	PROPN
fumecheng-10464	550	4	.	.	PROPN
fumecheng-10464	550	5	,	,	PUNCT
fumecheng-10464	550	6	2021	2021	NUM
fumecheng-10464	550	7	,	,	PUNCT
fumecheng-10464	550	8	generalized	generalize	VERB
fumecheng-10464	550	9	variational	variational	ADJ
fumecheng-10464	550	10	principle	principle	NOUN
fumecheng-10464	550	11	and	and	CCONJ
fumecheng-10464	550	12	periodic	periodic	ADJ
fumecheng-10464	550	13	wave	wave	NOUN
fumecheng-10464	550	14	solution	solution	NOUN
fumecheng-10464	550	15	to	to	ADP
fumecheng-10464	550	16	the	the	DET
fumecheng-10464	550	17	modified	modify	VERB
fumecheng-10464	550	18	equal	equal	ADJ
fumecheng-10464	550	19	widthburgers	widthburger	NOUN
fumecheng-10464	550	20	equation	equation	NOUN
fumecheng-10464	550	21	in	in	ADP
fumecheng-10464	550	22	nonlinear	nonlinear	ADJ
fumecheng-10464	550	23	dispersion	dispersion	NOUN
fumecheng-10464	550	24	media	medium	NOUN
fumecheng-10464	550	25	,	,	PUNCT
fumecheng-10464	550	26	physics	physics	NOUN
fumecheng-10464	550	27	letters	letter	NOUN
fumecheng-10464	550	28	a	a	DET
fumecheng-10464	550	29	,	,	PUNCT
fumecheng-10464	550	30	419(17	419(17	NUM
fumecheng-10464	550	31	)	)	PUNCT
fumecheng-10464	550	32	,	,	PUNCT
fumecheng-10464	550	33	doi	doi	NOUN
fumecheng-10464	550	34	:	:	PUNCT
fumecheng-10464	550	35	10.1016	10.1016	NUM
fumecheng-10464	550	36	/	/	SYM
fumecheng-10464	550	37	j.physleta	j.physleta	PROPN
fumecheng-10464	550	38	.	.	PUNCT
fumecheng-10464	551	1	2021.127723	2021.127723	NUM
fumecheng-10464	551	2	.	.	NOUN
fumecheng-10464	552	1	20	20	NUM
fumecheng-10464	552	2	j.-h	j.-h	NOUN
fumecheng-10464	552	3	.	.	PUNCT
fumecheng-10464	553	1	he	he	PRON
fumecheng-10464	553	2	,	,	PUNCT
fumecheng-10464	553	3	g.	g.	PROPN
fumecheng-10464	553	4	m.	m.	PROPN
fumecheng-10464	553	5	moatimid	moatimid	PROPN
fumecheng-10464	553	6	,	,	PUNCT
fumecheng-10464	553	7	m.	m.	PROPN
fumecheng-10464	553	8	h.	h.	PROPN
fumecheng-10464	553	9	zekry	zekry	PROPN
fumecheng-10464	553	10	appendix	appendix	VERB
fumecheng-10464	553	11	the	the	DET
fumecheng-10464	553	12	function	function	NOUN
fumecheng-10464	553	13	x2(t	x2(t	PRON
fumecheng-10464	553	14	)	)	PUNCT
fumecheng-10464	553	15	that	that	PRON
fumecheng-10464	553	16	appears	appear	VERB
fumecheng-10464	553	17	in	in	ADP
fumecheng-10464	553	18	eq	eq	ADP
fumecheng-10464	553	19	.	.	PUNCT
fumecheng-10464	554	1	(	(	PUNCT
fumecheng-10464	554	2	16	16	NUM
fumecheng-10464	554	3	)	)	PUNCT
fumecheng-10464	554	4	may	may	AUX
fumecheng-10464	554	5	be	be	AUX
fumecheng-10464	554	6	written	write	VERB
fumecheng-10464	554	7	as	as	SCONJ
fumecheng-10464	554	8	follows	follow	VERB
fumecheng-10464	554	9	:	:	PUNCT
fumecheng-10464	554	10	2	2	NUM
fumecheng-10464	554	11	2	2	NUM
fumecheng-10464	554	12	2	2	NUM
fumecheng-10464	554	13	21	21	NUM
fumecheng-10464	554	14	2	2	NUM
fumecheng-10464	554	15	2	2	NUM
fumecheng-10464	554	16	2	2	NUM
fumecheng-10464	554	17	222	222	NUM
fumecheng-10464	554	18	2	2	NUM
fumecheng-10464	554	19	2	2	NUM
fumecheng-10464	554	20	2	2	NUM
fumecheng-10464	554	21	2	2	NUM
fumecheng-10464	554	22	2	2	NUM
fumecheng-10464	554	23	2	2	NUM
fumecheng-10464	554	24	2	2	NUM
fumecheng-10464	554	25	8	8	NUM
fumecheng-10464	554	26	1536	1536	NUM
fumecheng-10464	554	27	(	(	PUNCT
fumecheng-10464	554	28	)	)	PUNCT
fumecheng-10464	554	29	sin	sin	NOUN
fumecheng-10464	554	30	36	36	NUM
fumecheng-10464	554	31	3	3	NUM
fumecheng-10464	554	32	(	(	PUNCT
fumecheng-10464	554	33	)	)	PUNCT
fumecheng-10464	554	34	sin3	sin3	PROPN
fumecheng-10464	554	35	(	(	PUNCT
fumecheng-10464	554	36	3	3	NUM
fumecheng-10464	554	37	5	5	NUM
fumecheng-10464	554	38	)	)	PUNCT
fumecheng-10464	554	39	sin5	sin5	NOUN
fumecheng-10464	554	40	sin	sin	VERB
fumecheng-10464	554	41	1	1	NUM
fumecheng-10464	554	42	(	(	PUNCT
fumecheng-10464	554	43	1	1	NUM
fumecheng-10464	554	44	)	)	PUNCT
fumecheng-10464	554	45	768	768	NUM
fumecheng-10464	554	46	(	(	PUNCT
fumecheng-10464	554	47	2	2	NUM
fumecheng-10464	554	48	)	)	PUNCT
fumecheng-10464	554	49	768	768	NUM
fumecheng-10464	554	50	(	(	PUNCT
fumecheng-10464	554	51	2	2	X
fumecheng-10464	554	52	)	)	PUNCT
fumecheng-10464	554	53	sin	sin	NOUN
fumecheng-10464	554	54	(	(	PUNCT
fumecheng-10464	554	55	(	(	PUNCT
fumecheng-10464	554	56	2	2	NUM
fumecheng-10464	554	57	)	)	PUNCT
fumecheng-10464	554	58	)	)	PUNCT
fumecheng-10464	554	59	sin	sin	NOUN
fumecheng-10464	554	60	(	(	PUNCT
fumecheng-10464	554	61	(	(	PUNCT
fumecheng-10464	554	62	2	2	NUM
fumecheng-10464	554	63	)	)	PUNCT
fumecheng-10464	554	64	)	)	PUNCT
fumecheng-10464	555	1	(	(	PUNCT
fumecheng-10464	555	2	)	)	PUNCT
fumecheng-10464	555	3	cos	cos	X
fumecheng-10464	555	4	(	(	PUNCT
fumecheng-10464	555	5	1	1	NUM
fumecheng-10464	555	6	)	)	PUNCT
fumecheng-10464	555	7	(	(	PUNCT
fumecheng-10464	555	8	1	1	NUM
fumecheng-10464	555	9	)	)	PUNCT
fumecheng-10464	555	10	(	(	PUNCT
fumecheng-10464	555	11	3	3	X
fumecheng-10464	555	12	)	)	PUNCT
fumecheng-10464	555	13	(	(	PUNCT
fumecheng-10464	555	14	1	1	X
fumecheng-10464	555	15	)	)	PUNCT
fumecheng-10464	555	16	(	(	PUNCT
fumecheng-10464	555	17	1	1	X
fumecheng-10464	555	18	)	)	PUNCT
fumecheng-10464	555	19	(	(	PUNCT
fumecheng-10464	555	20	3	3	X
fumecheng-10464	555	21	)	)	SYM
fumecheng-10464	555	22	1	1	NUM
fumecheng-10464	555	23	(	(	PUNCT
fumecheng-10464	555	24	)	)	PUNCT
fumecheng-10464	555	25	3072	3072	NUM
fumecheng-10464	555	26	8	8	NUM
fumecheng-10464	555	27	36	36	NUM
fumecheng-10464	555	28	3	3	NUM
fumecheng-10464	555	29	(	(	PUNCT
fumecheng-10464	555	30	)	)	PUNCT
fumecheng-10464	555	31	(	(	PUNCT
fumecheng-10464	556	1	f	f	NOUN
fumecheng-10464	556	2	f	f	X
fumecheng-10464	556	3	x	x	SYM
fumecheng-10464	556	4	t	t	PROPN
fumecheng-10464	556	5	t	t	PROPN
fumecheng-10464	556	6	t	t	PROPN
fumecheng-10464	556	7	t	t	PROPN
fumecheng-10464	556	8	t	t	PROPN
fumecheng-10464	556	9	f	f	PROPN
fumecheng-10464	556	10	f	f	PROPN
fumecheng-10464	556	11	t	t	PROPN
fumecheng-10464	556	12	t	t	PROPN
fumecheng-10464	556	13	x	x	SYM
fumecheng-10464	556	14	t	t	PROPN
fumecheng-10464	556	15	t	t	NOUN
fumecheng-10464	556	16	x	x	PUNCT
fumecheng-10464	556	17	x	x	X
fumecheng-10464	556	18	f	f	PROPN
fumecheng-10464	556	19	t	t	NOUN
fumecheng-10464	556	20			NOUN
fumecheng-10464	556	21			NOUN
fumecheng-10464	556	22			NOUN
fumecheng-10464	556	23			NOUN
fumecheng-10464	556	24			NOUN
fumecheng-10464	556	25			NOUN
fumecheng-10464	556	26			NOUN
fumecheng-10464	556	27			NOUN
fumecheng-10464	556	28			NOUN
fumecheng-10464	556	29			NOUN
fumecheng-10464	556	30			NOUN
fumecheng-10464	556	31			NOUN
fumecheng-10464	556	32			X
fumecheng-10464	557	1			NOUN
fumecheng-10464	557	2	+	+	X
fumecheng-10464	558	1	+	+	PUNCT
fumecheng-10464	558	2	+	+	PUNCT
fumecheng-10464	558	3	+	+	CCONJ
fumecheng-10464	558	4	−	−	PROPN
fumecheng-10464	558	5	−	−	NUM
fumecheng-10464	558	6			PROPN
fumecheng-10464	559	1	−	−	PROPN
fumecheng-10464	559	2			PROPN
fumecheng-10464	559	3			PROPN
fumecheng-10464	560	1	−	−	PRON
fumecheng-10464	560	2			NOUN
fumecheng-10464	561	1	−	−	NUM
fumecheng-10464	561	2			PROPN
fumecheng-10464	561	3	+	+	CCONJ
fumecheng-10464	561	4			NUM
fumecheng-10464	561	5	−	−	ADP
fumecheng-10464	562	1	+	+	NOUN
fumecheng-10464	562	2			PROPN
fumecheng-10464	562	3	+	+	NOUN
fumecheng-10464	562	4			NOUN
fumecheng-10464	562	5	−	−	NUM
fumecheng-10464	562	6	−	−	PROPN
fumecheng-10464	563	1	+	+	NOUN
fumecheng-10464	563	2			NOUN
fumecheng-10464	563	3	+	+	CCONJ
fumecheng-10464	563	4	+	+	NUM
fumecheng-10464	563	5			PROPN
fumecheng-10464	563	6	−	−	PRON
fumecheng-10464	563	7			PROPN
fumecheng-10464	563	8	−	−	PROPN
fumecheng-10464	564	1	+	+	PROPN
fumecheng-10464	564	2			PROPN
fumecheng-10464	564	3			PROPN
fumecheng-10464	564	4	−	−	PROPN
fumecheng-10464	564	5			PROPN
fumecheng-10464	565	1	−	−	PROPN
fumecheng-10464	565	2	−	−	PROPN
fumecheng-10464	566	1	+	+	NOUN
fumecheng-10464	566	2			PROPN
fumecheng-10464	566	3	=	=	PUNCT
fumecheng-10464	566	4	−	−	PROPN
fumecheng-10464	567	1	+	+	CCONJ
fumecheng-10464	567	2	+	+	CCONJ
fumecheng-10464	567	3	−	−	PROPN
fumecheng-10464	567	4			NOUN
fumecheng-10464	567	5	−	−	NOUN
fumecheng-10464	567	6	2	2	NUM
fumecheng-10464	567	7	2	2	NUM
fumecheng-10464	567	8	2	2	NUM
fumecheng-10464	567	9	2	2	NUM
fumecheng-10464	567	10	2	2	NUM
fumecheng-10464	567	11	2	2	NUM
fumecheng-10464	567	12	,	,	PUNCT
fumecheng-10464	567	13	4608	4608	NUM
fumecheng-10464	567	14	2304	2304	NUM
fumecheng-10464	567	15	)	)	PUNCT
fumecheng-10464	567	16	cos3	cos3	PROPN
fumecheng-10464	567	17	cos	cos	PROPN
fumecheng-10464	567	18	cos	cos	PROPN
fumecheng-10464	567	19	(	(	PUNCT
fumecheng-10464	567	20	(	(	PUNCT
fumecheng-10464	567	21	2	2	NUM
fumecheng-10464	567	22	)	)	PUNCT
fumecheng-10464	567	23	)	)	PUNCT
fumecheng-10464	567	24	1	1	NUM
fumecheng-10464	567	25	(	(	PUNCT
fumecheng-10464	567	26	1	1	NUM
fumecheng-10464	567	27	)	)	PUNCT
fumecheng-10464	567	28	(	(	PUNCT
fumecheng-10464	567	29	1	1	X
fumecheng-10464	567	30	)	)	PUNCT
fumecheng-10464	567	31	(	(	PUNCT
fumecheng-10464	567	32	3	3	NUM
fumecheng-10464	567	33	2	2	NUM
fumecheng-10464	567	34	)	)	PUNCT
fumecheng-10464	567	35	2304	2304	NUM
fumecheng-10464	567	36	cos	cos	PROPN
fumecheng-10464	567	37	(	(	PUNCT
fumecheng-10464	567	38	(	(	PUNCT
fumecheng-10464	567	39	2	2	NUM
fumecheng-10464	567	40	)	)	PUNCT
fumecheng-10464	567	41	)	)	PUNCT
fumecheng-10464	567	42	(	(	PUNCT
fumecheng-10464	567	43	1	1	X
fumecheng-10464	567	44	)	)	PUNCT
fumecheng-10464	567	45	(	(	PUNCT
fumecheng-10464	567	46	3	3	NUM
fumecheng-10464	567	47	2	2	NUM
fumecheng-10464	567	48	)	)	PUNCT
fumecheng-10464	568	1	f	f	PROPN
fumecheng-10464	569	1	f	f	PROPN
fumecheng-10464	569	2	t	t	PROPN
fumecheng-10464	569	3	t	t	PROPN
fumecheng-10464	569	4	t	t	PROPN
fumecheng-10464	569	5	f	f	PROPN
fumecheng-10464	569	6	t	t	PROPN
fumecheng-10464	569	7			PROPN
fumecheng-10464	569	8			PROPN
fumecheng-10464	569	9			PROPN
fumecheng-10464	569	10			NOUN
fumecheng-10464	570	1			ADP
fumecheng-10464	570	2			NUM
fumecheng-10464	570	3			NUM
fumecheng-10464	570	4			NUM
fumecheng-10464	570	5			NUM
fumecheng-10464	570	6			NUM
fumecheng-10464	570	7			NUM
fumecheng-10464	570	8			NUM
fumecheng-10464	570	9			NUM
fumecheng-10464	570	10			NUM
fumecheng-10464	570	11			NUM
fumecheng-10464	570	12			NUM
fumecheng-10464	570	13			PROPN
fumecheng-10464	570	14			NOUN
fumecheng-10464	570	15			PROPN
fumecheng-10464	570	16	−	−	NUM
fumecheng-10464	570	17			PROPN
fumecheng-10464	571	1	+	+	CCONJ
fumecheng-10464	572	1	+	+	NUM
fumecheng-10464	572	2			X
fumecheng-10464	572	3	+	+	ADJ
fumecheng-10464	572	4			PROPN
fumecheng-10464	572	5			SYM
fumecheng-10464	572	6			NUM
fumecheng-10464	572	7	−	−	PROPN
fumecheng-10464	572	8			PROPN
fumecheng-10464	573	1	+	+	CCONJ
fumecheng-10464	573	2	−	−	PROPN
fumecheng-10464	573	3	+	+	NUM
fumecheng-10464	573	4			NUM
fumecheng-10464	574	1	+	+	NOUN
fumecheng-10464	574	2			NOUN
fumecheng-10464	574	3			NOUN
fumecheng-10464	574	4			NUM
fumecheng-10464	574	5			NUM
fumecheng-10464	574	6			NUM
fumecheng-10464	574	7			NUM
fumecheng-10464	574	8	−	−	PROPN
fumecheng-10464	574	9	+	+	CCONJ
fumecheng-10464	574	10			NUM
fumecheng-10464	574	11			NUM
fumecheng-10464	574	12			NOUN
fumecheng-10464	574	13	−	−	ADP
fumecheng-10464	574	14	−	−	PROPN
fumecheng-10464	574	15	+	+	NUM
fumecheng-10464	574	16			NUM
fumecheng-10464	575	1	+	+	CCONJ
fumecheng-10464	575	2			ADP
fumecheng-10464	575	3			NOUN
fumecheng-10464	575	4	2	2	NUM
fumecheng-10464	575	5	4	4	NUM
fumecheng-10464	575	6	2	2	NUM
fumecheng-10464	575	7	2	2	NUM
fumecheng-10464	575	8	2	2	NUM
fumecheng-10464	575	9	21	21	NUM
fumecheng-10464	575	10	2	2	NUM
fumecheng-10464	575	11	2	2	NUM
fumecheng-10464	575	12	2	2	NUM
fumecheng-10464	575	13	2	2	NUM
fumecheng-10464	575	14	24	24	NUM
fumecheng-10464	575	15	96	96	NUM
fumecheng-10464	575	16	(	(	PUNCT
fumecheng-10464	575	17	3	3	NUM
fumecheng-10464	575	18	78	78	NUM
fumecheng-10464	575	19	11	11	NUM
fumecheng-10464	575	20	)	)	PUNCT
fumecheng-10464	575	21	(	(	PUNCT
fumecheng-10464	575	22	)	)	PUNCT
fumecheng-10464	575	23	(	(	PUNCT
fumecheng-10464	575	24	813	813	NUM
fumecheng-10464	575	25	216	216	NUM
fumecheng-10464	575	26	)	)	PUNCT
fumecheng-10464	575	27	48	48	NUM
fumecheng-10464	575	28	(	(	PUNCT
fumecheng-10464	575	29	13	13	NUM
fumecheng-10464	575	30	)	)	PUNCT
fumecheng-10464	575	31	(	(	PUNCT
fumecheng-10464	575	32	73	73	NUM
fumecheng-10464	575	33	72	72	NUM
fumecheng-10464	575	34	)	)	PUNCT
fumecheng-10464	575	35	1	1	NUM
fumecheng-10464	575	36	(	(	PUNCT
fumecheng-10464	575	37	9	9	NUM
fumecheng-10464	575	38	)	)	PUNCT
fumecheng-10464	575	39	(	(	PUNCT
fumecheng-10464	575	40	1	1	X
fumecheng-10464	575	41	)	)	PUNCT
fumecheng-10464	575	42	f	f	NOUN
fumecheng-10464	576	1	f	f	NOUN
fumecheng-10464	576	2	x	x	SYM
fumecheng-10464	576	3	t	t	PROPN
fumecheng-10464	576	4	t	t	PROPN
fumecheng-10464	576	5	t	t	PROPN
fumecheng-10464	576	6	t	t	PRON
fumecheng-10464	576	7			NOUN
fumecheng-10464	576	8			NOUN
fumecheng-10464	576	9			NOUN
fumecheng-10464	576	10			NOUN
fumecheng-10464	576	11			NOUN
fumecheng-10464	576	12	−	−	PROPN
fumecheng-10464	576	13			PROPN
fumecheng-10464	577	1	+	+	CCONJ
fumecheng-10464	577	2			PROPN
fumecheng-10464	577	3	=	=	PUNCT
fumecheng-10464	578	1	−	−	PROPN
fumecheng-10464	578	2	−	−	PROPN
fumecheng-10464	579	1	+	+	CCONJ
fumecheng-10464	579	2	+	+	PUNCT
fumecheng-10464	580	1	+	+	CCONJ
fumecheng-10464	580	2	+	+	ADJ
fumecheng-10464	580	3			PROPN
fumecheng-10464	580	4			PROPN
fumecheng-10464	581	1			PROPN
fumecheng-10464	581	2			NOUN
fumecheng-10464	581	3	−	−	PROPN
fumecheng-10464	581	4			PROPN
fumecheng-10464	582	1	−	−	PROPN
fumecheng-10464	582	2			PROPN
fumecheng-10464	583	1	−	−	NUM
fumecheng-10464	583	2			NOUN
fumecheng-10464	583	3	,	,	PUNCT
fumecheng-10464	583	4	and	and	CCONJ
fumecheng-10464	583	5	2	2	NUM
fumecheng-10464	583	6	4	4	NUM
fumecheng-10464	583	7	2	2	NUM
fumecheng-10464	583	8	4	4	NUM
fumecheng-10464	583	9	2	2	NUM
fumecheng-10464	583	10	2	2	NUM
fumecheng-10464	583	11	2	2	NUM
fumecheng-10464	583	12	22	22	NUM
fumecheng-10464	583	13	2	2	NUM
fumecheng-10464	583	14	2	2	NUM
fumecheng-10464	583	15	2	2	NUM
fumecheng-10464	583	16	288	288	NUM
fumecheng-10464	583	17	(	(	PUNCT
fumecheng-10464	583	18	(	(	PUNCT
fumecheng-10464	583	19	183	183	NUM
fumecheng-10464	583	20	10	10	NUM
fumecheng-10464	583	21	)	)	PUNCT
fumecheng-10464	583	22	4	4	NUM
fumecheng-10464	583	23	(	(	PUNCT
fumecheng-10464	583	24	9	9	NUM
fumecheng-10464	583	25	10	10	NUM
fumecheng-10464	583	26	)	)	PUNCT
fumecheng-10464	583	27	)	)	PUNCT
fumecheng-10464	584	1	(	(	PUNCT
fumecheng-10464	584	2	)	)	PUNCT
fumecheng-10464	584	3	44	44	NUM
fumecheng-10464	584	4	864	864	NUM
fumecheng-10464	584	5	48	48	NUM
fumecheng-10464	584	6	(	(	PUNCT
fumecheng-10464	584	7	24	24	NUM
fumecheng-10464	584	8	)	)	PUNCT
fumecheng-10464	584	9	(	(	PUNCT
fumecheng-10464	584	10	9	9	NUM
fumecheng-10464	584	11	)	)	PUNCT
fumecheng-10464	584	12	(	(	PUNCT
fumecheng-10464	584	13	1	1	X
fumecheng-10464	584	14	)	)	PUNCT
fumecheng-10464	584	15	t	t	NOUN
fumecheng-10464	584	16	x	x	SYM
fumecheng-10464	584	17	t	t	PROPN
fumecheng-10464	584	18	t	t	PROPN
fumecheng-10464	584	19	t	t	PROPN
fumecheng-10464	584	20	f	f	PROPN
fumecheng-10464	584	21			PROPN
fumecheng-10464	584	22			NOUN
fumecheng-10464	584	23			PROPN
fumecheng-10464	584	24			PROPN
fumecheng-10464	584	25			PROPN
fumecheng-10464	584	26			NOUN
fumecheng-10464	584	27	−	−	ADP
fumecheng-10464	585	1	−	−	NUM
fumecheng-10464	586	1			PROPN
fumecheng-10464	587	1	+	+	NOUN
fumecheng-10464	587	2			PROPN
fumecheng-10464	588	1	+	+	CCONJ
fumecheng-10464	588	2	−	−	PROPN
fumecheng-10464	588	3			PROPN
fumecheng-10464	589	1	+	+	NOUN
fumecheng-10464	589	2			PROPN
fumecheng-10464	589	3	=	=	PUNCT
fumecheng-10464	589	4	−	−	PROPN
fumecheng-10464	590	1	+	+	CCONJ
fumecheng-10464	590	2	−	−	PROPN
fumecheng-10464	591	1	+	+	CCONJ
fumecheng-10464	591	2	+	+	NUM
fumecheng-10464	591	3			PROPN
fumecheng-10464	591	4	−	−	PROPN
fumecheng-10464	591	5			PROPN
fumecheng-10464	591	6	−	−	PROPN
fumecheng-10464	591	7	.	.	PUNCT
fumecheng-10464	592	1	the	the	DET
fumecheng-10464	592	2	function	function	NOUN
fumecheng-10464	592	3	x2(t	x2(t	PROPN
fumecheng-10464	592	4	)	)	PUNCT
fumecheng-10464	592	5	that	that	PRON
fumecheng-10464	592	6	appears	appear	VERB
fumecheng-10464	592	7	in	in	ADP
fumecheng-10464	592	8	eq	eq	ADP
fumecheng-10464	592	9	.	.	PUNCT
fumecheng-10464	593	1	(	(	PUNCT
fumecheng-10464	593	2	33	33	NUM
fumecheng-10464	593	3	)	)	PUNCT
fumecheng-10464	593	4	may	may	AUX
fumecheng-10464	593	5	be	be	AUX
fumecheng-10464	593	6	written	write	VERB
fumecheng-10464	593	7	as	as	SCONJ
fumecheng-10464	593	8	follows	follow	VERB
fumecheng-10464	593	9	:	:	PUNCT
fumecheng-10464	593	10	2	2	NUM
fumecheng-10464	593	11	2	2	NUM
fumecheng-10464	593	12	2	2	NUM
fumecheng-10464	593	13	21	21	NUM
fumecheng-10464	593	14	22	22	NUM
fumecheng-10464	593	15	23	23	NUM
fumecheng-10464	593	16	24	24	NUM
fumecheng-10464	593	17	4	4	NUM
fumecheng-10464	593	18	2	2	NUM
fumecheng-10464	593	19	2	2	NUM
fumecheng-10464	593	20	2	2	NUM
fumecheng-10464	593	21	2	2	NUM
fumecheng-10464	593	22	2	2	NUM
fumecheng-10464	593	23	2	2	NUM
fumecheng-10464	593	24	2	2	NUM
fumecheng-10464	593	25	2	2	NUM
fumecheng-10464	593	26	1	1	NUM
fumecheng-10464	593	27	cos	cos	PROPN
fumecheng-10464	593	28	sin	sin	PROPN
fumecheng-10464	593	29	cos3	cos3	PROPN
fumecheng-10464	593	30	sin3	sin3	PROPN
fumecheng-10464	593	31	(	(	PUNCT
fumecheng-10464	593	32	8	8	NUM
fumecheng-10464	593	33	cos5	cos5	NOUN
fumecheng-10464	593	34	(	(	PUNCT
fumecheng-10464	593	35	3	3	NUM
fumecheng-10464	593	36	5	5	NUM
fumecheng-10464	593	37	)	)	PUNCT
fumecheng-10464	593	38	sin5	sin5	NOUN
fumecheng-10464	593	39	)	)	PUNCT
fumecheng-10464	593	40	1	1	NUM
fumecheng-10464	593	41	96	96	NUM
fumecheng-10464	593	42	(	(	PUNCT
fumecheng-10464	593	43	3	3	NUM
fumecheng-10464	593	44	cos	cos	X
fumecheng-10464	593	45	sin	sin	NOUN
fumecheng-10464	593	46	)	)	PUNCT
fumecheng-10464	593	47	96	96	NUM
fumecheng-10464	594	1	(	(	PUNCT
fumecheng-10464	594	2	3	3	NUM
fumecheng-10464	594	3	cos	cos	PROPN
fumecheng-10464	594	4	(	(	PUNCT
fumecheng-10464	594	5	(	(	PUNCT
fumecheng-10464	594	6	2	2	NUM
fumecheng-10464	594	7	)	)	PUNCT
fumecheng-10464	594	8	)	)	PUNCT
fumecheng-10464	594	9	(	(	PUNCT
fumecheng-10464	594	10	2	2	X
fumecheng-10464	594	11	)	)	PUNCT
fumecheng-10464	594	12	sin	sin	NOUN
fumecheng-10464	594	13	(	(	PUNCT
fumecheng-10464	594	14	(	(	PUNCT
fumecheng-10464	594	15	2	2	NUM
fumecheng-10464	594	16	)	)	PUNCT
fumecheng-10464	594	17	)	)	PUNCT
fumecheng-10464	594	18	)	)	PUNCT
fumecheng-10464	594	19	(	(	PUNCT
fumecheng-10464	594	20	)	)	PUNCT
fumecheng-10464	594	21	sin	sin	NOUN
fumecheng-10464	594	22	96	96	NUM
fumecheng-10464	594	23	(	(	PUNCT
fumecheng-10464	594	24	)	)	PUNCT
fumecheng-10464	594	25	(	(	PUNCT
fumecheng-10464	594	26	3	3	NUM
fumecheng-10464	594	27	)	)	PUNCT
fumecheng-10464	594	28	(	(	PUNCT
fumecheng-10464	594	29	)	)	PUNCT
fumecheng-10464	594	30	96	96	NUM
fumecheng-10464	594	31	(	(	PUNCT
fumecheng-10464	594	32	3	3	NUM
fumecheng-10464	594	33	cos	cos	PROPN
fumecheng-10464	594	34	(	(	PUNCT
fumecheng-10464	594	35	(	(	PUNCT
fumecheng-10464	594	36	2	2	NUM
fumecheng-10464	594	37	)	)	PUNCT
fumecheng-10464	594	38	)	)	PUNCT
fumecheng-10464	594	39	(	(	PUNCT
fumecheng-10464	594	40	2	2	NUM
fumecheng-10464	594	41	x	x	SYM
fumecheng-10464	594	42	t	t	NOUN
fumecheng-10464	594	43	x	x	SYM
fumecheng-10464	594	44	t	t	NOUN
fumecheng-10464	594	45	x	x	SYM
fumecheng-10464	594	46	t	t	PROPN
fumecheng-10464	594	47	x	x	SYM
fumecheng-10464	594	48	t	t	PROPN
fumecheng-10464	594	49	t	t	PROPN
fumecheng-10464	594	50	t	t	PROPN
fumecheng-10464	594	51	f	f	PROPN
fumecheng-10464	594	52	t	t	PROPN
fumecheng-10464	594	53	t	t	PROPN
fumecheng-10464	594	54	f	f	PROPN
fumecheng-10464	594	55	t	t	PROPN
fumecheng-10464	594	56	t	t	PROPN
fumecheng-10464	594	57	x	x	PUNCT
fumecheng-10464	594	58	t	t	PROPN
fumecheng-10464	594	59	t	t	PROPN
fumecheng-10464	594	60	f	f	PROPN
fumecheng-10464	594	61	t	t	PROPN
fumecheng-10464	594	62			PROPN
fumecheng-10464	594	63			X
fumecheng-10464	594	64			X
fumecheng-10464	594	65			X
fumecheng-10464	594	66			NOUN
fumecheng-10464	594	67			PROPN
fumecheng-10464	594	68			NOUN
fumecheng-10464	594	69			NOUN
fumecheng-10464	594	70			NOUN
fumecheng-10464	594	71			X
fumecheng-10464	594	72			X
fumecheng-10464	594	73			ADJ
fumecheng-10464	594	74			NOUN
fumecheng-10464	594	75			NOUN
fumecheng-10464	594	76			NOUN
fumecheng-10464	594	77			NOUN
fumecheng-10464	594	78			NOUN
fumecheng-10464	594	79			X
fumecheng-10464	594	80			X
fumecheng-10464	594	81			X
fumecheng-10464	594	82			X
fumecheng-10464	594	83			X
fumecheng-10464	594	84			X
fumecheng-10464	594	85			PROPN
fumecheng-10464	594	86			NOUN
fumecheng-10464	594	87			NOUN
fumecheng-10464	594	88			NOUN
fumecheng-10464	594	89	+	+	X
fumecheng-10464	594	90	+	+	PUNCT
fumecheng-10464	594	91	+	+	PUNCT
fumecheng-10464	594	92	+	+	PUNCT
fumecheng-10464	594	93	+	+	CCONJ
fumecheng-10464	594	94	−	−	X
fumecheng-10464	595	1	+	+	CCONJ
fumecheng-10464	595	2	−	−	PROPN
fumecheng-10464	595	3			PROPN
fumecheng-10464	595	4	+	+	NUM
fumecheng-10464	595	5			PROPN
fumecheng-10464	595	6			PROPN
fumecheng-10464	595	7	−	−	PROPN
fumecheng-10464	595	8	−	−	NOUN
fumecheng-10464	595	9	+	+	CCONJ
fumecheng-10464	595	10			NUM
fumecheng-10464	595	11	−	−	PROPN
fumecheng-10464	595	12	−	−	PROPN
fumecheng-10464	595	13	=	=	PUNCT
fumecheng-10464	595	14	+	+	PUNCT
fumecheng-10464	595	15	+	+	CCONJ
fumecheng-10464	595	16	+	+	CCONJ
fumecheng-10464	595	17	−	−	PROPN
fumecheng-10464	595	18	−	−	PROPN
fumecheng-10464	595	19	−	−	PROPN
fumecheng-10464	595	20	−	−	PROPN
fumecheng-10464	595	21	+	+	X
fumecheng-10464	596	1	+	+	NUM
fumecheng-10464	596	2			NUM
fumecheng-10464	596	3	+	+	CCONJ
fumecheng-10464	596	4	2	2	NUM
fumecheng-10464	596	5	2	2	NUM
fumecheng-10464	596	6	2	2	NUM
fumecheng-10464	596	7	,	,	PUNCT
fumecheng-10464	596	8	)	)	PUNCT
fumecheng-10464	596	9	sin	sin	NOUN
fumecheng-10464	596	10	(	(	PUNCT
fumecheng-10464	596	11	(	(	PUNCT
fumecheng-10464	596	12	2	2	NUM
fumecheng-10464	596	13	)	)	PUNCT
fumecheng-10464	596	14	)	)	PUNCT
fumecheng-10464	596	15	)	)	PUNCT
fumecheng-10464	597	1	(	(	PUNCT
fumecheng-10464	597	2	3	3	X
fumecheng-10464	597	3	)	)	PUNCT
fumecheng-10464	597	4	(	(	PUNCT
fumecheng-10464	597	5	)	)	PUNCT
fumecheng-10464	597	6	t	t	ADJ
fumecheng-10464	597	7			VERB
fumecheng-10464	597	8			X
fumecheng-10464	597	9			X
fumecheng-10464	597	10			NOUN
fumecheng-10464	598	1			ADP
fumecheng-10464	598	2			NUM
fumecheng-10464	598	3			NUM
fumecheng-10464	598	4			NUM
fumecheng-10464	598	5			NUM
fumecheng-10464	598	6			NUM
fumecheng-10464	598	7			NOUN
fumecheng-10464	598	8			NUM
fumecheng-10464	598	9			NUM
fumecheng-10464	598	10			NOUN
fumecheng-10464	598	11			NUM
fumecheng-10464	598	12			NUM
fumecheng-10464	598	13			NUM
fumecheng-10464	598	14			NUM
fumecheng-10464	598	15	+	+	NUM
fumecheng-10464	598	16			NUM
fumecheng-10464	598	17			NUM
fumecheng-10464	598	18			NUM
fumecheng-10464	598	19	+	+	NUM
fumecheng-10464	598	20	−	−	NOUN
fumecheng-10464	598	21			NOUN
fumecheng-10464	598	22	2	2	NUM
fumecheng-10464	598	23	2	2	NUM
fumecheng-10464	598	24	2	2	NUM
fumecheng-10464	598	25	2	2	NUM
fumecheng-10464	598	26	2	2	NUM
fumecheng-10464	598	27	4	4	NUM
fumecheng-10464	598	28	2	2	NUM
fumecheng-10464	598	29	2	2	NUM
fumecheng-10464	598	30	4	4	NUM
fumecheng-10464	598	31	21	21	NUM
fumecheng-10464	598	32	4	4	NUM
fumecheng-10464	598	33	2	2	NUM
fumecheng-10464	598	34	2	2	NUM
fumecheng-10464	598	35	2	2	NUM
fumecheng-10464	598	36	2	2	NUM
fumecheng-10464	598	37	2	2	NUM
fumecheng-10464	598	38	(	(	PUNCT
fumecheng-10464	598	39	(	(	PUNCT
fumecheng-10464	598	40	9	9	NUM
fumecheng-10464	598	41	)	)	PUNCT
fumecheng-10464	598	42	(	(	PUNCT
fumecheng-10464	598	43	)	)	PUNCT
fumecheng-10464	598	44	36(111	36(111	NOUN
fumecheng-10464	598	45	18	18	NUM
fumecheng-10464	598	46	)	)	PUNCT
fumecheng-10464	598	47	)	)	PUNCT
fumecheng-10464	599	1	(	(	PUNCT
fumecheng-10464	599	2	9	9	NUM
fumecheng-10464	599	3	)	)	PUNCT
fumecheng-10464	599	4	(	(	PUNCT
fumecheng-10464	599	5	)	)	PUNCT
fumecheng-10464	599	6	x	x	SYM
fumecheng-10464	600	1	f	f	PROPN
fumecheng-10464	600	2			PROPN
fumecheng-10464	600	3			PROPN
fumecheng-10464	600	4			NOUN
fumecheng-10464	600	5			NOUN
fumecheng-10464	600	6			X
fumecheng-10464	600	7			X
fumecheng-10464	600	8			X
fumecheng-10464	600	9			X
fumecheng-10464	600	10			X
fumecheng-10464	600	11			X
fumecheng-10464	600	12			PROPN
fumecheng-10464	600	13	=	=	PROPN
fumecheng-10464	600	14	−	−	PROPN
fumecheng-10464	600	15	−	−	PROPN
fumecheng-10464	600	16	+	+	CCONJ
fumecheng-10464	600	17	+	+	NUM
fumecheng-10464	600	18			PROPN
fumecheng-10464	600	19	−	−	NOUN
fumecheng-10464	600	20			NOUN
fumecheng-10464	600	21	−	−	NOUN
fumecheng-10464	600	22	−	−	NOUN
fumecheng-10464	600	23	,	,	PUNCT
fumecheng-10464	600	24			ADJ
fumecheng-10464	600	25			PROPN
fumecheng-10464	600	26			PROPN
fumecheng-10464	600	27			X
fumecheng-10464	600	28			NOUN
fumecheng-10464	600	29			X
fumecheng-10464	600	30			VERB
fumecheng-10464	600	31			PROPN
fumecheng-10464	600	32			INTJ
fumecheng-10464	600	33			PROPN
fumecheng-10464	600	34			NOUN
fumecheng-10464	601	1			PROPN
fumecheng-10464	601	2			PROPN
fumecheng-10464	601	3			PROPN
fumecheng-10464	602	1			PROPN
fumecheng-10464	602	2			NOUN
fumecheng-10464	602	3			PROPN
fumecheng-10464	603	1			PROPN
fumecheng-10464	603	2			NOUN
fumecheng-10464	604	1			PROPN
fumecheng-10464	604	2			PROPN
fumecheng-10464	604	3			PROPN
fumecheng-10464	605	1			PROPN
fumecheng-10464	605	2			NOUN
fumecheng-10464	605	3	−+−	−+−	NOUN
fumecheng-10464	605	4	−−−	−−−	PROPN
fumecheng-10464	606	1	+	+	NOUN
fumecheng-10464	606	2	−−−	−−−	ADJ
fumecheng-10464	606	3	−−	−−	ADJ
fumecheng-10464	606	4	=	=	PUNCT
fumecheng-10464	606	5	)	)	PUNCT
fumecheng-10464	606	6	18111(12	18111(12	NUM
fumecheng-10464	606	7	)	)	PUNCT
fumecheng-10464	606	8	)	)	PUNCT
fumecheng-10464	607	1	(	(	PUNCT
fumecheng-10464	607	2	9(29	9(29	NUM
fumecheng-10464	607	3	)	)	PUNCT
fumecheng-10464	607	4	)	)	PUNCT
fumecheng-10464	607	5	(	(	PUNCT
fumecheng-10464	607	6	9(42	9(42	NUM
fumecheng-10464	607	7	)	)	PUNCT
fumecheng-10464	607	8	)	)	PUNCT
fumecheng-10464	607	9	(	(	PUNCT
fumecheng-10464	607	10	9	9	NUM
fumecheng-10464	607	11	(	(	PUNCT
fumecheng-10464	607	12	1	1	NUM
fumecheng-10464	607	13	4224	4224	NUM
fumecheng-10464	607	14	22222	22222	NUM
fumecheng-10464	607	15	2222222	2222222	NUM
fumecheng-10464	607	16	22222422	22222422	NUM
fumecheng-10464	608	1			PROPN
fumecheng-10464	608	2			NOUN
fumecheng-10464	608	3			PROPN
fumecheng-10464	608	4			PROPN
fumecheng-10464	608	5	f	f	NOUN
fumecheng-10464	609	1	x	x	SYM
fumecheng-10464	609	2	2	2	NUM
fumecheng-10464	609	3	2	2	NUM
fumecheng-10464	609	4	23	23	NUM
fumecheng-10464	609	5	4	4	NUM
fumecheng-10464	609	6	2	2	NUM
fumecheng-10464	609	7	2	2	NUM
fumecheng-10464	609	8	2	2	NUM
fumecheng-10464	609	9	9	9	NUM
fumecheng-10464	609	10	(	(	PUNCT
fumecheng-10464	609	11	4	4	NUM
fumecheng-10464	609	12	(	(	PUNCT
fumecheng-10464	609	13	)	)	PUNCT
fumecheng-10464	609	14	)	)	PUNCT
fumecheng-10464	609	15	(	(	PUNCT
fumecheng-10464	609	16	)	)	PUNCT
fumecheng-10464	609	17	x	x	SYM
fumecheng-10464	609	18	f	f	PROPN
fumecheng-10464	609	19			PROPN
fumecheng-10464	609	20			PROPN
fumecheng-10464	609	21			NOUN
fumecheng-10464	609	22			X
fumecheng-10464	609	23			X
fumecheng-10464	609	24			X
fumecheng-10464	609	25	=	=	SYM
fumecheng-10464	610	1	−	−	PROPN
fumecheng-10464	610	2	−	−	PROPN
fumecheng-10464	610	3	−	−	PROPN
fumecheng-10464	610	4	,	,	PUNCT
fumecheng-10464	610	5	and	and	CCONJ
fumecheng-10464	610	6	2	2	NUM
fumecheng-10464	610	7	2	2	NUM
fumecheng-10464	610	8	2	2	NUM
fumecheng-10464	610	9	2	2	NUM
fumecheng-10464	610	10	2	2	NUM
fumecheng-10464	610	11	2	2	NUM
fumecheng-10464	610	12	24	24	NUM
fumecheng-10464	610	13	4	4	NUM
fumecheng-10464	610	14	2	2	NUM
fumecheng-10464	610	15	2	2	NUM
fumecheng-10464	610	16	2	2	NUM
fumecheng-10464	610	17	9	9	NUM
fumecheng-10464	610	18	(	(	PUNCT
fumecheng-10464	610	19	(	(	PUNCT
fumecheng-10464	610	20	)	)	PUNCT
fumecheng-10464	610	21	2	2	NUM
fumecheng-10464	610	22	(	(	PUNCT
fumecheng-10464	610	23	2	2	NUM
fumecheng-10464	610	24	(	(	PUNCT
fumecheng-10464	610	25	)	)	PUNCT
fumecheng-10464	610	26	)	)	PUNCT
fumecheng-10464	610	27	)	)	PUNCT
fumecheng-10464	611	1	(	(	PUNCT
fumecheng-10464	611	2	)	)	PUNCT
fumecheng-10464	611	3	x	x	SYM
fumecheng-10464	611	4	f	f	ADV
fumecheng-10464	611	5			X
fumecheng-10464	611	6			NOUN
fumecheng-10464	611	7			NOUN
fumecheng-10464	611	8			NOUN
fumecheng-10464	611	9			X
fumecheng-10464	611	10			X
fumecheng-10464	611	11			X
fumecheng-10464	611	12	=	=	SYM
fumecheng-10464	611	13	−	−	NOUN
fumecheng-10464	611	14	+	+	CCONJ
fumecheng-10464	611	15	−	−	PROPN
fumecheng-10464	611	16	+	+	CCONJ
fumecheng-10464	611	17	−	−	PROPN
fumecheng-10464	611	18	−	−	PROPN
fumecheng-10464	611	19	.	.	PUNCT