id	sid	tid	token	lemma	pos
fumecheng-10743	1	1	10743	10743	NUM
fumecheng-10743	1	2	facta	facta	PROPN
fumecheng-10743	1	3	universitatis	universitatis	PROPN
fumecheng-10743	1	4	series	series	NOUN
fumecheng-10743	1	5	:	:	PUNCT
fumecheng-10743	1	6	mechanical	mechanical	ADJ
fumecheng-10743	1	7	engineering	engineering	NOUN
fumecheng-10743	1	8	vol	vol	NOUN
fumecheng-10743	1	9	.	.	PROPN
fumecheng-10743	1	10	20	20	NUM
fumecheng-10743	1	11	,	,	PUNCT
fumecheng-10743	1	12	no	no	DET
fumecheng-10743	1	13	2	2	NUM
fumecheng-10743	1	14	,	,	PUNCT
fumecheng-10743	1	15	2022	2022	NUM
fumecheng-10743	1	16	,	,	PUNCT
fumecheng-10743	1	17	pp	pp	ADV
fumecheng-10743	1	18	.	.	PUNCT
fumecheng-10743	2	1	445	445	NUM
fumecheng-10743	2	2	455	455	NUM
fumecheng-10743	3	1	https://doi.org/10.22190/fume220420023	https://doi.org/10.22190/fume220420023	NOUN
fumecheng-10743	3	2	m	m	PROPN
fumecheng-10743	3	3	©	©	PROPN
fumecheng-10743	3	4	2022	2022	NUM
fumecheng-10743	3	5	by	by	ADP
fumecheng-10743	3	6	university	university	PROPN
fumecheng-10743	3	7	of	of	ADP
fumecheng-10743	3	8	niš	niš	PROPN
fumecheng-10743	3	9	,	,	PUNCT
fumecheng-10743	3	10	serbia	serbia	PROPN
fumecheng-10743	3	11	|	|	ADV
fumecheng-10743	3	12	creative	creative	ADJ
fumecheng-10743	3	13	commons	common	NOUN
fumecheng-10743	3	14	license	license	NOUN
fumecheng-10743	3	15	:	:	PUNCT
fumecheng-10743	3	16	cc	cc	VERB
fumecheng-10743	3	17	by	by	ADP
fumecheng-10743	3	18	-	-	PUNCT
fumecheng-10743	3	19	nc	nc	VERB
fumecheng-10743	3	20	-	-	PUNCT
fumecheng-10743	3	21	nd	nd	ADV
fumecheng-10743	3	22	original	original	ADJ
fumecheng-10743	3	23	scientific	scientific	ADJ
fumecheng-10743	3	24	paper	paper	ADV
fumecheng-10743	3	25	simplified	simplify	VERB
fumecheng-10743	3	26	hamiltonian	hamiltonian	ADJ
fumecheng-10743	3	27	-	-	PUNCT
fumecheng-10743	3	28	based	base	VERB
fumecheng-10743	3	29	frequency	frequency	NOUN
fumecheng-10743	3	30	-	-	PUNCT
fumecheng-10743	3	31	amplitude	amplitude	NOUN
fumecheng-10743	3	32	formulation	formulation	NOUN
fumecheng-10743	3	33	for	for	ADP
fumecheng-10743	3	34	nonlinear	nonlinear	ADJ
fumecheng-10743	3	35	vibration	vibration	NOUN
fumecheng-10743	3	36	systems	system	NOUN
fumecheng-10743	3	37	hongjin	hongjin	NOUN
fumecheng-10743	3	38	ma	ma	PROPN
fumecheng-10743	3	39	school	school	PROPN
fumecheng-10743	3	40	of	of	ADP
fumecheng-10743	3	41	science	science	PROPN
fumecheng-10743	3	42	,	,	PUNCT
fumecheng-10743	3	43	xi'an	xi'an	PROPN
fumecheng-10743	3	44	university	university	PROPN
fumecheng-10743	3	45	of	of	ADP
fumecheng-10743	3	46	architecture	architecture	NOUN
fumecheng-10743	3	47	and	and	CCONJ
fumecheng-10743	3	48	technology	technology	NOUN
fumecheng-10743	3	49	,	,	PUNCT
fumecheng-10743	3	50	xi’an	xi’an	PROPN
fumecheng-10743	3	51	,	,	PUNCT
fumecheng-10743	3	52	china	china	PROPN
fumecheng-10743	3	53	abstract	abstract	PROPN
fumecheng-10743	3	54	.	.	PUNCT
fumecheng-10743	4	1	the	the	DET
fumecheng-10743	4	2	hamiltonian	hamiltonian	NOUN
fumecheng-10743	4	3	-	-	PUNCT
fumecheng-10743	4	4	based	base	VERB
fumecheng-10743	4	5	frequency	frequency	NOUN
fumecheng-10743	4	6	formulation	formulation	NOUN
fumecheng-10743	4	7	has	have	AUX
fumecheng-10743	4	8	been	be	AUX
fumecheng-10743	4	9	hailed	hail	VERB
fumecheng-10743	4	10	as	as	ADP
fumecheng-10743	4	11	an	an	DET
fumecheng-10743	4	12	unprecedented	unprecedented	ADJ
fumecheng-10743	4	13	success	success	NOUN
fumecheng-10743	4	14	for	for	ADP
fumecheng-10743	4	15	it	it	PRON
fumecheng-10743	4	16	gives	give	VERB
fumecheng-10743	4	17	a	a	DET
fumecheng-10743	4	18	straightforward	straightforward	ADJ
fumecheng-10743	4	19	insight	insight	NOUN
fumecheng-10743	4	20	into	into	ADP
fumecheng-10743	4	21	a	a	DET
fumecheng-10743	4	22	complex	complex	ADJ
fumecheng-10743	4	23	nonlinear	nonlinear	ADJ
fumecheng-10743	4	24	vibration	vibration	NOUN
fumecheng-10743	4	25	system	system	NOUN
fumecheng-10743	4	26	with	with	ADP
fumecheng-10743	4	27	simple	simple	ADJ
fumecheng-10743	4	28	calculation	calculation	NOUN
fumecheng-10743	4	29	.	.	PUNCT
fumecheng-10743	5	1	this	this	DET
fumecheng-10743	5	2	paper	paper	NOUN
fumecheng-10743	5	3	gives	give	VERB
fumecheng-10743	5	4	a	a	DET
fumecheng-10743	5	5	systematical	systematical	ADJ
fumecheng-10743	5	6	analysis	analysis	NOUN
fumecheng-10743	5	7	of	of	ADP
fumecheng-10743	5	8	the	the	DET
fumecheng-10743	5	9	formulation	formulation	NOUN
fumecheng-10743	5	10	,	,	PUNCT
fumecheng-10743	5	11	and	and	CCONJ
fumecheng-10743	5	12	two	two	NUM
fumecheng-10743	5	13	simplified	simplified	ADJ
fumecheng-10743	5	14	formulations	formulation	NOUN
fumecheng-10743	5	15	are	be	AUX
fumecheng-10743	5	16	suggested	suggest	VERB
fumecheng-10743	5	17	.	.	PUNCT
fumecheng-10743	6	1	the	the	DET
fumecheng-10743	6	2	cubic	cubic	ADJ
fumecheng-10743	6	3	-	-	PUNCT
fumecheng-10743	6	4	quintic	quintic	ADJ
fumecheng-10743	6	5	duffing	duffing	NOUN
fumecheng-10743	6	6	oscillator	oscillator	NOUN
fumecheng-10743	6	7	is	be	AUX
fumecheng-10743	6	8	used	use	VERB
fumecheng-10743	6	9	as	as	ADP
fumecheng-10743	6	10	an	an	DET
fumecheng-10743	6	11	example	example	NOUN
fumecheng-10743	6	12	to	to	PART
fumecheng-10743	6	13	show	show	VERB
fumecheng-10743	6	14	extremely	extremely	ADV
fumecheng-10743	6	15	simple	simple	ADJ
fumecheng-10743	6	16	calculation	calculation	NOUN
fumecheng-10743	6	17	and	and	CCONJ
fumecheng-10743	6	18	remarkable	remarkable	ADJ
fumecheng-10743	6	19	accuracy	accuracy	NOUN
fumecheng-10743	6	20	.	.	PUNCT
fumecheng-10743	7	1	it	it	PRON
fumecheng-10743	7	2	can	can	AUX
fumecheng-10743	7	3	be	be	AUX
fumecheng-10743	7	4	used	use	VERB
fumecheng-10743	7	5	as	as	ADP
fumecheng-10743	7	6	a	a	DET
fumecheng-10743	7	7	paradigm	paradigm	NOUN
fumecheng-10743	7	8	for	for	ADP
fumecheng-10743	7	9	many	many	ADJ
fumecheng-10743	7	10	other	other	ADJ
fumecheng-10743	7	11	applications	application	NOUN
fumecheng-10743	7	12	,	,	PUNCT
fumecheng-10743	7	13	and	and	CCONJ
fumecheng-10743	7	14	the	the	DET
fumecheng-10743	7	15	one	one	NUM
fumecheng-10743	7	16	-	-	PUNCT
fumecheng-10743	7	17	step	step	NOUN
fumecheng-10743	7	18	solving	solving	NOUN
fumecheng-10743	7	19	process	process	NOUN
fumecheng-10743	7	20	has	have	AUX
fumecheng-10743	7	21	cleaned	clean	VERB
fumecheng-10743	7	22	up	up	ADP
fumecheng-10743	7	23	the	the	DET
fumecheng-10743	7	24	road	road	NOUN
fumecheng-10743	7	25	of	of	ADP
fumecheng-10743	7	26	the	the	DET
fumecheng-10743	7	27	nonlinear	nonlinear	ADJ
fumecheng-10743	7	28	vibration	vibration	NOUN
fumecheng-10743	7	29	theory	theory	NOUN
fumecheng-10743	7	30	.	.	PUNCT
fumecheng-10743	8	1	key	key	ADJ
fumecheng-10743	8	2	words	word	NOUN
fumecheng-10743	8	3	:	:	PUNCT
fumecheng-10743	8	4	he	he	PRON
fumecheng-10743	8	5	’s	’	VERB
fumecheng-10743	8	6	frequency	frequency	NOUN
fumecheng-10743	8	7	formulation	formulation	NOUN
fumecheng-10743	8	8	,	,	PUNCT
fumecheng-10743	8	9	duffing	duffe	VERB
fumecheng-10743	8	10	equation	equation	NOUN
fumecheng-10743	8	11	,	,	PUNCT
fumecheng-10743	8	12	hamilton	hamilton	PROPN
fumecheng-10743	8	13	principle	principle	PROPN
fumecheng-10743	8	14	,	,	PUNCT
fumecheng-10743	8	15	one	one	NUM
fumecheng-10743	8	16	-	-	PUNCT
fumecheng-10743	8	17	step	step	NOUN
fumecheng-10743	8	18	solving	solve	VERB
fumecheng-10743	8	19	1	1	NUM
fumecheng-10743	8	20	.	.	PUNCT
fumecheng-10743	9	1	introduction	introduction	NOUN
fumecheng-10743	9	2	nonlinear	nonlinear	ADJ
fumecheng-10743	9	3	vibration	vibration	NOUN
fumecheng-10743	9	4	systems	system	NOUN
fumecheng-10743	9	5	arise	arise	VERB
fumecheng-10743	9	6	everywhere	everywhere	ADV
fumecheng-10743	9	7	in	in	ADP
fumecheng-10743	9	8	mechanical	mechanical	ADJ
fumecheng-10743	9	9	engineering	engineering	NOUN
fumecheng-10743	9	10	,	,	PUNCT
fumecheng-10743	9	11	as	as	ADP
fumecheng-10743	9	12	in	in	ADP
fumecheng-10743	9	13	thin	thin	ADJ
fumecheng-10743	9	14	walled	walled	ADJ
fumecheng-10743	9	15	structures	structure	NOUN
fumecheng-10743	9	16	[	[	X
fumecheng-10743	9	17	1	1	NUM
fumecheng-10743	9	18	]	]	PUNCT
fumecheng-10743	9	19	,	,	PUNCT
fumecheng-10743	9	20	rotor	rotor	NOUN
fumecheng-10743	9	21	vibration	vibration	NOUN
fumecheng-10743	9	22	[	[	X
fumecheng-10743	9	23	2,3	2,3	NUM
fumecheng-10743	9	24	]	]	PUNCT
fumecheng-10743	9	25	,	,	PUNCT
fumecheng-10743	9	26	gyroscope	gyroscope	NOUN
fumecheng-10743	9	27	systems	system	NOUN
fumecheng-10743	9	28	[	[	X
fumecheng-10743	9	29	4,5	4,5	NUM
fumecheng-10743	9	30	]	]	PUNCT
fumecheng-10743	9	31	,	,	PUNCT
fumecheng-10743	9	32	micro	micro	ADJ
fumecheng-10743	9	33	-	-	ADJ
fumecheng-10743	9	34	electro	electro	ADJ
fumecheng-10743	9	35	mechanical	mechanical	ADJ
fumecheng-10743	9	36	systems	system	NOUN
fumecheng-10743	9	37	[	[	X
fumecheng-10743	9	38	6,7	6,7	NUM
fumecheng-10743	9	39	]	]	PUNCT
fumecheng-10743	9	40	,	,	PUNCT
fumecheng-10743	9	41	packaging	packaging	NOUN
fumecheng-10743	9	42	systems	system	NOUN
fumecheng-10743	9	43	[	[	X
fumecheng-10743	9	44	8	8	NUM
fumecheng-10743	9	45	]	]	PUNCT
fumecheng-10743	9	46	,	,	PUNCT
fumecheng-10743	9	47	building	build	VERB
fumecheng-10743	9	48	vibration	vibration	NOUN
fumecheng-10743	9	49	[	[	X
fumecheng-10743	9	50	9	9	NUM
fumecheng-10743	9	51	]	]	PUNCT
fumecheng-10743	9	52	,	,	PUNCT
fumecheng-10743	9	53	heavy	heavy	ADJ
fumecheng-10743	9	54	machinery	machinery	NOUN
fumecheng-10743	9	55	[	[	X
fumecheng-10743	9	56	10	10	NUM
fumecheng-10743	9	57	]	]	PUNCT
fumecheng-10743	9	58	,	,	PUNCT
fumecheng-10743	9	59	to	to	PART
fumecheng-10743	9	60	name	name	VERB
fumecheng-10743	9	61	but	but	CCONJ
fumecheng-10743	9	62	a	a	DET
fumecheng-10743	9	63	few	few	ADJ
fumecheng-10743	9	64	.	.	PUNCT
fumecheng-10743	10	1	the	the	DET
fumecheng-10743	10	2	most	most	ADV
fumecheng-10743	10	3	famous	famous	ADJ
fumecheng-10743	10	4	nonlinear	nonlinear	ADJ
fumecheng-10743	10	5	oscillators	oscillator	NOUN
fumecheng-10743	10	6	include	include	VERB
fumecheng-10743	10	7	the	the	DET
fumecheng-10743	10	8	pendulum	pendulum	ADJ
fumecheng-10743	10	9	systems	system	NOUN
fumecheng-10743	10	10	[	[	X
fumecheng-10743	10	11	11	11	NUM
fumecheng-10743	10	12	,	,	PUNCT
fumecheng-10743	10	13	12	12	NUM
fumecheng-10743	10	14	]	]	PUNCT
fumecheng-10743	10	15	,	,	PUNCT
fumecheng-10743	10	16	van	van	PROPN
fumecheng-10743	10	17	der	der	ADJ
fumecheng-10743	10	18	pol	pol	PROPN
fumecheng-10743	10	19	oscillator	oscillator	NOUN
fumecheng-10743	10	20	and	and	CCONJ
fumecheng-10743	10	21	duffing	duffe	VERB
fumecheng-10743	10	22	oscillator	oscillator	NOUN
fumecheng-10743	10	23	[	[	X
fumecheng-10743	10	24	13	13	NUM
fumecheng-10743	10	25	]	]	PUNCT
fumecheng-10743	10	26	.	.	PUNCT
fumecheng-10743	11	1	the	the	DET
fumecheng-10743	11	2	spring	spring	NOUN
fumecheng-10743	11	3	-	-	PUNCT
fumecheng-10743	11	4	pendulum	pendulum	NOUN
fumecheng-10743	11	5	systems	system	NOUN
fumecheng-10743	11	6	have	have	VERB
fumecheng-10743	11	7	many	many	ADJ
fumecheng-10743	11	8	applications	application	NOUN
fumecheng-10743	11	9	in	in	ADP
fumecheng-10743	11	10	satellites	satellite	NOUN
fumecheng-10743	11	11	,	,	PUNCT
fumecheng-10743	11	12	submarines	submarine	NOUN
fumecheng-10743	11	13	,	,	PUNCT
fumecheng-10743	11	14	aircraft	aircraft	NOUN
fumecheng-10743	11	15	,	,	PUNCT
fumecheng-10743	11	16	and	and	CCONJ
fumecheng-10743	11	17	energy	energy	NOUN
fumecheng-10743	11	18	harvesting	harvesting	NOUN
fumecheng-10743	11	19	device	device	NOUN
fumecheng-10743	11	20	[	[	X
fumecheng-10743	11	21	14	14	NUM
fumecheng-10743	11	22	]	]	PUNCT
fumecheng-10743	11	23	.	.	PUNCT
fumecheng-10743	12	1	the	the	DET
fumecheng-10743	12	2	recent	recent	ADJ
fumecheng-10743	12	3	research	research	NOUN
fumecheng-10743	12	4	frontier	frontier	NOUN
fumecheng-10743	12	5	in	in	ADP
fumecheng-10743	12	6	the	the	DET
fumecheng-10743	12	7	nonlinear	nonlinear	ADJ
fumecheng-10743	12	8	vibration	vibration	NOUN
fumecheng-10743	12	9	theory	theory	NOUN
fumecheng-10743	12	10	is	be	AUX
fumecheng-10743	12	11	the	the	DET
fumecheng-10743	12	12	fractal	fractal	ADJ
fumecheng-10743	12	13	vibration	vibration	NOUN
fumecheng-10743	12	14	;	;	PUNCT
fumecheng-10743	12	15	hence	hence	ADV
fumecheng-10743	12	16	the	the	DET
fumecheng-10743	12	17	description	description	NOUN
fumecheng-10743	12	18	of	of	ADP
fumecheng-10743	12	19	a	a	DET
fumecheng-10743	12	20	vibrating	vibrate	VERB
fumecheng-10743	12	21	system	system	NOUN
fumecheng-10743	12	22	in	in	ADP
fumecheng-10743	12	23	a	a	DET
fumecheng-10743	12	24	fractal	fractal	ADJ
fumecheng-10743	12	25	space	space	NOUN
fumecheng-10743	12	26	[	[	X
fumecheng-10743	12	27	15	15	NUM
fumecheng-10743	12	28	-	-	SYM
fumecheng-10743	12	29	18	18	NUM
fumecheng-10743	12	30	]	]	PUNCT
fumecheng-10743	12	31	.	.	PUNCT
fumecheng-10743	13	1	generally	generally	ADV
fumecheng-10743	13	2	a	a	DET
fumecheng-10743	13	3	nonlinear	nonlinear	ADJ
fumecheng-10743	13	4	vibration	vibration	NOUN
fumecheng-10743	13	5	system	system	NOUN
fumecheng-10743	13	6	is	be	AUX
fumecheng-10743	13	7	complex	complex	ADJ
fumecheng-10743	13	8	and	and	CCONJ
fumecheng-10743	13	9	it	it	PRON
fumecheng-10743	13	10	is	be	AUX
fumecheng-10743	13	11	difficult	difficult	ADJ
fumecheng-10743	13	12	to	to	PART
fumecheng-10743	13	13	solve	solve	VERB
fumecheng-10743	13	14	it	it	PRON
fumecheng-10743	13	15	exactly	exactly	ADV
fumecheng-10743	13	16	.	.	PUNCT
fumecheng-10743	14	1	in	in	ADP
fumecheng-10743	14	2	the	the	DET
fumecheng-10743	14	3	last	last	ADJ
fumecheng-10743	14	4	200	200	NUM
fumecheng-10743	14	5	years	year	NOUN
fumecheng-10743	14	6	,	,	PUNCT
fumecheng-10743	14	7	engineers	engineer	NOUN
fumecheng-10743	14	8	had	have	VERB
fumecheng-10743	14	9	little	little	ADJ
fumecheng-10743	14	10	mathematical	mathematical	ADJ
fumecheng-10743	14	11	tools	tool	NOUN
fumecheng-10743	14	12	.	.	PUNCT
fumecheng-10743	15	1	the	the	DET
fumecheng-10743	15	2	most	most	ADV
fumecheng-10743	15	3	available	available	ADJ
fumecheng-10743	15	4	one	one	NUM
fumecheng-10743	15	5	was	be	AUX
fumecheng-10743	15	6	the	the	DET
fumecheng-10743	15	7	perturbation	perturbation	NOUN
fumecheng-10743	15	8	method	method	NOUN
fumecheng-10743	15	9	.	.	PUNCT
fumecheng-10743	16	1	however	however	ADV
fumecheng-10743	16	2	,	,	PUNCT
fumecheng-10743	16	3	a	a	DET
fumecheng-10743	16	4	small	small	ADJ
fumecheng-10743	16	5	parameter	parameter	NOUN
fumecheng-10743	16	6	assumption	assumption	NOUN
fumecheng-10743	16	7	involved	involve	VERB
fumecheng-10743	16	8	in	in	ADP
fumecheng-10743	16	9	the	the	DET
fumecheng-10743	16	10	perturbation	perturbation	NOUN
fumecheng-10743	16	11	method	method	NOUN
fumecheng-10743	16	12	hinders	hinder	VERB
fumecheng-10743	16	13	its	its	PRON
fumecheng-10743	16	14	widely	widely	ADJ
fumecheng-10743	16	15	applications	application	NOUN
fumecheng-10743	16	16	for	for	ADP
fumecheng-10743	16	17	accurate	accurate	ADJ
fumecheng-10743	16	18	prediction	prediction	NOUN
fumecheng-10743	16	19	of	of	ADP
fumecheng-10743	16	20	the	the	DET
fumecheng-10743	16	21	periodic	periodic	ADJ
fumecheng-10743	16	22	properties	property	NOUN
fumecheng-10743	16	23	of	of	ADP
fumecheng-10743	16	24	a	a	DET
fumecheng-10743	16	25	practical	practical	ADJ
fumecheng-10743	16	26	problem	problem	NOUN
fumecheng-10743	16	27	;	;	PUNCT
fumecheng-10743	16	28	hence	hence	ADV
fumecheng-10743	16	29	it	it	PRON
fumecheng-10743	16	30	is	be	AUX
fumecheng-10743	16	31	valid	valid	ADJ
fumecheng-10743	16	32	only	only	ADV
fumecheng-10743	16	33	for	for	ADP
fumecheng-10743	16	34	weakly	weakly	ADJ
fumecheng-10743	16	35	nonlinear	nonlinear	ADJ
fumecheng-10743	16	36	oscillators	oscillator	NOUN
fumecheng-10743	16	37	.	.	PUNCT
fumecheng-10743	17	1	received	receive	VERB
fumecheng-10743	17	2	april	april	PROPN
fumecheng-10743	17	3	20	20	NUM
fumecheng-10743	17	4	,	,	PUNCT
fumecheng-10743	17	5	2022	2022	NUM
fumecheng-10743	17	6	/	/	SYM
fumecheng-10743	17	7	accepted	accept	VERB
fumecheng-10743	17	8	may	may	PROPN
fumecheng-10743	17	9	17	17	NUM
fumecheng-10743	17	10	,	,	PUNCT
fumecheng-10743	17	11	2022	2022	NUM
fumecheng-10743	17	12	corresponding	correspond	VERB
fumecheng-10743	17	13	author	author	NOUN
fumecheng-10743	17	14	:	:	PUNCT
fumecheng-10743	17	15	hongjin	hongjin	NOUN
fumecheng-10743	17	16	ma	ma	PROPN
fumecheng-10743	17	17	school	school	PROPN
fumecheng-10743	17	18	of	of	ADP
fumecheng-10743	17	19	science	science	PROPN
fumecheng-10743	17	20	,	,	PUNCT
fumecheng-10743	17	21	xi'an	xi'an	PROPN
fumecheng-10743	17	22	university	university	PROPN
fumecheng-10743	17	23	of	of	ADP
fumecheng-10743	17	24	architecture	architecture	NOUN
fumecheng-10743	17	25	and	and	CCONJ
fumecheng-10743	17	26	technology	technology	NOUN
fumecheng-10743	17	27	,	,	PUNCT
fumecheng-10743	17	28	xi’an	xi’an	PROPN
fumecheng-10743	17	29	,	,	PUNCT
fumecheng-10743	17	30	china	china	PROPN
fumecheng-10743	17	31	e	e	PROPN
fumecheng-10743	17	32	-	-	NOUN
fumecheng-10743	17	33	mail	mail	NOUN
fumecheng-10743	17	34	:	:	PUNCT
fumecheng-10743	17	35	hjma@xauat.edu.cn	hjma@xauat.edu.cn	PROPN
fumecheng-10743	17	36	446	446	NUM
fumecheng-10743	17	37	h.	h.	NOUN
fumecheng-10743	17	38	ma	ma	PROPN
fumecheng-10743	18	1	the	the	DET
fumecheng-10743	18	2	homotopy	homotopy	PROPN
fumecheng-10743	18	3	perturbation	perturbation	NOUN
fumecheng-10743	18	4	method	method	NOUN
fumecheng-10743	18	5	[	[	X
fumecheng-10743	18	6	19	19	NUM
fumecheng-10743	18	7	-	-	SYM
fumecheng-10743	18	8	21	21	NUM
fumecheng-10743	18	9	]	]	PUNCT
fumecheng-10743	18	10	and	and	CCONJ
fumecheng-10743	18	11	the	the	DET
fumecheng-10743	18	12	variational	variational	ADJ
fumecheng-10743	18	13	iteration	iteration	NOUN
fumecheng-10743	18	14	method	method	NOUN
fumecheng-10743	18	15	[	[	X
fumecheng-10743	18	16	22	22	NUM
fumecheng-10743	18	17	-	-	SYM
fumecheng-10743	18	18	24	24	NUM
fumecheng-10743	18	19	]	]	PUNCT
fumecheng-10743	18	20	are	be	AUX
fumecheng-10743	18	21	much	much	ADV
fumecheng-10743	18	22	advanced	advanced	ADJ
fumecheng-10743	18	23	ones	one	NOUN
fumecheng-10743	18	24	for	for	ADP
fumecheng-10743	18	25	strongly	strongly	ADV
fumecheng-10743	18	26	nonlinear	nonlinear	ADJ
fumecheng-10743	18	27	oscillators	oscillator	NOUN
fumecheng-10743	18	28	,	,	PUNCT
fumecheng-10743	18	29	but	but	CCONJ
fumecheng-10743	18	30	both	both	DET
fumecheng-10743	18	31	methods	method	NOUN
fumecheng-10743	18	32	require	require	VERB
fumecheng-10743	18	33	some	some	DET
fumecheng-10743	18	34	special	special	ADJ
fumecheng-10743	18	35	mathematics	mathematics	NOUN
fumecheng-10743	18	36	skills	skill	NOUN
fumecheng-10743	18	37	for	for	ADP
fumecheng-10743	18	38	problem	problem	NOUN
fumecheng-10743	18	39	-	-	PUNCT
fumecheng-10743	18	40	solving	solving	NOUN
fumecheng-10743	18	41	;	;	PUNCT
fumecheng-10743	18	42	especially	especially	ADV
fumecheng-10743	18	43	the	the	DET
fumecheng-10743	18	44	former	former	ADJ
fumecheng-10743	18	45	asks	ask	VERB
fumecheng-10743	18	46	for	for	ADP
fumecheng-10743	18	47	a	a	DET
fumecheng-10743	18	48	suitable	suitable	ADJ
fumecheng-10743	18	49	homotopy	homotopy	NOUN
fumecheng-10743	18	50	equation	equation	NOUN
fumecheng-10743	18	51	,	,	PUNCT
fumecheng-10743	18	52	and	and	CCONJ
fumecheng-10743	18	53	the	the	DET
fumecheng-10743	18	54	latter	latter	ADJ
fumecheng-10743	18	55	requires	require	VERB
fumecheng-10743	18	56	a	a	DET
fumecheng-10743	18	57	complex	complex	ADJ
fumecheng-10743	18	58	identification	identification	NOUN
fumecheng-10743	18	59	of	of	ADP
fumecheng-10743	18	60	the	the	DET
fumecheng-10743	18	61	lagrange	lagrange	NOUN
fumecheng-10743	18	62	multiplier	multiplier	ADV
fumecheng-10743	18	63	involved	involve	VERB
fumecheng-10743	18	64	in	in	ADP
fumecheng-10743	18	65	the	the	DET
fumecheng-10743	18	66	iteration	iteration	NOUN
fumecheng-10743	18	67	algorithm	algorithm	NOUN
fumecheng-10743	18	68	.	.	PUNCT
fumecheng-10743	19	1	for	for	ADP
fumecheng-10743	19	2	engineering	engineering	NOUN
fumecheng-10743	19	3	problems	problem	NOUN
fumecheng-10743	19	4	,	,	PUNCT
fumecheng-10743	19	5	as	as	SCONJ
fumecheng-10743	19	6	claimed	claim	VERB
fumecheng-10743	19	7	by	by	ADP
fumecheng-10743	19	8	the	the	DET
fumecheng-10743	19	9	chinese	chinese	ADJ
fumecheng-10743	19	10	mathematician	mathematician	NOUN
fumecheng-10743	19	11	ji	ji	PROPN
fumecheng-10743	19	12	-	-	PROPN
fumecheng-10743	19	13	huan	huan	PROPN
fumecheng-10743	19	14	he	he	PRON
fumecheng-10743	19	15	,	,	PUNCT
fumecheng-10743	19	16	the	the	DET
fumecheng-10743	19	17	simpler	simple	ADJ
fumecheng-10743	19	18	is	be	AUX
fumecheng-10743	19	19	better	well	ADJ
fumecheng-10743	19	20	for	for	ADP
fumecheng-10743	19	21	a	a	DET
fumecheng-10743	19	22	complex	complex	ADJ
fumecheng-10743	19	23	problem	problem	NOUN
fumecheng-10743	19	24	[	[	X
fumecheng-10743	19	25	18	18	NUM
fumecheng-10743	19	26	]	]	PUNCT
fumecheng-10743	19	27	.	.	PUNCT
fumecheng-10743	20	1	now	now	ADV
fumecheng-10743	20	2	the	the	DET
fumecheng-10743	20	3	condition	condition	NOUN
fumecheng-10743	20	4	is	be	AUX
fumecheng-10743	20	5	completely	completely	ADV
fumecheng-10743	20	6	changed	change	VERB
fumecheng-10743	20	7	;	;	PUNCT
fumecheng-10743	20	8	the	the	DET
fumecheng-10743	20	9	hamiltonian	hamiltonian	NOUN
fumecheng-10743	20	10	-	-	PUNCT
fumecheng-10743	20	11	based	base	VERB
fumecheng-10743	20	12	frequency	frequency	NOUN
fumecheng-10743	20	13	formulation	formulation	NOUN
fumecheng-10743	20	14	[	[	X
fumecheng-10743	20	15	25	25	NUM
fumecheng-10743	20	16	]	]	PUNCT
fumecheng-10743	20	17	sheds	shed	VERB
fumecheng-10743	20	18	a	a	DET
fumecheng-10743	20	19	promising	promising	ADJ
fumecheng-10743	20	20	light	light	NOUN
fumecheng-10743	20	21	on	on	ADP
fumecheng-10743	20	22	a	a	DET
fumecheng-10743	20	23	fast	fast	ADJ
fumecheng-10743	20	24	but	but	CCONJ
fumecheng-10743	20	25	reliable	reliable	ADJ
fumecheng-10743	20	26	insight	insight	NOUN
fumecheng-10743	20	27	into	into	ADP
fumecheng-10743	20	28	the	the	DET
fumecheng-10743	20	29	physical	physical	ADJ
fumecheng-10743	20	30	properties	property	NOUN
fumecheng-10743	20	31	of	of	ADP
fumecheng-10743	20	32	a	a	DET
fumecheng-10743	20	33	nonlinear	nonlinear	ADJ
fumecheng-10743	20	34	oscillator	oscillator	NOUN
fumecheng-10743	20	35	with	with	ADP
fumecheng-10743	20	36	simple	simple	ADJ
fumecheng-10743	20	37	calculation	calculation	NOUN
fumecheng-10743	20	38	.	.	PUNCT
fumecheng-10743	21	1	the	the	DET
fumecheng-10743	21	2	hamiltonian	hamiltonian	NOUN
fumecheng-10743	21	3	-	-	PUNCT
fumecheng-10743	21	4	based	base	VERB
fumecheng-10743	21	5	frequency	frequency	NOUN
fumecheng-10743	21	6	formulation	formulation	NOUN
fumecheng-10743	21	7	is	be	AUX
fumecheng-10743	21	8	mathematically	mathematically	ADV
fumecheng-10743	21	9	beautiful	beautiful	ADJ
fumecheng-10743	21	10	and	and	CCONJ
fumecheng-10743	21	11	physically	physically	ADV
fumecheng-10743	21	12	penetrating	penetrate	VERB
fumecheng-10743	21	13	since	since	SCONJ
fumecheng-10743	21	14	only	only	ADV
fumecheng-10743	21	15	a	a	DET
fumecheng-10743	21	16	simple	simple	ADJ
fumecheng-10743	21	17	integration	integration	NOUN
fumecheng-10743	21	18	calculation	calculation	NOUN
fumecheng-10743	21	19	is	be	AUX
fumecheng-10743	21	20	needed	need	VERB
fumecheng-10743	21	21	.	.	PUNCT
fumecheng-10743	22	1	it	it	PRON
fumecheng-10743	22	2	gives	give	VERB
fumecheng-10743	22	3	a	a	DET
fumecheng-10743	22	4	vivid	vivid	ADJ
fumecheng-10743	22	5	picture	picture	NOUN
fumecheng-10743	22	6	of	of	ADP
fumecheng-10743	22	7	the	the	DET
fumecheng-10743	22	8	whole	whole	ADJ
fumecheng-10743	22	9	solution	solution	NOUN
fumecheng-10743	22	10	properties	property	NOUN
fumecheng-10743	22	11	.	.	PUNCT
fumecheng-10743	23	1	the	the	DET
fumecheng-10743	23	2	2021	2021	NUM
fumecheng-10743	23	3	hamiltonian	hamiltonian	NOUN
fumecheng-10743	23	4	-	-	PUNCT
fumecheng-10743	23	5	based	base	VERB
fumecheng-10743	23	6	frequency	frequency	NOUN
fumecheng-10743	23	7	formulation	formulation	NOUN
fumecheng-10743	23	8	[	[	X
fumecheng-10743	23	9	25	25	NUM
fumecheng-10743	23	10	]	]	PUNCT
fumecheng-10743	23	11	is	be	AUX
fumecheng-10743	23	12	a	a	DET
fumecheng-10743	23	13	modification	modification	NOUN
fumecheng-10743	23	14	of	of	ADP
fumecheng-10743	23	15	he	he	PRON
fumecheng-10743	23	16	’s	’s	PART
fumecheng-10743	23	17	2006	2006	NUM
fumecheng-10743	23	18	frequency	frequency	NOUN
fumecheng-10743	23	19	formulation	formulation	NOUN
fumecheng-10743	23	20	[	[	X
fumecheng-10743	23	21	26	26	NUM
fumecheng-10743	23	22	]	]	PUNCT
fumecheng-10743	23	23	.	.	PUNCT
fumecheng-10743	24	1	the	the	DET
fumecheng-10743	24	2	formulation	formulation	NOUN
fumecheng-10743	24	3	observes	observe	VERB
fumecheng-10743	24	4	a	a	DET
fumecheng-10743	24	5	nonlinear	nonlinear	ADJ
fumecheng-10743	24	6	vibration	vibration	NOUN
fumecheng-10743	24	7	system	system	NOUN
fumecheng-10743	24	8	in	in	ADP
fumecheng-10743	24	9	an	an	DET
fumecheng-10743	24	10	energy	energy	NOUN
fumecheng-10743	24	11	view	view	NOUN
fumecheng-10743	24	12	by	by	ADP
fumecheng-10743	24	13	establishing	establish	VERB
fumecheng-10743	24	14	a	a	DET
fumecheng-10743	24	15	hamilton	hamilton	PROPN
fumecheng-10743	24	16	principle	principle	PROPN
fumecheng-10743	24	17	,	,	PUNCT
fumecheng-10743	24	18	which	which	PRON
fumecheng-10743	24	19	can	can	AUX
fumecheng-10743	24	20	elucidate	elucidate	VERB
fumecheng-10743	24	21	clearly	clearly	ADV
fumecheng-10743	24	22	the	the	DET
fumecheng-10743	24	23	energy	energy	NOUN
fumecheng-10743	24	24	conservation	conservation	NOUN
fumecheng-10743	24	25	of	of	ADP
fumecheng-10743	24	26	the	the	DET
fumecheng-10743	24	27	vibrating	vibrating	NOUN
fumecheng-10743	24	28	process	process	NOUN
fumecheng-10743	24	29	,	,	PUNCT
fumecheng-10743	24	30	that	that	PRON
fumecheng-10743	24	31	is	be	AUX
fumecheng-10743	24	32	the	the	DET
fumecheng-10743	24	33	total	total	ADJ
fumecheng-10743	24	34	energy	energy	NOUN
fumecheng-10743	24	35	of	of	ADP
fumecheng-10743	24	36	kinetic	kinetic	ADJ
fumecheng-10743	24	37	and	and	CCONJ
fumecheng-10743	24	38	potential	potential	ADJ
fumecheng-10743	24	39	energy	energy	NOUN
fumecheng-10743	24	40	keeps	keep	VERB
fumecheng-10743	24	41	unchanged	unchanged	ADJ
fumecheng-10743	24	42	during	during	ADP
fumecheng-10743	24	43	oscillation	oscillation	NOUN
fumecheng-10743	24	44	.	.	PUNCT
fumecheng-10743	25	1	as	as	SCONJ
fumecheng-10743	25	2	the	the	DET
fumecheng-10743	25	3	formulation	formulation	NOUN
fumecheng-10743	25	4	is	be	AUX
fumecheng-10743	25	5	derived	derive	VERB
fumecheng-10743	25	6	from	from	ADP
fumecheng-10743	25	7	an	an	DET
fumecheng-10743	25	8	energy	energy	NOUN
fumecheng-10743	25	9	form	form	NOUN
fumecheng-10743	25	10	of	of	ADP
fumecheng-10743	25	11	the	the	DET
fumecheng-10743	25	12	nonlinear	nonlinear	ADJ
fumecheng-10743	25	13	oscillator	oscillator	NOUN
fumecheng-10743	25	14	,	,	PUNCT
fumecheng-10743	25	15	its	its	PRON
fumecheng-10743	25	16	approximate	approximate	ADJ
fumecheng-10743	25	17	solution	solution	NOUN
fumecheng-10743	25	18	is	be	AUX
fumecheng-10743	25	19	valid	valid	ADJ
fumecheng-10743	25	20	for	for	ADP
fumecheng-10743	25	21	the	the	DET
fumecheng-10743	25	22	whole	whole	ADJ
fumecheng-10743	25	23	solution	solution	NOUN
fumecheng-10743	25	24	domain	domain	NOUN
fumecheng-10743	25	25	without	without	ADP
fumecheng-10743	25	26	limitations	limitation	NOUN
fumecheng-10743	25	27	such	such	ADJ
fumecheng-10743	25	28	as	as	ADP
fumecheng-10743	25	29	those	those	PRON
fumecheng-10743	25	30	in	in	ADP
fumecheng-10743	25	31	the	the	DET
fumecheng-10743	25	32	traditional	traditional	ADJ
fumecheng-10743	25	33	perturbation	perturbation	NOUN
fumecheng-10743	25	34	method	method	NOUN
fumecheng-10743	25	35	.	.	PUNCT
fumecheng-10743	26	1	the	the	DET
fumecheng-10743	26	2	frequency	frequency	NOUN
fumecheng-10743	26	3	formulation	formulation	NOUN
fumecheng-10743	26	4	begins	begin	VERB
fumecheng-10743	26	5	with	with	ADP
fumecheng-10743	26	6	two	two	NUM
fumecheng-10743	26	7	arbitrary	arbitrary	ADJ
fumecheng-10743	26	8	guesses	guess	NOUN
fumecheng-10743	26	9	of	of	ADP
fumecheng-10743	26	10	the	the	DET
fumecheng-10743	26	11	frequency	frequency	NOUN
fumecheng-10743	26	12	,	,	PUNCT
fumecheng-10743	26	13	and	and	CCONJ
fumecheng-10743	26	14	two	two	NUM
fumecheng-10743	26	15	residual	residual	ADJ
fumecheng-10743	26	16	integrals	integral	NOUN
fumecheng-10743	26	17	have	have	VERB
fumecheng-10743	26	18	to	to	PART
fumecheng-10743	26	19	be	be	AUX
fumecheng-10743	26	20	calculated	calculate	VERB
fumecheng-10743	26	21	to	to	PART
fumecheng-10743	26	22	estimate	estimate	VERB
fumecheng-10743	26	23	an	an	DET
fumecheng-10743	26	24	accurate	accurate	ADJ
fumecheng-10743	26	25	frequency	frequency	NOUN
fumecheng-10743	26	26	.	.	PUNCT
fumecheng-10743	27	1	it	it	PRON
fumecheng-10743	27	2	is	be	AUX
fumecheng-10743	27	3	amazing	amazing	ADJ
fumecheng-10743	27	4	that	that	SCONJ
fumecheng-10743	27	5	the	the	DET
fumecheng-10743	27	6	accurate	accurate	ADJ
fumecheng-10743	27	7	result	result	NOUN
fumecheng-10743	27	8	does	do	AUX
fumecheng-10743	27	9	not	not	PART
fumecheng-10743	27	10	depend	depend	VERB
fumecheng-10743	27	11	upon	upon	SCONJ
fumecheng-10743	27	12	the	the	DET
fumecheng-10743	27	13	initial	initial	ADJ
fumecheng-10743	27	14	choice	choice	NOUN
fumecheng-10743	27	15	of	of	ADP
fumecheng-10743	27	16	two	two	NUM
fumecheng-10743	27	17	arbitrary	arbitrary	ADJ
fumecheng-10743	27	18	frequencies	frequency	NOUN
fumecheng-10743	27	19	even	even	ADV
fumecheng-10743	27	20	for	for	ADP
fumecheng-10743	27	21	strong	strong	ADJ
fumecheng-10743	27	22	nonlinearity	nonlinearity	NOUN
fumecheng-10743	27	23	.	.	PUNCT
fumecheng-10743	28	1	due	due	ADP
fumecheng-10743	28	2	to	to	ADP
fumecheng-10743	28	3	these	these	DET
fumecheng-10743	28	4	unprecedented	unprecedented	ADJ
fumecheng-10743	28	5	advantages	advantage	NOUN
fumecheng-10743	28	6	,	,	PUNCT
fumecheng-10743	28	7	the	the	DET
fumecheng-10743	28	8	formulation	formulation	NOUN
fumecheng-10743	28	9	caught	catch	VERB
fumecheng-10743	28	10	immediate	immediate	ADJ
fumecheng-10743	28	11	attention	attention	NOUN
fumecheng-10743	28	12	after	after	ADP
fumecheng-10743	28	13	publication	publication	NOUN
fumecheng-10743	28	14	due	due	ADP
fumecheng-10743	28	15	to	to	ADP
fumecheng-10743	28	16	its	its	PRON
fumecheng-10743	28	17	extremely	extremely	ADV
fumecheng-10743	28	18	simplicity	simplicity	NOUN
fumecheng-10743	28	19	and	and	CCONJ
fumecheng-10743	28	20	remarkable	remarkable	ADJ
fumecheng-10743	28	21	reliability	reliability	NOUN
fumecheng-10743	28	22	.	.	PUNCT
fumecheng-10743	29	1	it	it	PRON
fumecheng-10743	29	2	has	have	AUX
fumecheng-10743	29	3	been	be	AUX
fumecheng-10743	29	4	successfully	successfully	ADV
fumecheng-10743	29	5	applied	apply	VERB
fumecheng-10743	29	6	to	to	ADP
fumecheng-10743	29	7	kundu	kundu	NOUN
fumecheng-10743	29	8	-	-	PUNCT
fumecheng-10743	29	9	mukherjee	mukherjee	NOUN
fumecheng-10743	29	10	-	-	PUNCT
fumecheng-10743	29	11	naskar	naskar	NOUN
fumecheng-10743	29	12	oscillator	oscillator	NOUN
fumecheng-10743	29	13	[	[	X
fumecheng-10743	29	14	27	27	NUM
fumecheng-10743	29	15	]	]	PUNCT
fumecheng-10743	29	16	,	,	PUNCT
fumecheng-10743	29	17	nonlinear	nonlinear	ADJ
fumecheng-10743	29	18	vibration	vibration	NOUN
fumecheng-10743	29	19	of	of	ADP
fumecheng-10743	29	20	embedded	embed	VERB
fumecheng-10743	29	21	carbon	carbon	NOUN
fumecheng-10743	29	22	nanotube	nanotube	NOUN
fumecheng-10743	29	23	[	[	X
fumecheng-10743	29	24	28	28	NUM
fumecheng-10743	29	25	]	]	PUNCT
fumecheng-10743	29	26	,	,	PUNCT
fumecheng-10743	29	27	fractal	fractal	ADJ
fumecheng-10743	29	28	vibration	vibration	NOUN
fumecheng-10743	29	29	systems	system	NOUN
fumecheng-10743	29	30	[	[	X
fumecheng-10743	29	31	29,30	29,30	NUM
fumecheng-10743	29	32	]	]	PUNCT
fumecheng-10743	29	33	,	,	PUNCT
fumecheng-10743	29	34	packaging	packaging	NOUN
fumecheng-10743	29	35	systems	system	NOUN
fumecheng-10743	29	36	[	[	X
fumecheng-10743	29	37	31	31	NUM
fumecheng-10743	29	38	]	]	PUNCT
fumecheng-10743	29	39	and	and	CCONJ
fumecheng-10743	29	40	mems	mem	VERB
fumecheng-10743	29	41	oscillators	oscillator	NOUN
fumecheng-10743	29	42	[	[	X
fumecheng-10743	29	43	32	32	NUM
fumecheng-10743	29	44	]	]	PUNCT
fumecheng-10743	29	45	.	.	PUNCT
fumecheng-10743	30	1	it	it	PRON
fumecheng-10743	30	2	has	have	AUX
fumecheng-10743	30	3	been	be	AUX
fumecheng-10743	30	4	hailed	hail	VERB
fumecheng-10743	30	5	as	as	ADP
fumecheng-10743	30	6	an	an	DET
fumecheng-10743	30	7	unprecedented	unprecedented	ADJ
fumecheng-10743	30	8	success	success	NOUN
fumecheng-10743	30	9	.	.	PUNCT
fumecheng-10743	31	1	though	though	SCONJ
fumecheng-10743	31	2	the	the	DET
fumecheng-10743	31	3	achievement	achievement	NOUN
fumecheng-10743	31	4	has	have	AUX
fumecheng-10743	31	5	contributed	contribute	VERB
fumecheng-10743	31	6	to	to	ADP
fumecheng-10743	31	7	the	the	DET
fumecheng-10743	31	8	fast	fast	ADJ
fumecheng-10743	31	9	development	development	NOUN
fumecheng-10743	31	10	of	of	ADP
fumecheng-10743	31	11	the	the	DET
fumecheng-10743	31	12	nonlinear	nonlinear	ADJ
fumecheng-10743	31	13	vibration	vibration	NOUN
fumecheng-10743	31	14	theory	theory	NOUN
fumecheng-10743	31	15	,	,	PUNCT
fumecheng-10743	31	16	the	the	DET
fumecheng-10743	31	17	solving	solving	NOUN
fumecheng-10743	31	18	process	process	NOUN
fumecheng-10743	31	19	is	be	AUX
fumecheng-10743	31	20	relative	relative	ADJ
fumecheng-10743	31	21	complex	complex	ADJ
fumecheng-10743	31	22	,	,	PUNCT
fumecheng-10743	31	23	so	so	SCONJ
fumecheng-10743	31	24	a	a	DET
fumecheng-10743	31	25	modification	modification	NOUN
fumecheng-10743	31	26	is	be	AUX
fumecheng-10743	31	27	needed	need	VERB
fumecheng-10743	31	28	.	.	PUNCT
fumecheng-10743	32	1	2	2	X
fumecheng-10743	32	2	.	.	X
fumecheng-10743	32	3	problem	problem	NOUN
fumecheng-10743	32	4	statement	statement	NOUN
fumecheng-10743	32	5	consider	consider	VERB
fumecheng-10743	32	6	the	the	DET
fumecheng-10743	32	7	following	follow	VERB
fumecheng-10743	32	8	conservative	conservative	ADJ
fumecheng-10743	32	9	oscillator	oscillator	NOUN
fumecheng-10743	32	10	[	[	X
fumecheng-10743	32	11	25	25	NUM
fumecheng-10743	32	12	]	]	X
fumecheng-10743	32	13	:	:	PUNCT
fumecheng-10743	32	14	(	(	PUNCT
fumecheng-10743	32	15	)	)	PUNCT
fumecheng-10743	32	16	0	0	NUM
fumecheng-10743	32	17	,	,	PUNCT
fumecheng-10743	32	18	(	(	PUNCT
fumecheng-10743	32	19	0	0	NUM
fumecheng-10743	32	20	)	)	PUNCT
fumecheng-10743	32	21	0	0	NUM
fumecheng-10743	33	1	(	(	PUNCT
fumecheng-10743	33	2	0)w	0)w	NOUN
fumecheng-10743	33	3	p	p	X
fumecheng-10743	33	4	w	w	PROPN
fumecheng-10743	33	5	w	w	PROPN
fumecheng-10743	33	6	w	w	PROPN
fumecheng-10743	33	7	b	b	NOUN
fumecheng-10743	33	8	+	+	NOUN
fumecheng-10743	33	9	=	=	PUNCT
fumecheng-10743	34	1	=	=	SYM
fumecheng-10743	34	2	=	=	SYM
fumecheng-10743	34	3	(	(	PUNCT
fumecheng-10743	34	4	1	1	NUM
fumecheng-10743	34	5	)	)	PUNCT
fumecheng-10743	34	6	where	where	SCONJ
fumecheng-10743	34	7	p(w	p(w	NOUN
fumecheng-10743	34	8	)	)	PUNCT
fumecheng-10743	34	9	is	be	AUX
fumecheng-10743	34	10	an	an	DET
fumecheng-10743	34	11	odd	odd	ADJ
fumecheng-10743	34	12	function	function	NOUN
fumecheng-10743	34	13	of	of	ADP
fumecheng-10743	34	14	the	the	DET
fumecheng-10743	34	15	displacement	displacement	NOUN
fumecheng-10743	34	16	w	w	PROPN
fumecheng-10743	34	17	and	and	CCONJ
fumecheng-10743	34	18	b	b	PROPN
fumecheng-10743	34	19	is	be	AUX
fumecheng-10743	34	20	the	the	DET
fumecheng-10743	34	21	displacement	displacement	ADJ
fumecheng-10743	34	22	amplitude	amplitude	NOUN
fumecheng-10743	34	23	.	.	PUNCT
fumecheng-10743	35	1	its	its	PRON
fumecheng-10743	35	2	hamilton	hamilton	PROPN
fumecheng-10743	35	3	principle	principle	NOUN
fumecheng-10743	35	4	can	can	AUX
fumecheng-10743	35	5	be	be	AUX
fumecheng-10743	35	6	easily	easily	ADV
fumecheng-10743	35	7	established	establish	VERB
fumecheng-10743	35	8	by	by	ADP
fumecheng-10743	35	9	the	the	DET
fumecheng-10743	35	10	semi	semi	ADJ
fumecheng-10743	35	11	-	-	ADJ
fumecheng-10743	35	12	inverse	inverse	ADJ
fumecheng-10743	35	13	method	method	NOUN
fumecheng-10743	35	14	[	[	X
fumecheng-10743	35	15	33	33	NUM
fumecheng-10743	35	16	]	]	PUNCT
fumecheng-10743	35	17	dtwpwwj	dtwpwwj	ADV
fumecheng-10743	35	18			PUNCT
fumecheng-10743	36	1			PROPN
fumecheng-10743	36	2			INTJ
fumecheng-10743	37	1			PROPN
fumecheng-10743	37	2			INTJ
fumecheng-10743	37	3			NUM
fumecheng-10743	37	4			ADP
fumecheng-10743	38	1	−=	−=	NUM
fumecheng-10743	38	2	)	)	PUNCT
fumecheng-10743	38	3	(	(	PUNCT
fumecheng-10743	38	4	2	2	NUM
fumecheng-10743	38	5	1	1	NUM
fumecheng-10743	38	6	)	)	PUNCT
fumecheng-10743	38	7	(	(	PUNCT
fumecheng-10743	38	8	2	2	NUM
fumecheng-10743	38	9	(	(	PUNCT
fumecheng-10743	38	10	2	2	NUM
fumecheng-10743	38	11	)	)	PUNCT
fumecheng-10743	38	12	where	where	SCONJ
fumecheng-10743	38	13	p(w	p(w	NOUN
fumecheng-10743	38	14	)	)	PUNCT
fumecheng-10743	38	15	is	be	AUX
fumecheng-10743	38	16	the	the	DET
fumecheng-10743	38	17	potential	potential	ADJ
fumecheng-10743	38	18	energy	energy	NOUN
fumecheng-10743	38	19	defined	define	VERB
fumecheng-10743	38	20	so	so	SCONJ
fumecheng-10743	39	1	that	that	SCONJ
fumecheng-10743	39	2	(	(	PUNCT
fumecheng-10743	39	3	)	)	PUNCT
fumecheng-10743	39	4	(	(	PUNCT
fumecheng-10743	39	5	)	)	PUNCT
fumecheng-10743	39	6	d	d	X
fumecheng-10743	39	7	p	p	X
fumecheng-10743	39	8	w	w	PROPN
fumecheng-10743	39	9	p	p	X
fumecheng-10743	39	10	dw	dw	PROPN
fumecheng-10743	39	11	w=	w=	PROPN
fumecheng-10743	39	12	(	(	PUNCT
fumecheng-10743	39	13	3	3	NUM
fumecheng-10743	39	14	)	)	PUNCT
fumecheng-10743	39	15	simplified	simplified	ADJ
fumecheng-10743	39	16	hamiltonian	hamiltonian	ADJ
fumecheng-10743	39	17	-	-	PUNCT
fumecheng-10743	39	18	based	base	VERB
fumecheng-10743	39	19	frequency	frequency	NOUN
fumecheng-10743	39	20	-	-	PUNCT
fumecheng-10743	39	21	amplitude	amplitude	NOUN
fumecheng-10743	39	22	formulation	formulation	NOUN
fumecheng-10743	39	23	for	for	ADP
fumecheng-10743	39	24	nonlinear	nonlinear	ADJ
fumecheng-10743	39	25	vibration	vibration	NOUN
fumecheng-10743	39	26	systems	system	NOUN
fumecheng-10743	39	27	447	447	NUM
fumecheng-10743	39	28	according	accord	VERB
fumecheng-10743	39	29	to	to	ADP
fumecheng-10743	39	30	hamilton	hamilton	PROPN
fumecheng-10743	39	31	principle	principle	PROPN
fumecheng-10743	39	32	,	,	PUNCT
fumecheng-10743	39	33	we	we	PRON
fumecheng-10743	39	34	have	have	VERB
fumecheng-10743	39	35	the	the	DET
fumecheng-10743	39	36	conversation	conversation	ADJ
fumecheng-10743	39	37	law	law	NOUN
fumecheng-10743	39	38	21	21	NUM
fumecheng-10743	39	39	(	(	PUNCT
fumecheng-10743	39	40	)	)	PUNCT
fumecheng-10743	39	41	2	2	NUM
fumecheng-10743	39	42	w	w	NOUN
fumecheng-10743	39	43	p	p	NOUN
fumecheng-10743	39	44	hw	hw	NOUN
fumecheng-10743	39	45	+	+	CCONJ
fumecheng-10743	39	46	=	=	SYM
fumecheng-10743	39	47	(	(	PUNCT
fumecheng-10743	39	48	4	4	NUM
fumecheng-10743	39	49	)	)	PUNCT
fumecheng-10743	39	50	where	where	SCONJ
fumecheng-10743	39	51	h	h	NOUN
fumecheng-10743	39	52	is	be	AUX
fumecheng-10743	39	53	the	the	DET
fumecheng-10743	39	54	hamiltonian	hamiltonian	ADJ
fumecheng-10743	39	55	constant	constant	NOUN
fumecheng-10743	39	56	,	,	PUNCT
fumecheng-10743	39	57	which	which	PRON
fumecheng-10743	39	58	depends	depend	VERB
fumecheng-10743	39	59	only	only	ADV
fumecheng-10743	39	60	upon	upon	SCONJ
fumecheng-10743	39	61	the	the	DET
fumecheng-10743	39	62	initial	initial	ADJ
fumecheng-10743	39	63	conditions	condition	NOUN
fumecheng-10743	39	64	,	,	PUNCT
fumecheng-10743	39	65	so	so	ADV
fumecheng-10743	39	66	the	the	DET
fumecheng-10743	39	67	following	follow	VERB
fumecheng-10743	39	68	first	first	ADJ
fumecheng-10743	39	69	-	-	PUNCT
fumecheng-10743	39	70	order	order	NOUN
fumecheng-10743	39	71	differential	differential	ADJ
fumecheng-10743	39	72	equation	equation	NOUN
fumecheng-10743	39	73	is	be	AUX
fumecheng-10743	39	74	obtained	obtain	VERB
fumecheng-10743	39	75	:	:	PUNCT
fumecheng-10743	39	76	0	0	NUM
fumecheng-10743	39	77	)	)	PUNCT
fumecheng-10743	39	78	(	(	PUNCT
fumecheng-10743	39	79	)	)	PUNCT
fumecheng-10743	39	80	(	(	PUNCT
fumecheng-10743	39	81	2	2	NUM
fumecheng-10743	39	82	1	1	NUM
fumecheng-10743	39	83	2	2	NUM
fumecheng-10743	39	84	=	=	NUM
fumecheng-10743	39	85	−+	−+	NOUN
fumecheng-10743	39	86	bpwpw	bpwpw	PROPN
fumecheng-10743	39	87	(	(	PUNCT
fumecheng-10743	39	88	5	5	NUM
fumecheng-10743	39	89	)	)	PUNCT
fumecheng-10743	39	90	the	the	DET
fumecheng-10743	39	91	hamiltonian	hamiltonian	NOUN
fumecheng-10743	39	92	-	-	PUNCT
fumecheng-10743	39	93	based	base	VERB
fumecheng-10743	39	94	frequency	frequency	NOUN
fumecheng-10743	39	95	formulation	formulation	NOUN
fumecheng-10743	39	96	is	be	AUX
fumecheng-10743	39	97	to	to	PART
fumecheng-10743	39	98	find	find	VERB
fumecheng-10743	39	99	an	an	DET
fumecheng-10743	39	100	approximate	approximate	ADJ
fumecheng-10743	39	101	solution	solution	NOUN
fumecheng-10743	39	102	in	in	ADP
fumecheng-10743	39	103	the	the	DET
fumecheng-10743	39	104	form	form	NOUN
fumecheng-10743	39	105	tbtw	tbtw	NOUN
fumecheng-10743	39	106	ωcos	ωco	NOUN
fumecheng-10743	39	107	)	)	PUNCT
fumecheng-10743	39	108	(	(	PUNCT
fumecheng-10743	39	109	=	=	SYM
fumecheng-10743	39	110	(	(	PUNCT
fumecheng-10743	39	111	6	6	NUM
fumecheng-10743	39	112	)	)	PUNCT
fumecheng-10743	39	113	where	where	SCONJ
fumecheng-10743	39	114	ω	ω	PROPN
fumecheng-10743	39	115	is	be	AUX
fumecheng-10743	39	116	the	the	DET
fumecheng-10743	39	117	frequency	frequency	NOUN
fumecheng-10743	39	118	to	to	PART
fumecheng-10743	39	119	be	be	AUX
fumecheng-10743	39	120	solved	solve	VERB
fumecheng-10743	39	121	later	later	ADV
fumecheng-10743	39	122	.	.	PUNCT
fumecheng-10743	40	1	the	the	DET
fumecheng-10743	40	2	hamiltonian	hamiltonian	NOUN
fumecheng-10743	40	3	-	-	PUNCT
fumecheng-10743	40	4	based	base	VERB
fumecheng-10743	40	5	frequency	frequency	NOUN
fumecheng-10743	40	6	formulation	formulation	NOUN
fumecheng-10743	40	7	begins	begin	VERB
fumecheng-10743	40	8	with	with	ADP
fumecheng-10743	40	9	two	two	NUM
fumecheng-10743	40	10	arbitrary	arbitrary	ADJ
fumecheng-10743	40	11	tries	try	NOUN
fumecheng-10743	40	12	ω1	ω1	PROPN
fumecheng-10743	40	13	and	and	CCONJ
fumecheng-10743	40	14	ω2	ω2	ADJ
fumecheng-10743	40	15	,	,	PUNCT
fumecheng-10743	40	16	and	and	CCONJ
fumecheng-10743	40	17	the	the	DET
fumecheng-10743	40	18	following	follow	VERB
fumecheng-10743	40	19	residual	residual	ADJ
fumecheng-10743	40	20	equations	equation	NOUN
fumecheng-10743	40	21	are	be	AUX
fumecheng-10743	40	22	obtained	obtain	VERB
fumecheng-10743	40	23	：	：	PUNCT
fumecheng-10743	40	24	2	2	NUM
fumecheng-10743	40	25	2	2	NUM
fumecheng-10743	40	26	2	2	NUM
fumecheng-10743	40	27	1	1	NUM
fumecheng-10743	40	28	1	1	NUM
fumecheng-10743	40	29	1	1	NUM
fumecheng-10743	40	30	1	1	NUM
fumecheng-10743	40	31	1	1	NUM
fumecheng-10743	40	32	(	(	PUNCT
fumecheng-10743	40	33	)	)	PUNCT
fumecheng-10743	40	34	sin	sin	NOUN
fumecheng-10743	40	35	(	(	PUNCT
fumecheng-10743	40	36	cos	cos	PROPN
fumecheng-10743	40	37	)	)	PUNCT
fumecheng-10743	40	38	(	(	PUNCT
fumecheng-10743	40	39	)	)	PUNCT
fumecheng-10743	40	40	2	2	NUM
fumecheng-10743	40	41	r	r	NOUN
fumecheng-10743	40	42	t	t	NOUN
fumecheng-10743	40	43	b	b	PROPN
fumecheng-10743	40	44	t	t	PROPN
fumecheng-10743	40	45	p	p	X
fumecheng-10743	40	46	b	b	PROPN
fumecheng-10743	40	47	t	t	PROPN
fumecheng-10743	40	48	p	p	NOUN
fumecheng-10743	40	49	b=	b=	NOUN
fumecheng-10743	40	50	+	+	CCONJ
fumecheng-10743	40	51	−ω	−ω	PROPN
fumecheng-10743	40	52	ω	ω	PROPN
fumecheng-10743	40	53	ω	ω	PROPN
fumecheng-10743	40	54	(	(	PUNCT
fumecheng-10743	40	55	7	7	NUM
fumecheng-10743	40	56	)	)	SYM
fumecheng-10743	40	57	2	2	NUM
fumecheng-10743	40	58	2	2	NUM
fumecheng-10743	40	59	2	2	NUM
fumecheng-10743	40	60	2	2	NUM
fumecheng-10743	40	61	2	2	NUM
fumecheng-10743	40	62	2	2	NUM
fumecheng-10743	40	63	2	2	NUM
fumecheng-10743	40	64	1	1	NUM
fumecheng-10743	40	65	(	(	PUNCT
fumecheng-10743	40	66	)	)	PUNCT
fumecheng-10743	40	67	sin	sin	NOUN
fumecheng-10743	40	68	(	(	PUNCT
fumecheng-10743	40	69	cos	cos	PROPN
fumecheng-10743	40	70	)	)	PUNCT
fumecheng-10743	40	71	(	(	PUNCT
fumecheng-10743	40	72	)	)	PUNCT
fumecheng-10743	40	73	2	2	NUM
fumecheng-10743	40	74	r	r	NOUN
fumecheng-10743	40	75	t	t	NOUN
fumecheng-10743	40	76	b	b	PROPN
fumecheng-10743	40	77	t	t	PROPN
fumecheng-10743	40	78	p	p	X
fumecheng-10743	40	79	b	b	PROPN
fumecheng-10743	40	80	t	t	PROPN
fumecheng-10743	40	81	p	p	NOUN
fumecheng-10743	40	82	b=	b=	NOUN
fumecheng-10743	40	83	+	+	CCONJ
fumecheng-10743	40	84	−ω	−ω	PROPN
fumecheng-10743	40	85	ω	ω	PROPN
fumecheng-10743	40	86	ω	ω	PROPN
fumecheng-10743	40	87	(	(	PUNCT
fumecheng-10743	40	88	8)	8)	NUM
fumecheng-10743	40	89	the	the	DET
fumecheng-10743	40	90	residual	residual	ADJ
fumecheng-10743	40	91	integrals	integral	NOUN
fumecheng-10743	40	92	are	be	AUX
fumecheng-10743	40	93	defined	define	VERB
fumecheng-10743	40	94	as	as	ADP
fumecheng-10743	40	95	tdtr	tdtr	PROPN
fumecheng-10743	40	96	t	t	NOUN
fumecheng-10743	40	97	r	r	NOUN
fumecheng-10743	40	98	t	t	PROPN
fumecheng-10743	40	99	1	1	NUM
fumecheng-10743	40	100	4/	4/	NUM
fumecheng-10743	40	101	0	0	NUM
fumecheng-10743	40	102	1	1	NUM
fumecheng-10743	40	103	1	1	NUM
fumecheng-10743	40	104	1	1	NUM
fumecheng-10743	41	1	cos	cos	NOUN
fumecheng-10743	41	2	4~	4~	NOUN
fumecheng-10743	41	3	1	1	NUM
fumecheng-10743	41	4	=	=	NOUN
fumecheng-10743	41	5	(	(	PUNCT
fumecheng-10743	41	6	9	9	X
fumecheng-10743	41	7	)	)	PUNCT
fumecheng-10743	41	8	tdtr	tdtr	PROPN
fumecheng-10743	41	9	t	t	NOUN
fumecheng-10743	41	10	r	r	NOUN
fumecheng-10743	41	11	t	t	PROPN
fumecheng-10743	41	12	2	2	NUM
fumecheng-10743	41	13	4/	4/	NUM
fumecheng-10743	41	14	0	0	NUM
fumecheng-10743	41	15	2	2	NUM
fumecheng-10743	41	16	2	2	NUM
fumecheng-10743	41	17	2	2	NUM
fumecheng-10743	41	18	cos	cos	NOUN
fumecheng-10743	41	19	4~	4~	NOUN
fumecheng-10743	41	20	2	2	NUM
fumecheng-10743	41	21	=	=	NOUN
fumecheng-10743	41	22	(	(	PUNCT
fumecheng-10743	41	23	10	10	NUM
fumecheng-10743	41	24	)	)	PUNCT
fumecheng-10743	41	25	where	where	SCONJ
fumecheng-10743	41	26	t1=2π	t1=2π	PROPN
fumecheng-10743	41	27	/	/	SYM
fumecheng-10743	41	28	ω1	ω1	PROPN
fumecheng-10743	41	29	,	,	PUNCT
fumecheng-10743	41	30	t2=2π	t2=2π	PROPN
fumecheng-10743	41	31	/	/	SYM
fumecheng-10743	41	32	ω2	ω2	NUM
fumecheng-10743	41	33	.	.	PUNCT
fumecheng-10743	42	1	the	the	DET
fumecheng-10743	42	2	frequency	frequency	NOUN
fumecheng-10743	42	3	formulation	formulation	NOUN
fumecheng-10743	42	4	is	be	AUX
fumecheng-10743	42	5	[	[	X
fumecheng-10743	42	6	25	25	NUM
fumecheng-10743	42	7	]	]	SYM
fumecheng-10743	42	8	2	2	NUM
fumecheng-10743	42	9	2	2	NUM
fumecheng-10743	42	10	2	2	NUM
fumecheng-10743	42	11	1	1	NUM
fumecheng-10743	42	12	2	2	NUM
fumecheng-10743	42	13	2	2	NUM
fumecheng-10743	42	14	1	1	NUM
fumecheng-10743	42	15	1	1	NUM
fumecheng-10743	42	16	2	2	NUM
fumecheng-10743	42	17	r	r	NOUN
fumecheng-10743	42	18	r	r	NOUN
fumecheng-10743	42	19	r	r	NOUN
fumecheng-10743	42	20	r	r	NOUN
fumecheng-10743	42	21	=	=	PUNCT
fumecheng-10743	42	22	−	−	PROPN
fumecheng-10743	42	23	−	−	PROPN
fumecheng-10743	42	24	ω	ω	PROPN
fumecheng-10743	42	25	ω	ω	PROPN
fumecheng-10743	42	26	ω	ω	PROPN
fumecheng-10743	42	27	(	(	PUNCT
fumecheng-10743	42	28	11	11	NUM
fumecheng-10743	42	29	)	)	PUNCT
fumecheng-10743	42	30	we	we	PRON
fumecheng-10743	42	31	can	can	AUX
fumecheng-10743	42	32	see	see	VERB
fumecheng-10743	42	33	that	that	SCONJ
fumecheng-10743	42	34	the	the	DET
fumecheng-10743	42	35	frequency	frequency	NOUN
fumecheng-10743	42	36	formulation	formulation	NOUN
fumecheng-10743	42	37	requires	require	VERB
fumecheng-10743	42	38	only	only	ADV
fumecheng-10743	42	39	a	a	DET
fumecheng-10743	42	40	simple	simple	ADJ
fumecheng-10743	42	41	calculation	calculation	NOUN
fumecheng-10743	42	42	of	of	ADP
fumecheng-10743	42	43	two	two	NUM
fumecheng-10743	42	44	integrals	integral	NOUN
fumecheng-10743	42	45	,	,	PUNCT
fumecheng-10743	42	46	making	make	VERB
fumecheng-10743	42	47	it	it	PRON
fumecheng-10743	42	48	much	much	ADV
fumecheng-10743	42	49	attractive	attractive	ADJ
fumecheng-10743	42	50	and	and	CCONJ
fumecheng-10743	42	51	promising	promise	VERB
fumecheng-10743	42	52	in	in	ADP
fumecheng-10743	42	53	the	the	DET
fumecheng-10743	42	54	nonlinear	nonlinear	ADJ
fumecheng-10743	42	55	vibration	vibration	NOUN
fumecheng-10743	42	56	theory	theory	NOUN
fumecheng-10743	42	57	.	.	PUNCT
fumecheng-10743	43	1	3	3	X
fumecheng-10743	43	2	.	.	X
fumecheng-10743	43	3	modified	modify	VERB
fumecheng-10743	43	4	he	he	PRON
fumecheng-10743	43	5	’s	’s	PART
fumecheng-10743	43	6	frequency	frequency	NOUN
fumecheng-10743	43	7	formulations	formulation	NOUN
fumecheng-10743	43	8	the	the	DET
fumecheng-10743	43	9	present	present	ADJ
fumecheng-10743	43	10	author	author	NOUN
fumecheng-10743	43	11	shows	show	VERB
fumecheng-10743	43	12	an	an	DET
fumecheng-10743	43	13	interest	interest	NOUN
fumecheng-10743	43	14	in	in	ADP
fumecheng-10743	43	15	two	two	NUM
fumecheng-10743	43	16	arbitrary	arbitrary	ADJ
fumecheng-10743	43	17	choices	choice	NOUN
fumecheng-10743	43	18	of	of	ADP
fumecheng-10743	43	19	ω1	ω1	PROPN
fumecheng-10743	43	20	and	and	CCONJ
fumecheng-10743	43	21	ω2	ω2	ADJ
fumecheng-10743	43	22	,	,	PUNCT
fumecheng-10743	43	23	e.g.	e.g.	ADV
fumecheng-10743	43	24	,	,	PUNCT
fumecheng-10743	43	25	ω1=1	ω1=1	PROPN
fumecheng-10743	43	26	and	and	CCONJ
fumecheng-10743	43	27	ω2=2	ω2=2	NOUN
fumecheng-10743	43	28	,	,	PUNCT
fumecheng-10743	43	29	or	or	CCONJ
fumecheng-10743	43	30	ω1=100	ω1=100	NOUN
fumecheng-10743	43	31	and	and	CCONJ
fumecheng-10743	43	32	ω2=0.1	ω2=0.1	PROPN
fumecheng-10743	43	33	,	,	PUNCT
fumecheng-10743	43	34	all	all	DET
fumecheng-10743	43	35	cases	case	NOUN
fumecheng-10743	43	36	leading	lead	VERB
fumecheng-10743	43	37	to	to	ADP
fumecheng-10743	43	38	the	the	DET
fumecheng-10743	43	39	same	same	ADJ
fumecheng-10743	43	40	result	result	NOUN
fumecheng-10743	43	41	.	.	PUNCT
fumecheng-10743	44	1	this	this	DET
fumecheng-10743	44	2	two	two	NUM
fumecheng-10743	44	3	-	-	PUNCT
fumecheng-10743	44	4	trial	trial	NOUN
fumecheng-10743	44	5	assumption	assumption	NOUN
fumecheng-10743	44	6	goes	go	VERB
fumecheng-10743	44	7	back	back	ADV
fumecheng-10743	44	8	to	to	ADP
fumecheng-10743	44	9	an	an	DET
fumecheng-10743	44	10	ancient	ancient	ADJ
fumecheng-10743	44	11	chinese	chinese	ADJ
fumecheng-10743	44	12	algorithm	algorithm	NOUN
fumecheng-10743	44	13	[	[	X
fumecheng-10743	44	14	26	26	NUM
fumecheng-10743	44	15	]	]	X
fumecheng-10743	44	16	,	,	PUNCT
fumecheng-10743	44	17	which	which	PRON
fumecheng-10743	44	18	was	be	AUX
fumecheng-10743	44	19	developed	develop	VERB
fumecheng-10743	44	20	to	to	ADP
fumecheng-10743	44	21	he	he	PRON
fumecheng-10743	44	22	’s	’s	PART
fumecheng-10743	44	23	frequency	frequency	NOUN
fumecheng-10743	44	24	formulation	formulation	NOUN
fumecheng-10743	44	25	to	to	PART
fumecheng-10743	44	26	solve	solve	VERB
fumecheng-10743	44	27	nonlinear	nonlinear	ADJ
fumecheng-10743	44	28	oscillators	oscillator	NOUN
fumecheng-10743	44	29	by	by	ADP
fumecheng-10743	44	30	ji	ji	PROPN
fumecheng-10743	44	31	-	-	PROPN
fumecheng-10743	44	32	huan	huan	PROPN
fumecheng-10743	44	33	he	he	PRON
fumecheng-10743	45	1	[	[	X
fumecheng-10743	45	2	26	26	NUM
fumecheng-10743	45	3	]	]	PUNCT
fumecheng-10743	45	4	,	,	PUNCT
fumecheng-10743	45	5	and	and	CCONJ
fumecheng-10743	45	6	chun	chun	PROPN
fumecheng-10743	45	7	-	-	PUNCT
fumecheng-10743	45	8	hui	hui	PROPN
fumecheng-10743	46	1	he	he	PRON
fumecheng-10743	46	2	’s	’	VERB
fumecheng-10743	46	3	iteration	iteration	NOUN
fumecheng-10743	46	4	algorithm	algorithm	NOUN
fumecheng-10743	46	5	for	for	ADP
fumecheng-10743	46	6	numerical	numerical	ADJ
fumecheng-10743	46	7	simulation	simulation	PROPN
fumecheng-10743	47	1	[	[	X
fumecheng-10743	47	2	34,35	34,35	NOUN
fumecheng-10743	47	3	]	]	PUNCT
fumecheng-10743	47	4	.	.	PUNCT
fumecheng-10743	48	1	448	448	NUM
fumecheng-10743	48	2	h.	h.	PROPN
fumecheng-10743	48	3	ma	ma	PROPN
fumecheng-10743	49	1	it	it	PRON
fumecheng-10743	49	2	is	be	AUX
fumecheng-10743	49	3	amazing	amazing	ADJ
fumecheng-10743	49	4	that	that	SCONJ
fumecheng-10743	49	5	the	the	DET
fumecheng-10743	49	6	hamiltonian	hamiltonian	NOUN
fumecheng-10743	49	7	-	-	PUNCT
fumecheng-10743	49	8	based	base	VERB
fumecheng-10743	49	9	frequency	frequency	NOUN
fumecheng-10743	49	10	formulation	formulation	NOUN
fumecheng-10743	49	11	does	do	AUX
fumecheng-10743	49	12	not	not	PART
fumecheng-10743	49	13	depend	depend	VERB
fumecheng-10743	49	14	upon	upon	SCONJ
fumecheng-10743	49	15	the	the	DET
fumecheng-10743	49	16	choice	choice	NOUN
fumecheng-10743	49	17	of	of	ADP
fumecheng-10743	49	18	ω1	ω1	PROPN
fumecheng-10743	49	19	and	and	CCONJ
fumecheng-10743	49	20	ω2	ω2	NUM
fumecheng-10743	49	21	.	.	PUNCT
fumecheng-10743	50	1	here	here	ADV
fumecheng-10743	50	2	a	a	DET
fumecheng-10743	50	3	strict	strict	ADJ
fumecheng-10743	50	4	proof	proof	NOUN
fumecheng-10743	50	5	is	be	AUX
fumecheng-10743	50	6	given	give	VERB
fumecheng-10743	50	7	.	.	PUNCT
fumecheng-10743	51	1	from	from	ADP
fumecheng-10743	51	2	eqs	eqs	PROPN
fumecheng-10743	51	3	.	.	PUNCT
fumecheng-10743	52	1	(	(	PUNCT
fumecheng-10743	52	2	7	7	NUM
fumecheng-10743	52	3	)	)	PUNCT
fumecheng-10743	52	4	and	and	CCONJ
fumecheng-10743	52	5	(	(	PUNCT
fumecheng-10743	52	6	8)	8)	NUM
fumecheng-10743	52	7	,	,	PUNCT
fumecheng-10743	52	8	we	we	PRON
fumecheng-10743	52	9	have	have	VERB
fumecheng-10743	52	10	2	2	NUM
fumecheng-10743	52	11	2	2	NUM
fumecheng-10743	52	12	21	21	NUM
fumecheng-10743	52	13	1	1	NUM
fumecheng-10743	52	14	1	1	NUM
fumecheng-10743	52	15	1	1	NUM
fumecheng-10743	52	16	2	2	NUM
fumecheng-10743	52	17	2	2	NUM
fumecheng-10743	52	18	2	2	NUM
fumecheng-10743	52	19	2	2	NUM
fumecheng-10743	52	20	21	21	NUM
fumecheng-10743	52	21	1	1	NUM
fumecheng-10743	52	22	1	1	NUM
fumecheng-10743	52	23	1	1	NUM
fumecheng-10743	52	24	(	(	PUNCT
fumecheng-10743	52	25	)	)	PUNCT
fumecheng-10743	52	26	sin	sin	NOUN
fumecheng-10743	52	27	(	(	PUNCT
fumecheng-10743	52	28	cos	cos	PROPN
fumecheng-10743	52	29	)	)	PUNCT
fumecheng-10743	52	30	(	(	PUNCT
fumecheng-10743	52	31	)	)	PUNCT
fumecheng-10743	52	32	2	2	NUM
fumecheng-10743	52	33	2	2	NUM
fumecheng-10743	52	34	(	(	PUNCT
fumecheng-10743	52	35	)	)	PUNCT
fumecheng-10743	52	36	cos	cos	PROPN
fumecheng-10743	52	37	(	(	PUNCT
fumecheng-10743	52	38	)	)	PUNCT
fumecheng-10743	52	39	2	2	NUM
fumecheng-10743	52	40	2	2	NUM
fumecheng-10743	53	1	cos	cos	NOUN
fumecheng-10743	53	2	b	b	PROPN
fumecheng-10743	53	3	r	r	NOUN
fumecheng-10743	53	4	t	t	X
fumecheng-10743	53	5	t	t	NOUN
fumecheng-10743	53	6	p	p	X
fumecheng-10743	53	7	b	b	PROPN
fumecheng-10743	53	8	t	t	PROPN
fumecheng-10743	53	9	p	p	PROPN
fumecheng-10743	53	10	b	b	PROPN
fumecheng-10743	53	11	b	b	PROPN
fumecheng-10743	53	12	p	p	X
fumecheng-10743	53	13	b	b	PROPN
fumecheng-10743	53	14	b	b	PROPN
fumecheng-10743	53	15	t	t	PROPN
fumecheng-10743	53	16	p	p	PROPN
fumecheng-10743	53	17	b	b	PROPN
fumecheng-10743	53	18	t	t	NOUN
fumecheng-10743	53	19	=	=	PUNCT
fumecheng-10743	54	1	+	+	CCONJ
fumecheng-10743	54	2	−	−	NUM
fumecheng-10743	55	1	−	−	PROPN
fumecheng-10743	55	2	=	=	SYM
fumecheng-10743	56	1	−	−	PROPN
fumecheng-10743	57	1	+	+	CCONJ
fumecheng-10743	57	2	ω	ω	PROPN
fumecheng-10743	57	3	ω	ω	PROPN
fumecheng-10743	57	4	ω	ω	PROPN
fumecheng-10743	57	5	ω	ω	PROPN
fumecheng-10743	57	6	ω	ω	PROPN
fumecheng-10743	57	7	ω	ω	PROPN
fumecheng-10743	57	8	ω	ω	PROPN
fumecheng-10743	57	9	(	(	PUNCT
fumecheng-10743	57	10	12	12	NUM
fumecheng-10743	57	11	)	)	SYM
fumecheng-10743	57	12	2	2	NUM
fumecheng-10743	57	13	2	2	NUM
fumecheng-10743	57	14	22	22	NUM
fumecheng-10743	57	15	2	2	NUM
fumecheng-10743	57	16	2	2	NUM
fumecheng-10743	57	17	2	2	NUM
fumecheng-10743	57	18	2	2	NUM
fumecheng-10743	57	19	2	2	NUM
fumecheng-10743	57	20	2	2	NUM
fumecheng-10743	57	21	2	2	NUM
fumecheng-10743	57	22	22	22	NUM
fumecheng-10743	57	23	2	2	NUM
fumecheng-10743	57	24	2	2	NUM
fumecheng-10743	57	25	2	2	NUM
fumecheng-10743	57	26	(	(	PUNCT
fumecheng-10743	57	27	)	)	PUNCT
fumecheng-10743	57	28	sin	sin	NOUN
fumecheng-10743	57	29	(	(	PUNCT
fumecheng-10743	57	30	cos	cos	PROPN
fumecheng-10743	57	31	)	)	PUNCT
fumecheng-10743	57	32	(	(	PUNCT
fumecheng-10743	57	33	)	)	PUNCT
fumecheng-10743	57	34	2	2	NUM
fumecheng-10743	57	35	2	2	NUM
fumecheng-10743	57	36	(	(	PUNCT
fumecheng-10743	57	37	)	)	PUNCT
fumecheng-10743	57	38	cos	cos	PROPN
fumecheng-10743	57	39	(	(	PUNCT
fumecheng-10743	57	40	)	)	PUNCT
fumecheng-10743	57	41	2	2	NUM
fumecheng-10743	57	42	2	2	NUM
fumecheng-10743	57	43	cos	cos	NOUN
fumecheng-10743	57	44	b	b	PROPN
fumecheng-10743	57	45	r	r	NOUN
fumecheng-10743	57	46	t	t	X
fumecheng-10743	57	47	t	t	NOUN
fumecheng-10743	58	1	p	p	X
fumecheng-10743	58	2	b	b	PROPN
fumecheng-10743	58	3	t	t	PROPN
fumecheng-10743	58	4	p	p	PROPN
fumecheng-10743	58	5	b	b	PROPN
fumecheng-10743	58	6	b	b	PROPN
fumecheng-10743	58	7	p	p	X
fumecheng-10743	58	8	b	b	PROPN
fumecheng-10743	58	9	b	b	PROPN
fumecheng-10743	58	10	t	t	PROPN
fumecheng-10743	58	11	p	p	PROPN
fumecheng-10743	58	12	b	b	PROPN
fumecheng-10743	58	13	t	t	NOUN
fumecheng-10743	58	14	=	=	PUNCT
fumecheng-10743	59	1	+	+	CCONJ
fumecheng-10743	59	2	−	−	NUM
fumecheng-10743	60	1	−	−	PROPN
fumecheng-10743	60	2	=	=	SYM
fumecheng-10743	61	1	−	−	PROPN
fumecheng-10743	62	1	+	+	CCONJ
fumecheng-10743	62	2	ω	ω	PROPN
fumecheng-10743	62	3	ω	ω	PROPN
fumecheng-10743	62	4	ω	ω	PROPN
fumecheng-10743	62	5	ω	ω	PROPN
fumecheng-10743	62	6	ω	ω	PROPN
fumecheng-10743	62	7	ω	ω	PROPN
fumecheng-10743	62	8	ω	ω	PROPN
fumecheng-10743	62	9	(	(	PUNCT
fumecheng-10743	62	10	13	13	NUM
fumecheng-10743	62	11	)	)	PUNCT
fumecheng-10743	62	12	the	the	DET
fumecheng-10743	62	13	residual	residual	ADJ
fumecheng-10743	62	14	integrals	integral	NOUN
fumecheng-10743	62	15	become	become	VERB
fumecheng-10743	62	16	1	1	NUM
fumecheng-10743	62	17	2	2	NUM
fumecheng-10743	62	18	2	2	NUM
fumecheng-10743	62	19	/	/	SYM
fumecheng-10743	62	20	4	4	NUM
fumecheng-10743	62	21	1	1	NUM
fumecheng-10743	62	22	21	21	NUM
fumecheng-10743	62	23	1	1	NUM
fumecheng-10743	62	24	1	1	NUM
fumecheng-10743	62	25	1	1	NUM
fumecheng-10743	62	26	0	0	NUM
fumecheng-10743	62	27	0	0	NUM
fumecheng-10743	62	28	1	1	NUM
fumecheng-10743	62	29	6	6	NUM
fumecheng-10743	62	30	(	(	PUNCT
fumecheng-10743	62	31	)	)	SYM
fumecheng-10743	62	32	4	4	NUM
fumecheng-10743	62	33	2	2	NUM
fumecheng-10743	62	34	cos	cos	NOUN
fumecheng-10743	62	35	(	(	PUNCT
fumecheng-10743	62	36	1	1	NUM
fumecheng-10743	62	37	)	)	PUNCT
fumecheng-10743	62	38	3	3	NUM
fumecheng-10743	62	39	t	t	NOUN
fumecheng-10743	62	40	b	b	PROPN
fumecheng-10743	62	41	p	p	X
fumecheng-10743	62	42	b	b	NOUN
fumecheng-10743	62	43	r	r	NOUN
fumecheng-10743	62	44	r	r	NOUN
fumecheng-10743	62	45	tdt	tdt	PROPN
fumecheng-10743	62	46	p	p	PROPN
fumecheng-10743	62	47	b	b	PROPN
fumecheng-10743	62	48	x	x	X
fumecheng-10743	62	49	dx	dx	PROPN
fumecheng-10743	62	50	t	t	PROPN
fumecheng-10743	62	51			PROPN
fumecheng-10743	62	52			PROPN
fumecheng-10743	62	53	−	−	NOUN
fumecheng-10743	62	54	=	=	SYM
fumecheng-10743	62	55	=	=	PUNCT
fumecheng-10743	63	1	+	+	NUM
fumecheng-10743	63	2	−	−	NOUN
fumecheng-10743	63	3			PROPN
fumecheng-10743	63	4	ω	ω	PROPN
fumecheng-10743	63	5	ω	ω	PROPN
fumecheng-10743	63	6	(	(	PUNCT
fumecheng-10743	63	7	14	14	NUM
fumecheng-10743	63	8	)	)	SYM
fumecheng-10743	63	9	2	2	NUM
fumecheng-10743	63	10	2	2	NUM
fumecheng-10743	63	11	2	2	NUM
fumecheng-10743	63	12	/	/	SYM
fumecheng-10743	63	13	4	4	NUM
fumecheng-10743	63	14	1	1	NUM
fumecheng-10743	63	15	22	22	NUM
fumecheng-10743	63	16	2	2	NUM
fumecheng-10743	63	17	2	2	NUM
fumecheng-10743	63	18	0	0	NUM
fumecheng-10743	63	19	0	0	NUM
fumecheng-10743	63	20	2	2	NUM
fumecheng-10743	63	21	6	6	NUM
fumecheng-10743	63	22	(	(	PUNCT
fumecheng-10743	63	23	)	)	SYM
fumecheng-10743	63	24	4	4	NUM
fumecheng-10743	63	25	2	2	NUM
fumecheng-10743	63	26	cos	cos	NOUN
fumecheng-10743	63	27	(	(	PUNCT
fumecheng-10743	63	28	1	1	NUM
fumecheng-10743	63	29	)	)	PUNCT
fumecheng-10743	63	30	3	3	NUM
fumecheng-10743	63	31	t	t	NOUN
fumecheng-10743	63	32	b	b	PROPN
fumecheng-10743	63	33	p	p	X
fumecheng-10743	63	34	b	b	NOUN
fumecheng-10743	63	35	r	r	NOUN
fumecheng-10743	63	36	r	r	NOUN
fumecheng-10743	63	37	tdt	tdt	PROPN
fumecheng-10743	63	38	p	p	PROPN
fumecheng-10743	63	39	b	b	PROPN
fumecheng-10743	63	40	x	x	X
fumecheng-10743	63	41	dx	dx	PROPN
fumecheng-10743	63	42	t	t	PROPN
fumecheng-10743	63	43			PROPN
fumecheng-10743	63	44			PROPN
fumecheng-10743	63	45	−	−	NOUN
fumecheng-10743	63	46	=	=	SYM
fumecheng-10743	63	47	=	=	PUNCT
fumecheng-10743	64	1	+	+	NUM
fumecheng-10743	64	2	−	−	NOUN
fumecheng-10743	64	3	2	2	NOUN
fumecheng-10743	64	4	ω	ω	PROPN
fumecheng-10743	64	5	ω	ω	PROPN
fumecheng-10743	64	6	(	(	PUNCT
fumecheng-10743	64	7	15	15	NUM
fumecheng-10743	64	8	)	)	PUNCT
fumecheng-10743	64	9	so	so	ADV
fumecheng-10743	64	10	a	a	DET
fumecheng-10743	64	11	modified	modify	VERB
fumecheng-10743	64	12	frequency	frequency	NOUN
fumecheng-10743	64	13	formulation	formulation	NOUN
fumecheng-10743	64	14	is	be	AUX
fumecheng-10743	64	15	obtained	obtain	VERB
fumecheng-10743	64	16	,	,	PUNCT
fumecheng-10743	64	17	which	which	PRON
fumecheng-10743	64	18	is	be	AUX
fumecheng-10743	64	19	2	2	NUM
fumecheng-10743	64	20	2	2	NUM
fumecheng-10743	64	21	1	1	NUM
fumecheng-10743	64	22	2	2	NUM
fumecheng-10743	64	23	2	2	NUM
fumecheng-10743	64	24	2	2	NUM
fumecheng-10743	64	25	2	2	NUM
fumecheng-10743	64	26	1	1	NUM
fumecheng-10743	64	27	2	2	NUM
fumecheng-10743	64	28	2	2	NUM
fumecheng-10743	64	29	1	1	NUM
fumecheng-10743	64	30	1	1	NUM
fumecheng-10743	64	31	2	2	NUM
fumecheng-10743	64	32	2	2	NUM
fumecheng-10743	64	33	2	2	NUM
fumecheng-10743	64	34	2	2	NUM
fumecheng-10743	64	35	2	2	NUM
fumecheng-10743	64	36	1	1	NUM
fumecheng-10743	64	37	1	1	NUM
fumecheng-10743	64	38	2	2	NUM
fumecheng-10743	64	39	2	2	NUM
fumecheng-10743	64	40	2	2	NUM
fumecheng-10743	64	41	21	21	NUM
fumecheng-10743	64	42	2	2	NUM
fumecheng-10743	64	43	2	2	NUM
fumecheng-10743	64	44	1	1	NUM
fumecheng-10743	64	45	0	0	NUM
fumecheng-10743	64	46	0	0	NUM
fumecheng-10743	64	47	2	2	NUM
fumecheng-10743	64	48	2	2	NUM
fumecheng-10743	64	49	2	2	NUM
fumecheng-10743	64	50	2	2	NUM
fumecheng-10743	64	51	1	1	NUM
fumecheng-10743	64	52	2	2	NUM
fumecheng-10743	64	53	1	1	NUM
fumecheng-10743	64	54	2	2	NUM
fumecheng-10743	64	55	2	2	NUM
fumecheng-10743	64	56	2	2	NUM
fumecheng-10743	64	57	1	1	NUM
fumecheng-10743	64	58	2	2	NUM
fumecheng-10743	64	59	0	0	NUM
fumecheng-10743	64	60	2	2	NUM
fumecheng-10743	64	61	2	2	NUM
fumecheng-10743	64	62	2	2	NUM
fumecheng-10743	64	63	1	1	NUM
fumecheng-10743	64	64	2	2	NUM
fumecheng-10743	64	65	2	2	NUM
fumecheng-10743	64	66	+	+	NUM
fumecheng-10743	64	67	6	6	NUM
fumecheng-10743	64	68	(	(	PUNCT
fumecheng-10743	64	69	)	)	PUNCT
fumecheng-10743	64	70	6	6	NUM
fumecheng-10743	64	71	(	(	PUNCT
fumecheng-10743	64	72	)	)	SYM
fumecheng-10743	64	73	2	2	NUM
fumecheng-10743	64	74	2	2	NUM
fumecheng-10743	64	75	(	(	PUNCT
fumecheng-10743	64	76	1	1	NUM
fumecheng-10743	64	77	)	)	PUNCT
fumecheng-10743	64	78	(	(	PUNCT
fumecheng-10743	64	79	1	1	X
fumecheng-10743	64	80	)	)	PUNCT
fumecheng-10743	64	81	3	3	NUM
fumecheng-10743	64	82	3	3	NUM
fumecheng-10743	64	83	6	6	NUM
fumecheng-10743	64	84	(	(	PUNCT
fumecheng-10743	64	85	)	)	PUNCT
fumecheng-10743	64	86	6	6	NUM
fumecheng-10743	64	87	(	(	PUNCT
fumecheng-10743	64	88	)	)	PUNCT
fumecheng-10743	64	89	3	3	NUM
fumecheng-10743	64	90	3	3	NUM
fumecheng-10743	64	91	6	6	NUM
fumecheng-10743	64	92	(	(	PUNCT
fumecheng-10743	64	93	)	)	PUNCT
fumecheng-10743	64	94	2	2	NUM
fumecheng-10743	64	95	(	(	PUNCT
fumecheng-10743	64	96	1	1	NUM
fumecheng-10743	64	97	)	)	PUNCT
fumecheng-10743	64	98	(	(	PUNCT
fumecheng-10743	64	99	)	)	PUNCT
fumecheng-10743	64	100	3	3	NUM
fumecheng-10743	64	101	3	3	NUM
fumecheng-10743	64	102	6	6	NUM
fumecheng-10743	64	103	(	(	PUNCT
fumecheng-10743	64	104	)	)	PUNCT
fumecheng-10743	64	105	6	6	NUM
fumecheng-10743	64	106	(	(	PUNCT
fumecheng-10743	64	107	1	1	NUM
fumecheng-10743	64	108	)	)	PUNCT
fumecheng-10743	64	109	=	=	SYM
fumecheng-10743	65	1	=	=	PUNCT
fumecheng-10743	65	2	(	(	PUNCT
fumecheng-10743	65	3	)	)	PUNCT
fumecheng-10743	65	4	(	(	PUNCT
fumecheng-10743	65	5	)	)	PUNCT
fumecheng-10743	66	1	r	r	NOUN
fumecheng-10743	66	2	r	r	NOUN
fumecheng-10743	66	3	r	r	NOUN
fumecheng-10743	66	4	r	r	NOUN
fumecheng-10743	66	5	b	b	PROPN
fumecheng-10743	66	6	p	p	X
fumecheng-10743	66	7	b	b	PROPN
fumecheng-10743	66	8	b	b	PROPN
fumecheng-10743	66	9	p	p	X
fumecheng-10743	66	10	b	b	PROPN
fumecheng-10743	66	11	p	p	X
fumecheng-10743	66	12	b	b	PROPN
fumecheng-10743	66	13	x	x	X
fumecheng-10743	66	14	dx	dx	PROPN
fumecheng-10743	66	15	p	p	PROPN
fumecheng-10743	66	16	b	b	PROPN
fumecheng-10743	66	17	x	x	X
fumecheng-10743	67	1	dx	dx	PROPN
fumecheng-10743	67	2	b	b	PROPN
fumecheng-10743	67	3	p	p	X
fumecheng-10743	67	4	b	b	PROPN
fumecheng-10743	67	5	b	b	PROPN
fumecheng-10743	67	6	p	p	X
fumecheng-10743	67	7	b	b	PROPN
fumecheng-10743	67	8	p	p	X
fumecheng-10743	67	9	b	b	PROPN
fumecheng-10743	67	10	p	p	X
fumecheng-10743	67	11	b	b	PROPN
fumecheng-10743	67	12	x	x	X
fumecheng-10743	67	13	dx	dx	PROPN
fumecheng-10743	67	14	b	b	PROPN
fumecheng-10743	67	15	p	p	X
fumecheng-10743	67	16	b	b	PROPN
fumecheng-10743	67	17	p	p	X
fumecheng-10743	67	18	b	b	PROPN
fumecheng-10743	67	19	x	x	SYM
fumecheng-10743	67	20	d	d	X
fumecheng-10743	67	21			PROPN
fumecheng-10743	67	22			PROPN
fumecheng-10743	67	23			PROPN
fumecheng-10743	67	24			PROPN
fumecheng-10743	67	25			PROPN
fumecheng-10743	67	26			PROPN
fumecheng-10743	67	27			PROPN
fumecheng-10743	67	28			PROPN
fumecheng-10743	67	29			NOUN
fumecheng-10743	67	30	−	−	NOUN
fumecheng-10743	67	31	−	−	NOUN
fumecheng-10743	67	32	=	=	SYM
fumecheng-10743	68	1	−	−	PROPN
fumecheng-10743	68	2	−	−	PROPN
fumecheng-10743	68	3	−	−	PROPN
fumecheng-10743	69	1	+	+	CCONJ
fumecheng-10743	69	2	−	−	PROPN
fumecheng-10743	70	1	+	+	CCONJ
fumecheng-10743	70	2	−	−	PROPN
fumecheng-10743	70	3	−	−	NUM
fumecheng-10743	70	4	−	−	PROPN
fumecheng-10743	70	5	−	−	PROPN
fumecheng-10743	70	6	−	−	PROPN
fumecheng-10743	70	7	−	−	PROPN
fumecheng-10743	70	8	−	−	PROPN
fumecheng-10743	70	9	−	−	PROPN
fumecheng-10743	70	10	−	−	NOUN
fumecheng-10743	71	1	−	−	PROPN
fumecheng-10743	71	2	=	=	NOUN
fumecheng-10743	72	1			NOUN
fumecheng-10743	72	2			PROPN
fumecheng-10743	72	3			NOUN
fumecheng-10743	72	4			PROPN
fumecheng-10743	72	5			PROPN
fumecheng-10743	73	1			PROPN
fumecheng-10743	74	1			PROPN
fumecheng-10743	74	2			PROPN
fumecheng-10743	75	1			ADJ
fumecheng-10743	75	2			PROPN
fumecheng-10743	75	3			PROPN
fumecheng-10743	75	4			NOUN
fumecheng-10743	75	5			PUNCT
fumecheng-10743	75	6			PUNCT
fumecheng-10743	76	1	ω	ω	PROPN
fumecheng-10743	76	2	ω	ω	PROPN
fumecheng-10743	76	3	ω	ω	PROPN
fumecheng-10743	76	4	ω	ω	PROPN
fumecheng-10743	76	5	ω	ω	PROPN
fumecheng-10743	76	6	ω	ω	PROPN
fumecheng-10743	76	7	ω	ω	PROPN
fumecheng-10743	76	8	ω	ω	PROPN
fumecheng-10743	76	9	ω	ω	PROPN
fumecheng-10743	76	10	ω	ω	PROPN
fumecheng-10743	76	11	ω	ω	PROPN
fumecheng-10743	76	12	ω	ω	PROPN
fumecheng-10743	76	13	ω	ω	PROPN
fumecheng-10743	76	14	ω	ω	PROPN
fumecheng-10743	76	15	ω	ω	NUM
fumecheng-10743	76	16	1	1	NUM
fumecheng-10743	76	17	0	0	NUM
fumecheng-10743	76	18	2	2	NUM
fumecheng-10743	76	19	x	x	SYM
fumecheng-10743	76	20	b	b	NOUN
fumecheng-10743	76	21			X
fumecheng-10743	76	22	(	(	PUNCT
fumecheng-10743	76	23	16	16	NUM
fumecheng-10743	76	24	)	)	PUNCT
fumecheng-10743	76	25	this	this	DET
fumecheng-10743	76	26	modification	modification	NOUN
fumecheng-10743	76	27	seems	seem	VERB
fumecheng-10743	76	28	much	much	ADV
fumecheng-10743	76	29	simpler	simple	ADJ
fumecheng-10743	76	30	than	than	ADP
fumecheng-10743	76	31	the	the	DET
fumecheng-10743	76	32	original	original	ADJ
fumecheng-10743	76	33	one	one	NOUN
fumecheng-10743	76	34	because	because	SCONJ
fumecheng-10743	76	35	no	no	DET
fumecheng-10743	76	36	calculation	calculation	NOUN
fumecheng-10743	76	37	of	of	ADP
fumecheng-10743	76	38	integrals	integral	NOUN
fumecheng-10743	76	39	is	be	AUX
fumecheng-10743	76	40	needed	need	VERB
fumecheng-10743	76	41	,	,	PUNCT
fumecheng-10743	76	42	so	so	CCONJ
fumecheng-10743	76	43	it	it	PRON
fumecheng-10743	76	44	is	be	AUX
fumecheng-10743	76	45	easily	easily	ADV
fumecheng-10743	76	46	applicable	applicable	ADJ
fumecheng-10743	76	47	.	.	PUNCT
fumecheng-10743	77	1	simplified	simplified	ADJ
fumecheng-10743	77	2	hamiltonian	hamiltonian	ADJ
fumecheng-10743	77	3	-	-	PUNCT
fumecheng-10743	77	4	based	base	VERB
fumecheng-10743	77	5	frequency	frequency	NOUN
fumecheng-10743	77	6	-	-	PUNCT
fumecheng-10743	77	7	amplitude	amplitude	NOUN
fumecheng-10743	77	8	formulation	formulation	NOUN
fumecheng-10743	77	9	for	for	ADP
fumecheng-10743	77	10	nonlinear	nonlinear	ADJ
fumecheng-10743	77	11	vibration	vibration	NOUN
fumecheng-10743	77	12	systems	system	NOUN
fumecheng-10743	77	13	449	449	NUM
fumecheng-10743	77	14	alternatively	alternatively	ADV
fumecheng-10743	77	15	,	,	PUNCT
fumecheng-10743	77	16	we	we	PRON
fumecheng-10743	77	17	locate	locate	VERB
fumecheng-10743	77	18	at	at	ADP
fumecheng-10743	77	19	[	[	X
fumecheng-10743	77	20	26	26	NUM
fumecheng-10743	77	21	]	]	SYM
fumecheng-10743	77	22	1	1	NUM
fumecheng-10743	77	23	2	2	NUM
fumecheng-10743	77	24	cos	cos	NOUN
fumecheng-10743	77	25	cost	cost	VERB
fumecheng-10743	77	26	t	t	NOUN
fumecheng-10743	77	27	k=	k=	X
fumecheng-10743	78	1	=	=	SYM
fumecheng-10743	78	2	ω	ω	PROPN
fumecheng-10743	78	3	ω	ω	PROPN
fumecheng-10743	78	4	(	(	PUNCT
fumecheng-10743	78	5	17	17	NUM
fumecheng-10743	78	6	)	)	PUNCT
fumecheng-10743	78	7	eqs	eqs	PROPN
fumecheng-10743	78	8	.	.	PUNCT
fumecheng-10743	79	1	(	(	PUNCT
fumecheng-10743	79	2	7	7	NUM
fumecheng-10743	79	3	)	)	PUNCT
fumecheng-10743	79	4	and	and	CCONJ
fumecheng-10743	79	5	(	(	PUNCT
fumecheng-10743	79	6	8)	8)	NUM
fumecheng-10743	79	7	become	become	VERB
fumecheng-10743	79	8	2	2	NUM
fumecheng-10743	79	9	2	2	NUM
fumecheng-10743	79	10	2	2	NUM
fumecheng-10743	79	11	1	1	NUM
fumecheng-10743	79	12	1	1	NUM
fumecheng-10743	79	13	1	1	NUM
fumecheng-10743	79	14	(	(	PUNCT
fumecheng-10743	79	15	1	1	NUM
fumecheng-10743	79	16	)	)	PUNCT
fumecheng-10743	79	17	(	(	PUNCT
fumecheng-10743	79	18	)	)	PUNCT
fumecheng-10743	79	19	(	(	PUNCT
fumecheng-10743	79	20	)	)	PUNCT
fumecheng-10743	79	21	2	2	NUM
fumecheng-10743	79	22	r	r	NOUN
fumecheng-10743	79	23	b	b	PROPN
fumecheng-10743	79	24	k	k	X
fumecheng-10743	79	25	p	p	X
fumecheng-10743	79	26	kb	kb	PROPN
fumecheng-10743	79	27	p	p	PROPN
fumecheng-10743	79	28	b=	b=	NOUN
fumecheng-10743	79	29	−	−	PROPN
fumecheng-10743	80	1	+	+	CCONJ
fumecheng-10743	80	2	−ω	−ω	ADJ
fumecheng-10743	80	3	(	(	PUNCT
fumecheng-10743	80	4	18	18	NUM
fumecheng-10743	80	5	)	)	SYM
fumecheng-10743	80	6	2	2	NUM
fumecheng-10743	80	7	2	2	NUM
fumecheng-10743	80	8	2	2	NUM
fumecheng-10743	80	9	2	2	NUM
fumecheng-10743	80	10	2	2	NUM
fumecheng-10743	80	11	1	1	NUM
fumecheng-10743	80	12	(	(	PUNCT
fumecheng-10743	80	13	1	1	NUM
fumecheng-10743	80	14	)	)	PUNCT
fumecheng-10743	80	15	(	(	PUNCT
fumecheng-10743	80	16	)	)	PUNCT
fumecheng-10743	80	17	(	(	PUNCT
fumecheng-10743	80	18	)	)	PUNCT
fumecheng-10743	80	19	2	2	NUM
fumecheng-10743	80	20	r	r	NOUN
fumecheng-10743	80	21	b	b	PROPN
fumecheng-10743	80	22	k	k	X
fumecheng-10743	80	23	p	p	X
fumecheng-10743	80	24	kb	kb	PROPN
fumecheng-10743	80	25	p	p	PROPN
fumecheng-10743	80	26	b=	b=	NOUN
fumecheng-10743	80	27	−	−	PROPN
fumecheng-10743	81	1	+	+	CCONJ
fumecheng-10743	81	2	−ω	−ω	ADJ
fumecheng-10743	81	3	(	(	PUNCT
fumecheng-10743	81	4	19	19	NUM
fumecheng-10743	81	5	)	)	PUNCT
fumecheng-10743	81	6	another	another	DET
fumecheng-10743	81	7	modification	modification	NOUN
fumecheng-10743	81	8	of	of	ADP
fumecheng-10743	81	9	the	the	DET
fumecheng-10743	81	10	hamiltonian	hamiltonian	NOUN
fumecheng-10743	81	11	-	-	PUNCT
fumecheng-10743	81	12	based	base	VERB
fumecheng-10743	81	13	frequency	frequency	NOUN
fumecheng-10743	81	14	formulation	formulation	NOUN
fumecheng-10743	81	15	is	be	AUX
fumecheng-10743	81	16	2	2	NUM
fumecheng-10743	81	17	2	2	NUM
fumecheng-10743	81	18	2	2	NUM
fumecheng-10743	81	19	2	2	NUM
fumecheng-10743	81	20	1	1	NUM
fumecheng-10743	81	21	1	1	NUM
fumecheng-10743	81	22	2	2	NUM
fumecheng-10743	81	23	1	1	NUM
fumecheng-10743	81	24	2	2	NUM
fumecheng-10743	81	25	2	2	NUM
fumecheng-10743	81	26	2	2	NUM
fumecheng-10743	81	27	2	2	NUM
fumecheng-10743	81	28	2	2	NUM
fumecheng-10743	81	29	2	2	NUM
fumecheng-10743	81	30	2	2	NUM
fumecheng-10743	81	31	2	2	NUM
fumecheng-10743	81	32	2	2	NUM
fumecheng-10743	81	33	2	2	NUM
fumecheng-10743	81	34	1	1	NUM
fumecheng-10743	81	35	1	1	NUM
fumecheng-10743	81	36	2	2	NUM
fumecheng-10743	81	37	2	2	NUM
fumecheng-10743	81	38	2	2	NUM
fumecheng-10743	81	39	2	2	NUM
fumecheng-10743	81	40	2	2	NUM
fumecheng-10743	81	41	2	2	NUM
fumecheng-10743	81	42	2	2	NUM
fumecheng-10743	81	43	1	1	NUM
fumecheng-10743	81	44	2	2	NUM
fumecheng-10743	81	45	2	2	NUM
fumecheng-10743	81	46	2	2	NUM
fumecheng-10743	81	47	2	2	NUM
fumecheng-10743	81	48	2	2	NUM
fumecheng-10743	81	49	2	2	NUM
fumecheng-10743	81	50	1	1	NUM
fumecheng-10743	81	51	2	2	NUM
fumecheng-10743	81	52	1	1	NUM
fumecheng-10743	81	53	2	2	NUM
fumecheng-10743	81	54	2	2	NUM
fumecheng-10743	81	55	2	2	NUM
fumecheng-10743	81	56	2	2	NUM
fumecheng-10743	81	57	1	1	NUM
fumecheng-10743	81	58	2	2	NUM
fumecheng-10743	81	59	1	1	NUM
fumecheng-10743	81	60	1	1	NUM
fumecheng-10743	81	61	(	(	PUNCT
fumecheng-10743	81	62	(	(	PUNCT
fumecheng-10743	81	63	1	1	NUM
fumecheng-10743	81	64	)	)	PUNCT
fumecheng-10743	81	65	(	(	PUNCT
fumecheng-10743	81	66	)	)	PUNCT
fumecheng-10743	81	67	(	(	PUNCT
fumecheng-10743	81	68	)	)	PUNCT
fumecheng-10743	81	69	)	)	PUNCT
fumecheng-10743	82	1	(	(	PUNCT
fumecheng-10743	82	2	(	(	PUNCT
fumecheng-10743	82	3	1	1	X
fumecheng-10743	82	4	)	)	PUNCT
fumecheng-10743	82	5	(	(	PUNCT
fumecheng-10743	82	6	)	)	PUNCT
fumecheng-10743	82	7	(	(	PUNCT
fumecheng-10743	82	8	)	)	PUNCT
fumecheng-10743	82	9	)	)	PUNCT
fumecheng-10743	82	10	2	2	NUM
fumecheng-10743	82	11	2	2	NUM
fumecheng-10743	82	12	1	1	NUM
fumecheng-10743	82	13	1	1	NUM
fumecheng-10743	82	14	(	(	PUNCT
fumecheng-10743	82	15	(	(	PUNCT
fumecheng-10743	82	16	1	1	NUM
fumecheng-10743	82	17	)	)	PUNCT
fumecheng-10743	82	18	(	(	PUNCT
fumecheng-10743	82	19	)	)	PUNCT
fumecheng-10743	82	20	(	(	PUNCT
fumecheng-10743	82	21	)	)	PUNCT
fumecheng-10743	82	22	)	)	PUNCT
fumecheng-10743	83	1	(	(	PUNCT
fumecheng-10743	83	2	(	(	PUNCT
fumecheng-10743	83	3	1	1	X
fumecheng-10743	83	4	)	)	PUNCT
fumecheng-10743	83	5	(	(	PUNCT
fumecheng-10743	83	6	)	)	PUNCT
fumecheng-10743	83	7	(	(	PUNCT
fumecheng-10743	83	8	)	)	PUNCT
fumecheng-10743	83	9	)	)	PUNCT
fumecheng-10743	83	10	2	2	NUM
fumecheng-10743	83	11	2	2	NUM
fumecheng-10743	83	12	(	(	PUNCT
fumecheng-10743	83	13	)	)	PUNCT
fumecheng-10743	83	14	(	(	PUNCT
fumecheng-10743	83	15	)	)	PUNCT
fumecheng-10743	83	16	(	(	PUNCT
fumecheng-10743	83	17	)	)	PUNCT
fumecheng-10743	83	18	(	(	PUNCT
fumecheng-10743	83	19	)	)	PUNCT
fumecheng-10743	83	20	1	1	NUM
fumecheng-10743	83	21	(	(	PUNCT
fumecheng-10743	83	22	1	1	NUM
fumecheng-10743	83	23	)	)	PUNCT
fumecheng-10743	83	24	(	(	PUNCT
fumecheng-10743	83	25	)	)	PUNCT
fumecheng-10743	83	26	2	2	NUM
fumecheng-10743	83	27	(	(	PUNCT
fumecheng-10743	83	28	)	)	PUNCT
fumecheng-10743	83	29	(	(	PUNCT
fumecheng-10743	83	30	)	)	PUNCT
fumecheng-10743	83	31	1	1	NUM
fumecheng-10743	83	32	(	(	PUNCT
fumecheng-10743	83	33	1	1	NUM
fumecheng-10743	83	34	2	2	NUM
fumecheng-10743	83	35	r	r	NOUN
fumecheng-10743	83	36	r	r	NOUN
fumecheng-10743	83	37	r	r	NOUN
fumecheng-10743	83	38	r	r	NOUN
fumecheng-10743	83	39	b	b	NOUN
fumecheng-10743	83	40	k	k	X
fumecheng-10743	83	41	p	p	X
fumecheng-10743	83	42	kb	kb	PROPN
fumecheng-10743	83	43	p	p	PROPN
fumecheng-10743	83	44	b	b	PROPN
fumecheng-10743	83	45	b	b	PROPN
fumecheng-10743	83	46	k	k	X
fumecheng-10743	83	47	p	p	X
fumecheng-10743	83	48	kb	kb	PROPN
fumecheng-10743	83	49	p	p	PROPN
fumecheng-10743	83	50	b	b	PROPN
fumecheng-10743	83	51	b	b	PROPN
fumecheng-10743	83	52	k	k	X
fumecheng-10743	83	53	p	p	X
fumecheng-10743	83	54	kb	kb	PROPN
fumecheng-10743	83	55	p	p	PROPN
fumecheng-10743	83	56	b	b	PROPN
fumecheng-10743	83	57	b	b	PROPN
fumecheng-10743	83	58	k	k	X
fumecheng-10743	83	59	p	p	X
fumecheng-10743	83	60	kb	kb	PROPN
fumecheng-10743	83	61	p	p	PROPN
fumecheng-10743	83	62	b	b	PROPN
fumecheng-10743	83	63	p	p	X
fumecheng-10743	83	64	kb	kb	PROPN
fumecheng-10743	83	65	p	p	PROPN
fumecheng-10743	83	66	b	b	PROPN
fumecheng-10743	83	67	k	k	PROPN
fumecheng-10743	83	68	b	b	PROPN
fumecheng-10743	83	69	p	p	X
fumecheng-10743	83	70	b	b	PROPN
fumecheng-10743	83	71	p	p	X
fumecheng-10743	83	72	kb	kb	PROPN
fumecheng-10743	84	1	−	−	PROPN
fumecheng-10743	84	2	=	=	PUNCT
fumecheng-10743	85	1	−	−	PROPN
fumecheng-10743	85	2	−	−	PROPN
fumecheng-10743	86	1	+	+	CCONJ
fumecheng-10743	86	2	−	−	PROPN
fumecheng-10743	86	3	−	−	NUM
fumecheng-10743	86	4	−	−	PROPN
fumecheng-10743	87	1	+	+	CCONJ
fumecheng-10743	87	2	−	−	PROPN
fumecheng-10743	87	3	=	=	SYM
fumecheng-10743	87	4	−	−	PROPN
fumecheng-10743	88	1	+	+	CCONJ
fumecheng-10743	88	2	−	−	PROPN
fumecheng-10743	88	3	−	−	NUM
fumecheng-10743	88	4	−	−	PROPN
fumecheng-10743	89	1	+	+	CCONJ
fumecheng-10743	89	2	−	−	PROPN
fumecheng-10743	89	3	−	−	NUM
fumecheng-10743	89	4	−	−	NOUN
fumecheng-10743	90	1	−	−	PROPN
fumecheng-10743	90	2	=	=	SYM
fumecheng-10743	91	1	−	−	PROPN
fumecheng-10743	91	2	−	−	NOUN
fumecheng-10743	91	3	−	−	PROPN
fumecheng-10743	92	1	=	=	SYM
fumecheng-10743	93	1	−	−	PROPN
fumecheng-10743	93	2	ω	ω	PROPN
fumecheng-10743	93	3	ω	ω	PROPN
fumecheng-10743	93	4	ω	ω	PROPN
fumecheng-10743	93	5	ω	ω	PROPN
fumecheng-10743	93	6	ω	ω	PROPN
fumecheng-10743	93	7	ω	ω	PROPN
fumecheng-10743	93	8	ω	ω	PROPN
fumecheng-10743	93	9	ω	ω	PROPN
fumecheng-10743	93	10	ω	ω	PROPN
fumecheng-10743	93	11	ω	ω	PROPN
fumecheng-10743	93	12	ω	ω	PROPN
fumecheng-10743	93	13	ω	ω	PROPN
fumecheng-10743	93	14	ω	ω	PROPN
fumecheng-10743	93	15	ω	ω	PROPN
fumecheng-10743	93	16	ω	ω	NUM
fumecheng-10743	93	17	2	2	NUM
fumecheng-10743	93	18	2	2	NUM
fumecheng-10743	93	19	)	)	PUNCT
fumecheng-10743	93	20	k	k	PROPN
fumecheng-10743	93	21	b	b	PROPN
fumecheng-10743	93	22	(	(	PUNCT
fumecheng-10743	93	23	20	20	NUM
fumecheng-10743	93	24	)	)	PUNCT
fumecheng-10743	93	25	we	we	PRON
fumecheng-10743	93	26	recommend	recommend	VERB
fumecheng-10743	93	27	k=1/√2	k=1/√2	PROPN
fumecheng-10743	93	28	,	,	PUNCT
fumecheng-10743	93	29	the	the	DET
fumecheng-10743	93	30	simplified	simplified	ADJ
fumecheng-10743	93	31	hamiltonian	hamiltonian	NOUN
fumecheng-10743	93	32	-	-	PUNCT
fumecheng-10743	93	33	based	base	VERB
fumecheng-10743	93	34	frequency	frequency	NOUN
fumecheng-10743	93	35	formulation	formulation	NOUN
fumecheng-10743	93	36	is	be	AUX
fumecheng-10743	93	37	2	2	NUM
fumecheng-10743	93	38	2	2	NUM
fumecheng-10743	93	39	4	4	NUM
fumecheng-10743	93	40	(	(	PUNCT
fumecheng-10743	93	41	(	(	PUNCT
fumecheng-10743	93	42	)	)	PUNCT
fumecheng-10743	93	43	(	(	PUNCT
fumecheng-10743	93	44	/	/	SYM
fumecheng-10743	93	45	2))p	2))p	NUM
fumecheng-10743	94	1	b	b	NOUN
fumecheng-10743	94	2	p	p	X
fumecheng-10743	94	3	b	b	PROPN
fumecheng-10743	94	4	b	b	NOUN
fumecheng-10743	94	5	−	−	PROPN
fumecheng-10743	94	6	=	=	SYM
fumecheng-10743	94	7	ω	ω	PROPN
fumecheng-10743	94	8	(	(	PUNCT
fumecheng-10743	94	9	21	21	NUM
fumecheng-10743	94	10	)	)	PUNCT
fumecheng-10743	94	11	it	it	PRON
fumecheng-10743	94	12	is	be	AUX
fumecheng-10743	94	13	astonishing	astonishing	ADJ
fumecheng-10743	94	14	that	that	SCONJ
fumecheng-10743	94	15	all	all	DET
fumecheng-10743	94	16	intermediate	intermediate	ADJ
fumecheng-10743	94	17	steps	step	NOUN
fumecheng-10743	94	18	involved	involve	VERB
fumecheng-10743	94	19	in	in	ADP
fumecheng-10743	94	20	the	the	DET
fumecheng-10743	94	21	original	original	ADJ
fumecheng-10743	94	22	hamiltonian	hamiltonian	NOUN
fumecheng-10743	94	23	-	-	PUNCT
fumecheng-10743	94	24	based	base	VERB
fumecheng-10743	94	25	frequency	frequency	NOUN
fumecheng-10743	94	26	formulation	formulation	NOUN
fumecheng-10743	94	27	have	have	AUX
fumecheng-10743	94	28	disappeared	disappear	VERB
fumecheng-10743	94	29	,	,	PUNCT
fumecheng-10743	94	30	making	make	VERB
fumecheng-10743	94	31	the	the	DET
fumecheng-10743	94	32	two	two	NUM
fumecheng-10743	94	33	modified	modify	VERB
fumecheng-10743	94	34	formulations	formulation	NOUN
fumecheng-10743	94	35	unprecedentedly	unprecedentedly	ADV
fumecheng-10743	94	36	simple	simple	ADJ
fumecheng-10743	94	37	.	.	PUNCT
fumecheng-10743	95	1	4	4	X
fumecheng-10743	95	2	.	.	X
fumecheng-10743	95	3	examples	example	NOUN
fumecheng-10743	95	4	consider	consider	VERB
fumecheng-10743	95	5	the	the	DET
fumecheng-10743	95	6	following	follow	VERB
fumecheng-10743	95	7	well	well	ADV
fumecheng-10743	95	8	-	-	PUNCT
fumecheng-10743	95	9	known	know	VERB
fumecheng-10743	95	10	duffing	duffing	NOUN
fumecheng-10743	95	11	equation	equation	NOUN
fumecheng-10743	95	12	[	[	X
fumecheng-10743	95	13	25	25	NUM
fumecheng-10743	95	14	]	]	SYM
fumecheng-10743	95	15	3	3	NUM
fumecheng-10743	95	16	0	0	NUM
fumecheng-10743	95	17	,	,	PUNCT
fumecheng-10743	95	18	(	(	PUNCT
fumecheng-10743	95	19	0	0	NUM
fumecheng-10743	95	20	)	)	PUNCT
fumecheng-10743	95	21	0	0	NUM
fumecheng-10743	96	1	(	(	PUNCT
fumecheng-10743	96	2	0)w	0)w	PROPN
fumecheng-10743	96	3	w	w	PROPN
fumecheng-10743	96	4	w	w	PROPN
fumecheng-10743	96	5	w	w	PROPN
fumecheng-10743	96	6	w	w	PROPN
fumecheng-10743	96	7	b	b	NOUN
fumecheng-10743	96	8	+	+	NOUN
fumecheng-10743	96	9	+	+	X
fumecheng-10743	97	1	=	=	SYM
fumecheng-10743	97	2	=	=	SYM
fumecheng-10743	97	3	=	=	SYM
fumecheng-10743	97	4	ε	ε	PROPN
fumecheng-10743	97	5	(	(	PUNCT
fumecheng-10743	97	6	22	22	NUM
fumecheng-10743	97	7	)	)	PUNCT
fumecheng-10743	97	8	for	for	ADP
fumecheng-10743	97	9	this	this	DET
fumecheng-10743	97	10	example	example	NOUN
fumecheng-10743	97	11	,	,	PUNCT
fumecheng-10743	97	12	we	we	PRON
fumecheng-10743	97	13	have	have	VERB
fumecheng-10743	97	14	2	2	NUM
fumecheng-10743	97	15	41	41	NUM
fumecheng-10743	97	16	1	1	NUM
fumecheng-10743	97	17	(	(	PUNCT
fumecheng-10743	97	18	)	)	PUNCT
fumecheng-10743	97	19	2	2	NUM
fumecheng-10743	97	20	4	4	NUM
fumecheng-10743	97	21	p	p	NOUN
fumecheng-10743	97	22	w	w	PROPN
fumecheng-10743	97	23	w	w	PROPN
fumecheng-10743	97	24	w=	w=	NOUN
fumecheng-10743	97	25	+	+	CCONJ
fumecheng-10743	97	26	ε	ε	PROPN
fumecheng-10743	97	27	(	(	PUNCT
fumecheng-10743	97	28	23	23	NUM
fumecheng-10743	97	29	)	)	PUNCT
fumecheng-10743	97	30	in	in	ADP
fumecheng-10743	97	31	order	order	NOUN
fumecheng-10743	97	32	to	to	PART
fumecheng-10743	97	33	compare	compare	VERB
fumecheng-10743	97	34	the	the	DET
fumecheng-10743	97	35	two	two	NUM
fumecheng-10743	97	36	modifications	modification	NOUN
fumecheng-10743	97	37	with	with	ADP
fumecheng-10743	97	38	the	the	DET
fumecheng-10743	97	39	original	original	ADJ
fumecheng-10743	97	40	one	one	NOUN
fumecheng-10743	97	41	,	,	PUNCT
fumecheng-10743	97	42	we	we	PRON
fumecheng-10743	97	43	illustrate	illustrate	VERB
fumecheng-10743	97	44	first	first	ADV
fumecheng-10743	97	45	the	the	DET
fumecheng-10743	97	46	solving	solving	NOUN
fumecheng-10743	97	47	process	process	NOUN
fumecheng-10743	97	48	of	of	ADP
fumecheng-10743	97	49	the	the	DET
fumecheng-10743	97	50	original	original	ADJ
fumecheng-10743	97	51	hamiltonian	hamiltonian	NOUN
fumecheng-10743	97	52	-	-	PUNCT
fumecheng-10743	97	53	based	base	VERB
fumecheng-10743	97	54	frequency	frequency	NOUN
fumecheng-10743	97	55	formulation	formulation	NOUN
fumecheng-10743	97	56	,	,	PUNCT
fumecheng-10743	97	57	which	which	PRON
fumecheng-10743	97	58	begins	begin	VERB
fumecheng-10743	97	59	with	with	ADP
fumecheng-10743	97	60	two	two	NUM
fumecheng-10743	97	61	arbitrary	arbitrary	ADJ
fumecheng-10743	97	62	choices	choice	NOUN
fumecheng-10743	97	63	ω1	ω1	PROPN
fumecheng-10743	97	64	and	and	CCONJ
fumecheng-10743	97	65	ω2	ω2	ADJ
fumecheng-10743	97	66	,	,	PUNCT
fumecheng-10743	97	67	and	and	CCONJ
fumecheng-10743	97	68	the	the	DET
fumecheng-10743	97	69	following	follow	VERB
fumecheng-10743	97	70	residual	residual	ADJ
fumecheng-10743	97	71	equations	equation	NOUN
fumecheng-10743	97	72	are	be	AUX
fumecheng-10743	97	73	obtained	obtain	VERB
fumecheng-10743	97	74	:	:	PUNCT
fumecheng-10743	97	75	450	450	NUM
fumecheng-10743	97	76	h.	h.	PROPN
fumecheng-10743	97	77	ma	ma	PROPN
fumecheng-10743	97	78	2	2	NUM
fumecheng-10743	97	79	2	2	NUM
fumecheng-10743	97	80	2	2	NUM
fumecheng-10743	97	81	1	1	NUM
fumecheng-10743	97	82	1	1	NUM
fumecheng-10743	97	83	1	1	NUM
fumecheng-10743	97	84	1	1	NUM
fumecheng-10743	97	85	2	2	NUM
fumecheng-10743	97	86	2	2	NUM
fumecheng-10743	97	87	2	2	NUM
fumecheng-10743	97	88	2	2	NUM
fumecheng-10743	97	89	2	2	NUM
fumecheng-10743	97	90	4	4	NUM
fumecheng-10743	97	91	2	2	NUM
fumecheng-10743	97	92	41	41	NUM
fumecheng-10743	97	93	1	1	NUM
fumecheng-10743	97	94	1	1	NUM
fumecheng-10743	97	95	1	1	NUM
fumecheng-10743	97	96	1	1	NUM
fumecheng-10743	97	97	(	(	PUNCT
fumecheng-10743	97	98	)	)	PUNCT
fumecheng-10743	97	99	sin	sin	NOUN
fumecheng-10743	97	100	(	(	PUNCT
fumecheng-10743	97	101	cos	cos	PROPN
fumecheng-10743	97	102	)	)	PUNCT
fumecheng-10743	97	103	(	(	PUNCT
fumecheng-10743	97	104	)	)	PUNCT
fumecheng-10743	97	105	2	2	NUM
fumecheng-10743	97	106	2	2	NUM
fumecheng-10743	97	107	(	(	PUNCT
fumecheng-10743	97	108	)	)	PUNCT
fumecheng-10743	97	109	cos	cos	PROPN
fumecheng-10743	97	110	cos	cos	PROPN
fumecheng-10743	97	111	2	2	NUM
fumecheng-10743	97	112	2	2	NUM
fumecheng-10743	97	113	4	4	NUM
fumecheng-10743	97	114	r	r	NOUN
fumecheng-10743	97	115	t	t	NOUN
fumecheng-10743	97	116	b	b	NOUN
fumecheng-10743	97	117	t	t	PROPN
fumecheng-10743	97	118	p	p	X
fumecheng-10743	97	119	b	b	PROPN
fumecheng-10743	97	120	t	t	PROPN
fumecheng-10743	97	121	p	p	PROPN
fumecheng-10743	97	122	b	b	PROPN
fumecheng-10743	97	123	b	b	PROPN
fumecheng-10743	97	124	p	p	PROPN
fumecheng-10743	97	125	b	b	PROPN
fumecheng-10743	97	126	b	b	PROPN
fumecheng-10743	97	127	b	b	PROPN
fumecheng-10743	97	128	b	b	PROPN
fumecheng-10743	97	129	t	t	NOUN
fumecheng-10743	97	130	t	t	NOUN
fumecheng-10743	97	131	=	=	PUNCT
fumecheng-10743	98	1	+	+	CCONJ
fumecheng-10743	98	2	−	−	NOUN
fumecheng-10743	99	1	−	−	NOUN
fumecheng-10743	99	2	−	−	PROPN
fumecheng-10743	100	1	=	=	SYM
fumecheng-10743	101	1	+	+	PUNCT
fumecheng-10743	102	1	+	+	NUM
fumecheng-10743	102	2	ω	ω	PROPN
fumecheng-10743	102	3	ω	ω	PROPN
fumecheng-10743	102	4	ω	ω	PROPN
fumecheng-10743	102	5	ω	ω	PROPN
fumecheng-10743	102	6	ω	ω	PROPN
fumecheng-10743	102	7	ε	ε	PROPN
fumecheng-10743	102	8	ω	ω	PROPN
fumecheng-10743	102	9	ω	ω	PROPN
fumecheng-10743	102	10	(	(	PUNCT
fumecheng-10743	102	11	24	24	NUM
fumecheng-10743	102	12	)	)	PUNCT
fumecheng-10743	102	13	2	2	NUM
fumecheng-10743	102	14	2	2	NUM
fumecheng-10743	102	15	2	2	NUM
fumecheng-10743	102	16	2	2	NUM
fumecheng-10743	102	17	2	2	NUM
fumecheng-10743	102	18	2	2	NUM
fumecheng-10743	102	19	2	2	NUM
fumecheng-10743	102	20	2	2	NUM
fumecheng-10743	102	21	2	2	NUM
fumecheng-10743	102	22	2	2	NUM
fumecheng-10743	102	23	2	2	NUM
fumecheng-10743	102	24	2	2	NUM
fumecheng-10743	102	25	4	4	NUM
fumecheng-10743	102	26	2	2	NUM
fumecheng-10743	102	27	42	42	NUM
fumecheng-10743	102	28	2	2	NUM
fumecheng-10743	102	29	2	2	NUM
fumecheng-10743	102	30	2	2	NUM
fumecheng-10743	102	31	1	1	NUM
fumecheng-10743	102	32	(	(	PUNCT
fumecheng-10743	102	33	)	)	PUNCT
fumecheng-10743	102	34	sin	sin	NOUN
fumecheng-10743	102	35	(	(	PUNCT
fumecheng-10743	102	36	cos	cos	PROPN
fumecheng-10743	102	37	)	)	PUNCT
fumecheng-10743	102	38	(	(	PUNCT
fumecheng-10743	102	39	)	)	PUNCT
fumecheng-10743	102	40	2	2	NUM
fumecheng-10743	102	41	2	2	NUM
fumecheng-10743	102	42	(	(	PUNCT
fumecheng-10743	102	43	)	)	PUNCT
fumecheng-10743	102	44	cos	cos	PROPN
fumecheng-10743	102	45	cos	cos	PROPN
fumecheng-10743	102	46	2	2	NUM
fumecheng-10743	102	47	2	2	NUM
fumecheng-10743	102	48	4	4	NUM
fumecheng-10743	102	49	r	r	NOUN
fumecheng-10743	102	50	t	t	NOUN
fumecheng-10743	102	51	b	b	NOUN
fumecheng-10743	102	52	t	t	PROPN
fumecheng-10743	102	53	p	p	X
fumecheng-10743	102	54	b	b	PROPN
fumecheng-10743	102	55	t	t	PROPN
fumecheng-10743	102	56	p	p	PROPN
fumecheng-10743	102	57	b	b	PROPN
fumecheng-10743	102	58	b	b	PROPN
fumecheng-10743	102	59	p	p	PROPN
fumecheng-10743	102	60	b	b	PROPN
fumecheng-10743	102	61	b	b	PROPN
fumecheng-10743	102	62	b	b	PROPN
fumecheng-10743	102	63	b	b	PROPN
fumecheng-10743	102	64	t	t	NOUN
fumecheng-10743	102	65	t	t	NOUN
fumecheng-10743	102	66	=	=	PUNCT
fumecheng-10743	103	1	+	+	CCONJ
fumecheng-10743	103	2	−	−	NOUN
fumecheng-10743	104	1	−	−	NOUN
fumecheng-10743	104	2	−	−	PROPN
fumecheng-10743	105	1	=	=	SYM
fumecheng-10743	106	1	+	+	PUNCT
fumecheng-10743	107	1	+	+	NUM
fumecheng-10743	107	2	ω	ω	PROPN
fumecheng-10743	107	3	ω	ω	PROPN
fumecheng-10743	107	4	ω	ω	PROPN
fumecheng-10743	107	5	ω	ω	PROPN
fumecheng-10743	107	6	ω	ω	PROPN
fumecheng-10743	107	7	ε	ε	PROPN
fumecheng-10743	107	8	ω	ω	PROPN
fumecheng-10743	107	9	ω	ω	PROPN
fumecheng-10743	107	10	(	(	PUNCT
fumecheng-10743	107	11	25	25	NUM
fumecheng-10743	107	12	)	)	PUNCT
fumecheng-10743	107	13	the	the	DET
fumecheng-10743	107	14	residual	residual	ADJ
fumecheng-10743	107	15	integrals	integral	NOUN
fumecheng-10743	107	16	are	be	AUX
fumecheng-10743	107	17	:	:	PUNCT
fumecheng-10743	107	18	1	1	NUM
fumecheng-10743	107	19	2	2	NUM
fumecheng-10743	107	20	4	4	NUM
fumecheng-10743	107	21	2	2	NUM
fumecheng-10743	107	22	/	/	SYM
fumecheng-10743	107	23	4	4	NUM
fumecheng-10743	107	24	2	2	NUM
fumecheng-10743	107	25	1	1	NUM
fumecheng-10743	107	26	1	1	NUM
fumecheng-10743	107	27	1	1	NUM
fumecheng-10743	107	28	1	1	NUM
fumecheng-10743	107	29	0	0	NUM
fumecheng-10743	107	30	1	1	NUM
fumecheng-10743	107	31	4	4	NUM
fumecheng-10743	107	32	4	4	NUM
fumecheng-10743	107	33	10	10	NUM
fumecheng-10743	107	34	30	30	NUM
fumecheng-10743	107	35	(	(	PUNCT
fumecheng-10743	107	36	)	)	PUNCT
fumecheng-10743	107	37	cos	cos	ADP
fumecheng-10743	107	38	3	3	NUM
fumecheng-10743	107	39	15	15	NUM
fumecheng-10743	107	40	t	t	PROPN
fumecheng-10743	107	41	b	b	PROPN
fumecheng-10743	107	42	b	b	PROPN
fumecheng-10743	107	43	b	b	PROPN
fumecheng-10743	107	44	p	p	X
fumecheng-10743	107	45	b	b	NOUN
fumecheng-10743	107	46	r	r	NOUN
fumecheng-10743	107	47	r	r	NOUN
fumecheng-10743	107	48	tdt	tdt	PROPN
fumecheng-10743	107	49	t	t	PROPN
fumecheng-10743	107	50			PROPN
fumecheng-10743	107	51			PROPN
fumecheng-10743	107	52	+	+	CCONJ
fumecheng-10743	107	53	−	−	NOUN
fumecheng-10743	107	54	=	=	SYM
fumecheng-10743	108	1	=	=	PUNCT
fumecheng-10743	108	2	+	+	ADJ
fumecheng-10743	108	3			X
fumecheng-10743	108	4	ε	ε	PROPN
fumecheng-10743	108	5	ω	ω	PROPN
fumecheng-10743	108	6	ω	ω	PROPN
fumecheng-10743	108	7	(	(	PUNCT
fumecheng-10743	108	8	26	26	NUM
fumecheng-10743	108	9	)	)	PUNCT
fumecheng-10743	108	10	2	2	NUM
fumecheng-10743	108	11	4	4	NUM
fumecheng-10743	108	12	4	4	NUM
fumecheng-10743	108	13	2	2	NUM
fumecheng-10743	108	14	/	/	SYM
fumecheng-10743	108	15	4	4	NUM
fumecheng-10743	108	16	2	2	NUM
fumecheng-10743	108	17	2	2	NUM
fumecheng-10743	108	18	2	2	NUM
fumecheng-10743	108	19	2	2	NUM
fumecheng-10743	108	20	2	2	NUM
fumecheng-10743	108	21	0	0	NUM
fumecheng-10743	108	22	2	2	NUM
fumecheng-10743	108	23	4	4	NUM
fumecheng-10743	108	24	4	4	NUM
fumecheng-10743	108	25	10	10	NUM
fumecheng-10743	108	26	30	30	NUM
fumecheng-10743	108	27	(	(	PUNCT
fumecheng-10743	108	28	)	)	PUNCT
fumecheng-10743	108	29	cos	cos	ADP
fumecheng-10743	108	30	3	3	NUM
fumecheng-10743	108	31	15	15	NUM
fumecheng-10743	108	32	t	t	PROPN
fumecheng-10743	108	33	b	b	PROPN
fumecheng-10743	108	34	b	b	PROPN
fumecheng-10743	108	35	b	b	PROPN
fumecheng-10743	108	36	p	p	X
fumecheng-10743	108	37	b	b	NOUN
fumecheng-10743	108	38	r	r	NOUN
fumecheng-10743	108	39	r	r	NOUN
fumecheng-10743	108	40	tdt	tdt	PROPN
fumecheng-10743	108	41	t	t	PROPN
fumecheng-10743	108	42			PROPN
fumecheng-10743	108	43			PROPN
fumecheng-10743	109	1	+	+	CCONJ
fumecheng-10743	109	2	−	−	NOUN
fumecheng-10743	109	3	=	=	SYM
fumecheng-10743	110	1	=	=	PUNCT
fumecheng-10743	110	2	+	+	ADJ
fumecheng-10743	110	3			X
fumecheng-10743	110	4	ε	ε	PROPN
fumecheng-10743	110	5	ω	ω	PROPN
fumecheng-10743	110	6	ω	ω	PROPN
fumecheng-10743	110	7	(	(	PUNCT
fumecheng-10743	110	8	27	27	NUM
fumecheng-10743	110	9	)	)	PUNCT
fumecheng-10743	110	10	the	the	DET
fumecheng-10743	110	11	hamiltonian	hamiltonian	NOUN
fumecheng-10743	110	12	-	-	PUNCT
fumecheng-10743	110	13	based	base	VERB
fumecheng-10743	110	14	frequency	frequency	NOUN
fumecheng-10743	110	15	formulation	formulation	NOUN
fumecheng-10743	110	16	leads	lead	VERB
fumecheng-10743	110	17	to	to	ADP
fumecheng-10743	110	18	the	the	DET
fumecheng-10743	110	19	result	result	NOUN
fumecheng-10743	110	20	2	2	NUM
fumecheng-10743	110	21	2	2	NUM
fumecheng-10743	110	22	2	2	NUM
fumecheng-10743	110	23	21	21	NUM
fumecheng-10743	110	24	2	2	NUM
fumecheng-10743	110	25	2	2	NUM
fumecheng-10743	110	26	1	1	NUM
fumecheng-10743	110	27	1	1	NUM
fumecheng-10743	110	28	2	2	NUM
fumecheng-10743	110	29	7	7	NUM
fumecheng-10743	110	30	1	1	NUM
fumecheng-10743	110	31	10	10	NUM
fumecheng-10743	110	32	r	r	NOUN
fumecheng-10743	110	33	r	r	NOUN
fumecheng-10743	110	34	b	b	NOUN
fumecheng-10743	110	35	r	r	NOUN
fumecheng-10743	110	36	r	r	NOUN
fumecheng-10743	110	37	=	=	PUNCT
fumecheng-10743	110	38	=	=	SYM
fumecheng-10743	111	1	−	−	PROPN
fumecheng-10743	112	1	+	+	CCONJ
fumecheng-10743	112	2	−	−	PROPN
fumecheng-10743	112	3	ω	ω	NUM
fumecheng-10743	112	4	ω	ω	PROPN
fumecheng-10743	112	5	ω	ω	PROPN
fumecheng-10743	112	6	ε	ε	PROPN
fumecheng-10743	112	7	(	(	PUNCT
fumecheng-10743	112	8	28	28	NUM
fumecheng-10743	112	9	)	)	PUNCT
fumecheng-10743	112	10	now	now	ADV
fumecheng-10743	112	11	the	the	DET
fumecheng-10743	112	12	modified	modified	ADJ
fumecheng-10743	112	13	formulation	formulation	NOUN
fumecheng-10743	112	14	of	of	ADP
fumecheng-10743	112	15	eq	eq	PROPN
fumecheng-10743	112	16	.	.	PUNCT
fumecheng-10743	112	17	(	(	PUNCT
fumecheng-10743	112	18	16	16	NUM
fumecheng-10743	112	19	)	)	PUNCT
fumecheng-10743	112	20	gives	give	VERB
fumecheng-10743	112	21	a	a	DET
fumecheng-10743	112	22	one	one	NUM
fumecheng-10743	112	23	-	-	PUNCT
fumecheng-10743	112	24	step	step	NOUN
fumecheng-10743	112	25	solving	solving	NOUN
fumecheng-10743	112	26	process	process	NOUN
fumecheng-10743	112	27	:	:	PUNCT
fumecheng-10743	112	28	1	1	NUM
fumecheng-10743	112	29	2	2	NUM
fumecheng-10743	112	30	2	2	NUM
fumecheng-10743	112	31	0	0	NUM
fumecheng-10743	112	32	2	2	NUM
fumecheng-10743	112	33	1	1	NUM
fumecheng-10743	112	34	2	2	NUM
fumecheng-10743	112	35	4	4	NUM
fumecheng-10743	112	36	2	2	NUM
fumecheng-10743	112	37	2	2	NUM
fumecheng-10743	112	38	4	4	NUM
fumecheng-10743	112	39	4	4	NUM
fumecheng-10743	112	40	2	2	NUM
fumecheng-10743	112	41	0	0	NUM
fumecheng-10743	112	42	2	2	NUM
fumecheng-10743	112	43	2	2	NUM
fumecheng-10743	112	44	4	4	NUM
fumecheng-10743	112	45	2	2	NUM
fumecheng-10743	112	46	4	4	NUM
fumecheng-10743	112	47	2	2	NUM
fumecheng-10743	112	48	2	2	NUM
fumecheng-10743	112	49	4	4	NUM
fumecheng-10743	112	50	2	2	NUM
fumecheng-10743	112	51	2	2	NUM
fumecheng-10743	112	52	6	6	NUM
fumecheng-10743	112	53	(	(	PUNCT
fumecheng-10743	112	54	)	)	PUNCT
fumecheng-10743	112	55	6	6	NUM
fumecheng-10743	112	56	(	(	PUNCT
fumecheng-10743	112	57	1	1	NUM
fumecheng-10743	112	58	)	)	SYM
fumecheng-10743	112	59	1	1	NUM
fumecheng-10743	112	60	1	1	NUM
fumecheng-10743	112	61	1	1	NUM
fumecheng-10743	112	62	1	1	NUM
fumecheng-10743	112	63	6	6	NUM
fumecheng-10743	112	64	6	6	NUM
fumecheng-10743	112	65	(	(	PUNCT
fumecheng-10743	112	66	1	1	NUM
fumecheng-10743	112	67	)	)	PUNCT
fumecheng-10743	112	68	(	(	PUNCT
fumecheng-10743	112	69	2	2	NUM
fumecheng-10743	112	70	1	1	NUM
fumecheng-10743	112	71	)	)	PUNCT
fumecheng-10743	112	72	2	2	NUM
fumecheng-10743	112	73	4	4	NUM
fumecheng-10743	112	74	2	2	NUM
fumecheng-10743	112	75	4	4	NUM
fumecheng-10743	112	76	3	3	NUM
fumecheng-10743	112	77	4	4	NUM
fumecheng-10743	112	78	3	3	NUM
fumecheng-10743	112	79	2	2	NUM
fumecheng-10743	112	80	2	2	NUM
fumecheng-10743	112	81	5	5	NUM
fumecheng-10743	112	82	7	7	NUM
fumecheng-10743	112	83	10	10	NUM
fumecheng-10743	112	84	7	7	NUM
fumecheng-10743	112	85	1	1	NUM
fumecheng-10743	112	86	10	10	NUM
fumecheng-10743	112	87	p	p	NOUN
fumecheng-10743	112	88	b	b	PROPN
fumecheng-10743	112	89	p	p	X
fumecheng-10743	112	90	b	b	PROPN
fumecheng-10743	112	91	x	x	X
fumecheng-10743	112	92	dx	dx	PROPN
fumecheng-10743	112	93	b	b	PROPN
fumecheng-10743	112	94	b	b	PROPN
fumecheng-10743	112	95	b	b	PROPN
fumecheng-10743	112	96	b	b	PROPN
fumecheng-10743	112	97	x	x	SYM
fumecheng-10743	112	98	b	b	PROPN
fumecheng-10743	112	99	x	x	SYM
fumecheng-10743	112	100	x	x	PROPN
fumecheng-10743	112	101	dx	dx	PROPN
fumecheng-10743	112	102	b	b	PROPN
fumecheng-10743	112	103	b	b	PROPN
fumecheng-10743	112	104	b	b	PROPN
fumecheng-10743	112	105	b	b	PROPN
fumecheng-10743	112	106	b	b	PROPN
fumecheng-10743	112	107	b	b	PROPN
fumecheng-10743	112	108	b	b	PROPN
fumecheng-10743	112	109	b	b	PROPN
fumecheng-10743	112	110	b	b	PROPN
fumecheng-10743	112	111	b	b	NOUN
fumecheng-10743	112	112	−	−	NOUN
fumecheng-10743	113	1	−	−	PROPN
fumecheng-10743	114	1	=	=	SYM
fumecheng-10743	115	1	+	+	NUM
fumecheng-10743	115	2	−	−	PROPN
fumecheng-10743	116	1	−	−	PROPN
fumecheng-10743	117	1	+	+	CCONJ
fumecheng-10743	117	2	−	−	PROPN
fumecheng-10743	118	1	+	+	CCONJ
fumecheng-10743	118	2	=	=	SYM
fumecheng-10743	119	1	+	+	NUM
fumecheng-10743	119	2	−	−	PROPN
fumecheng-10743	120	1	+	+	CCONJ
fumecheng-10743	120	2	=	=	SYM
fumecheng-10743	121	1	+	+	NUM
fumecheng-10743	121	2	=	=	SYM
fumecheng-10743	121	3	=	=	SYM
fumecheng-10743	122	1	+	+	NUM
fumecheng-10743	122	2			NOUN
fumecheng-10743	122	3			PROPN
fumecheng-10743	122	4			NOUN
fumecheng-10743	122	5			PROPN
fumecheng-10743	122	6			PROPN
fumecheng-10743	122	7			PROPN
fumecheng-10743	123	1			PROPN
fumecheng-10743	123	2			PROPN
fumecheng-10743	124	1			ADJ
fumecheng-10743	124	2			PROPN
fumecheng-10743	124	3			PROPN
fumecheng-10743	124	4			NOUN
fumecheng-10743	125	1			NOUN
fumecheng-10743	125	2			NOUN
fumecheng-10743	125	3			NOUN
fumecheng-10743	125	4			PROPN
fumecheng-10743	125	5			PROPN
fumecheng-10743	126	1			PROPN
fumecheng-10743	127	1			PROPN
fumecheng-10743	127	2			PROPN
fumecheng-10743	128	1			ADJ
fumecheng-10743	128	2			PROPN
fumecheng-10743	128	3			PROPN
fumecheng-10743	128	4			NOUN
fumecheng-10743	128	5			PUNCT
fumecheng-10743	128	6			PROPN
fumecheng-10743	128	7	ω	ω	X
fumecheng-10743	128	8	ε	ε	PROPN
fumecheng-10743	128	9	ε	ε	PROPN
fumecheng-10743	128	10	ε	ε	PROPN
fumecheng-10743	128	11	ε	ε	PROPN
fumecheng-10743	128	12	ε	ε	PROPN
fumecheng-10743	128	13	ε	ε	PROPN
fumecheng-10743	128	14	(	(	PUNCT
fumecheng-10743	128	15	29	29	NUM
fumecheng-10743	128	16	)	)	PUNCT
fumecheng-10743	128	17	which	which	PRON
fumecheng-10743	128	18	is	be	AUX
fumecheng-10743	128	19	the	the	DET
fumecheng-10743	128	20	same	same	ADJ
fumecheng-10743	128	21	as	as	ADP
fumecheng-10743	128	22	eq	eq	ADP
fumecheng-10743	128	23	.	.	PUNCT
fumecheng-10743	129	1	(	(	PUNCT
fumecheng-10743	129	2	28	28	NUM
fumecheng-10743	129	3	)	)	PUNCT
fumecheng-10743	129	4	.	.	PUNCT
fumecheng-10743	130	1	simplified	simplify	VERB
fumecheng-10743	130	2	hamiltonian	hamiltonian	ADJ
fumecheng-10743	130	3	-	-	PUNCT
fumecheng-10743	130	4	based	base	VERB
fumecheng-10743	130	5	frequency	frequency	NOUN
fumecheng-10743	130	6	-	-	PUNCT
fumecheng-10743	130	7	amplitude	amplitude	NOUN
fumecheng-10743	130	8	formulation	formulation	NOUN
fumecheng-10743	130	9	for	for	ADP
fumecheng-10743	130	10	nonlinear	nonlinear	ADJ
fumecheng-10743	130	11	vibration	vibration	NOUN
fumecheng-10743	130	12	systems	system	NOUN
fumecheng-10743	130	13	451	451	NUM
fumecheng-10743	130	14	the	the	DET
fumecheng-10743	130	15	modified	modify	VERB
fumecheng-10743	130	16	formulation	formulation	NOUN
fumecheng-10743	130	17	of	of	ADP
fumecheng-10743	130	18	eq	eq	PROPN
fumecheng-10743	130	19	.	.	PUNCT
fumecheng-10743	131	1	(	(	PUNCT
fumecheng-10743	131	2	21	21	NUM
fumecheng-10743	131	3	)	)	PUNCT
fumecheng-10743	131	4	is	be	AUX
fumecheng-10743	131	5	also	also	ADV
fumecheng-10743	131	6	simple	simple	ADJ
fumecheng-10743	131	7	,	,	PUNCT
fumecheng-10743	131	8	which	which	PRON
fumecheng-10743	131	9	leads	lead	VERB
fumecheng-10743	131	10	to	to	ADP
fumecheng-10743	131	11	the	the	DET
fumecheng-10743	131	12	following	follow	VERB
fumecheng-10743	131	13	result	result	NOUN
fumecheng-10743	131	14	2	2	NUM
fumecheng-10743	131	15	2	2	NUM
fumecheng-10743	131	16	2	2	NUM
fumecheng-10743	131	17	4	4	NUM
fumecheng-10743	131	18	2	2	NUM
fumecheng-10743	131	19	4	4	NUM
fumecheng-10743	131	20	2	2	NUM
fumecheng-10743	131	21	2	2	NUM
fumecheng-10743	131	22	4	4	NUM
fumecheng-10743	131	23	2	2	NUM
fumecheng-10743	131	24	2	2	NUM
fumecheng-10743	131	25	4	4	NUM
fumecheng-10743	131	26	(	(	PUNCT
fumecheng-10743	131	27	(	(	PUNCT
fumecheng-10743	131	28	)	)	PUNCT
fumecheng-10743	131	29	(	(	PUNCT
fumecheng-10743	131	30	/	/	SYM
fumecheng-10743	131	31	2	2	NUM
fumecheng-10743	131	32	)	)	PUNCT
fumecheng-10743	131	33	)	)	PUNCT
fumecheng-10743	132	1	1	1	NUM
fumecheng-10743	132	2	1	1	NUM
fumecheng-10743	132	3	1	1	NUM
fumecheng-10743	132	4	1	1	NUM
fumecheng-10743	132	5	4	4	NUM
fumecheng-10743	132	6	2	2	NUM
fumecheng-10743	132	7	4	4	NUM
fumecheng-10743	132	8	4	4	NUM
fumecheng-10743	132	9	16	16	NUM
fumecheng-10743	132	10	3	3	NUM
fumecheng-10743	132	11	4	4	NUM
fumecheng-10743	132	12	3	3	NUM
fumecheng-10743	132	13	1	1	NUM
fumecheng-10743	132	14	4	4	NUM
fumecheng-10743	132	15	p	p	NOUN
fumecheng-10743	132	16	b	b	PROPN
fumecheng-10743	132	17	p	p	X
fumecheng-10743	132	18	b	b	PROPN
fumecheng-10743	132	19	b	b	PROPN
fumecheng-10743	132	20	b	b	PROPN
fumecheng-10743	132	21	b	b	PROPN
fumecheng-10743	132	22	b	b	PROPN
fumecheng-10743	132	23	b	b	PROPN
fumecheng-10743	132	24	b	b	PROPN
fumecheng-10743	132	25	b	b	PROPN
fumecheng-10743	132	26	b	b	PROPN
fumecheng-10743	132	27	b	b	PROPN
fumecheng-10743	132	28	b	b	PROPN
fumecheng-10743	132	29	−	−	NOUN
fumecheng-10743	132	30	=	=	NOUN
fumecheng-10743	132	31			NOUN
fumecheng-10743	132	32			NOUN
fumecheng-10743	132	33	+	+	CCONJ
fumecheng-10743	132	34	−	−	PROPN
fumecheng-10743	132	35	−	−	PROPN
fumecheng-10743	132	36			PROPN
fumecheng-10743	132	37			PROPN
fumecheng-10743	132	38			NOUN
fumecheng-10743	132	39	=	=	PUNCT
fumecheng-10743	133	1	+	+	PUNCT
fumecheng-10743	133	2	=	=	SYM
fumecheng-10743	133	3	=	=	SYM
fumecheng-10743	134	1	+	+	NUM
fumecheng-10743	134	2	ω	ω	NUM
fumecheng-10743	134	3	ε	ε	PROPN
fumecheng-10743	134	4	ε	ε	PROPN
fumecheng-10743	134	5	ε	ε	PROPN
fumecheng-10743	134	6	ε	ε	PROPN
fumecheng-10743	134	7	(	(	PUNCT
fumecheng-10743	134	8	30	30	NUM
fumecheng-10743	134	9	)	)	PUNCT
fumecheng-10743	134	10	this	this	DET
fumecheng-10743	134	11	result	result	NOUN
fumecheng-10743	134	12	is	be	AUX
fumecheng-10743	134	13	the	the	DET
fumecheng-10743	134	14	same	same	ADJ
fumecheng-10743	134	15	as	as	ADP
fumecheng-10743	134	16	those	those	PRON
fumecheng-10743	134	17	obtained	obtain	VERB
fumecheng-10743	134	18	by	by	ADP
fumecheng-10743	134	19	the	the	DET
fumecheng-10743	134	20	variational	variational	ADJ
fumecheng-10743	134	21	iteration	iteration	NOUN
fumecheng-10743	134	22	method	method	NOUN
fumecheng-10743	134	23	or	or	CCONJ
fumecheng-10743	134	24	the	the	DET
fumecheng-10743	134	25	homotopy	homotopy	NOUN
fumecheng-10743	134	26	perturbation	perturbation	NOUN
fumecheng-10743	134	27	method	method	NOUN
fumecheng-10743	134	28	[	[	X
fumecheng-10743	134	29	26	26	NUM
fumecheng-10743	134	30	]	]	PUNCT
fumecheng-10743	134	31	.	.	PUNCT
fumecheng-10743	135	1	consider	consider	VERB
fumecheng-10743	135	2	another	another	DET
fumecheng-10743	135	3	example	example	NOUN
fumecheng-10743	135	4	of	of	ADP
fumecheng-10743	135	5	the	the	DET
fumecheng-10743	135	6	cubic	cubic	ADJ
fumecheng-10743	135	7	-	-	PUNCT
fumecheng-10743	135	8	quintic	quintic	ADJ
fumecheng-10743	135	9	duffing	duffing	NOUN
fumecheng-10743	135	10	oscillator	oscillator	NOUN
fumecheng-10743	135	11	:	:	PUNCT
fumecheng-10743	135	12	3	3	NUM
fumecheng-10743	135	13	5	5	NUM
fumecheng-10743	135	14	0	0	NUM
fumecheng-10743	135	15	,	,	PUNCT
fumecheng-10743	135	16	(	(	PUNCT
fumecheng-10743	135	17	0	0	NUM
fumecheng-10743	135	18	)	)	PUNCT
fumecheng-10743	135	19	0	0	NUM
fumecheng-10743	136	1	(	(	PUNCT
fumecheng-10743	136	2	0)w	0)w	NOUN
fumecheng-10743	136	3	w	w	NOUN
fumecheng-10743	137	1	aw	aw	INTJ
fumecheng-10743	137	2	bw	bw	PROPN
fumecheng-10743	137	3	w	w	PROPN
fumecheng-10743	137	4	w	w	PROPN
fumecheng-10743	137	5	b	b	NOUN
fumecheng-10743	137	6	+	+	NOUN
fumecheng-10743	137	7	+	+	X
fumecheng-10743	138	1	+	+	PUNCT
fumecheng-10743	138	2	=	=	SYM
fumecheng-10743	138	3	=	=	SYM
fumecheng-10743	138	4	=	=	SYM
fumecheng-10743	138	5	(	(	PUNCT
fumecheng-10743	138	6	31	31	NUM
fumecheng-10743	138	7	)	)	PUNCT
fumecheng-10743	138	8	the	the	DET
fumecheng-10743	138	9	original	original	ADJ
fumecheng-10743	138	10	hamiltonian	hamiltonian	NOUN
fumecheng-10743	138	11	-	-	PUNCT
fumecheng-10743	138	12	based	base	VERB
fumecheng-10743	138	13	frequency	frequency	NOUN
fumecheng-10743	138	14	formulation	formulation	NOUN
fumecheng-10743	138	15	is	be	AUX
fumecheng-10743	138	16	to	to	PART
fumecheng-10743	138	17	calculate	calculate	VERB
fumecheng-10743	138	18	the	the	DET
fumecheng-10743	138	19	residuals	residual	NOUN
fumecheng-10743	138	20	:	:	PUNCT
fumecheng-10743	138	21	2	2	NUM
fumecheng-10743	138	22	2	2	NUM
fumecheng-10743	138	23	2	2	NUM
fumecheng-10743	138	24	1	1	NUM
fumecheng-10743	138	25	1	1	NUM
fumecheng-10743	138	26	1	1	NUM
fumecheng-10743	138	27	1	1	NUM
fumecheng-10743	138	28	2	2	NUM
fumecheng-10743	138	29	2	2	NUM
fumecheng-10743	138	30	2	2	NUM
fumecheng-10743	138	31	2	2	NUM
fumecheng-10743	138	32	2	2	NUM
fumecheng-10743	138	33	4	4	NUM
fumecheng-10743	138	34	6	6	NUM
fumecheng-10743	138	35	2	2	NUM
fumecheng-10743	138	36	4	4	NUM
fumecheng-10743	138	37	61	61	NUM
fumecheng-10743	138	38	1	1	NUM
fumecheng-10743	138	39	1	1	NUM
fumecheng-10743	138	40	1	1	NUM
fumecheng-10743	138	41	1	1	NUM
fumecheng-10743	138	42	1	1	NUM
fumecheng-10743	138	43	(	(	PUNCT
fumecheng-10743	138	44	)	)	PUNCT
fumecheng-10743	138	45	sin	sin	NOUN
fumecheng-10743	138	46	(	(	PUNCT
fumecheng-10743	138	47	cos	cos	PROPN
fumecheng-10743	138	48	)	)	PUNCT
fumecheng-10743	138	49	(	(	PUNCT
fumecheng-10743	138	50	)	)	PUNCT
fumecheng-10743	138	51	2	2	NUM
fumecheng-10743	138	52	2	2	NUM
fumecheng-10743	138	53	(	(	PUNCT
fumecheng-10743	138	54	)	)	PUNCT
fumecheng-10743	138	55	cos	cos	PROPN
fumecheng-10743	138	56	cos	cos	PROPN
fumecheng-10743	138	57	cos	cos	PROPN
fumecheng-10743	138	58	2	2	NUM
fumecheng-10743	138	59	2	2	NUM
fumecheng-10743	138	60	4	4	NUM
fumecheng-10743	138	61	6	6	NUM
fumecheng-10743	138	62	r	r	NOUN
fumecheng-10743	138	63	t	t	NOUN
fumecheng-10743	138	64	b	b	NOUN
fumecheng-10743	138	65	t	t	PROPN
fumecheng-10743	138	66	p	p	X
fumecheng-10743	138	67	b	b	PROPN
fumecheng-10743	138	68	t	t	PROPN
fumecheng-10743	138	69	p	p	PROPN
fumecheng-10743	138	70	b	b	PROPN
fumecheng-10743	138	71	b	b	PROPN
fumecheng-10743	138	72	p	p	PROPN
fumecheng-10743	138	73	b	b	PROPN
fumecheng-10743	138	74	b	b	PROPN
fumecheng-10743	138	75	b	b	X
fumecheng-10743	138	76	ab	ab	PROPN
fumecheng-10743	138	77	bb	bb	NOUN
fumecheng-10743	138	78	t	t	PROPN
fumecheng-10743	138	79	t	t	NOUN
fumecheng-10743	138	80	t	t	PROPN
fumecheng-10743	138	81	=	=	PUNCT
fumecheng-10743	139	1	+	+	CCONJ
fumecheng-10743	139	2	−	−	NOUN
fumecheng-10743	140	1	−	−	NOUN
fumecheng-10743	140	2	−	−	NOUN
fumecheng-10743	141	1	=	=	PUNCT
fumecheng-10743	142	1	+	+	PUNCT
fumecheng-10743	142	2	+	+	CCONJ
fumecheng-10743	142	3	+	+	CCONJ
fumecheng-10743	142	4	ω	ω	PROPN
fumecheng-10743	142	5	ω	ω	PROPN
fumecheng-10743	142	6	ω	ω	PROPN
fumecheng-10743	142	7	ω	ω	PROPN
fumecheng-10743	142	8	ω	ω	PROPN
fumecheng-10743	142	9	ω	ω	PROPN
fumecheng-10743	142	10	ω	ω	PROPN
fumecheng-10743	142	11	ω	ω	PROPN
fumecheng-10743	142	12	(	(	PUNCT
fumecheng-10743	142	13	32	32	NUM
fumecheng-10743	142	14	)	)	SYM
fumecheng-10743	142	15	2	2	NUM
fumecheng-10743	142	16	2	2	NUM
fumecheng-10743	142	17	2	2	NUM
fumecheng-10743	142	18	2	2	NUM
fumecheng-10743	142	19	2	2	NUM
fumecheng-10743	142	20	2	2	NUM
fumecheng-10743	142	21	2	2	NUM
fumecheng-10743	142	22	2	2	NUM
fumecheng-10743	142	23	2	2	NUM
fumecheng-10743	142	24	2	2	NUM
fumecheng-10743	142	25	2	2	NUM
fumecheng-10743	142	26	2	2	NUM
fumecheng-10743	142	27	4	4	NUM
fumecheng-10743	142	28	6	6	NUM
fumecheng-10743	142	29	2	2	NUM
fumecheng-10743	142	30	4	4	NUM
fumecheng-10743	142	31	62	62	NUM
fumecheng-10743	142	32	2	2	NUM
fumecheng-10743	142	33	2	2	NUM
fumecheng-10743	142	34	2	2	NUM
fumecheng-10743	142	35	2	2	NUM
fumecheng-10743	142	36	1	1	NUM
fumecheng-10743	142	37	(	(	PUNCT
fumecheng-10743	142	38	)	)	PUNCT
fumecheng-10743	142	39	sin	sin	NOUN
fumecheng-10743	142	40	(	(	PUNCT
fumecheng-10743	142	41	cos	cos	PROPN
fumecheng-10743	142	42	)	)	PUNCT
fumecheng-10743	142	43	(	(	PUNCT
fumecheng-10743	142	44	)	)	PUNCT
fumecheng-10743	142	45	2	2	NUM
fumecheng-10743	142	46	2	2	NUM
fumecheng-10743	142	47	(	(	PUNCT
fumecheng-10743	142	48	)	)	PUNCT
fumecheng-10743	142	49	cos	cos	PROPN
fumecheng-10743	142	50	cos	cos	PROPN
fumecheng-10743	142	51	cos	cos	PROPN
fumecheng-10743	142	52	2	2	NUM
fumecheng-10743	142	53	2	2	NUM
fumecheng-10743	142	54	4	4	NUM
fumecheng-10743	142	55	6	6	NUM
fumecheng-10743	142	56	r	r	NOUN
fumecheng-10743	142	57	t	t	NOUN
fumecheng-10743	142	58	b	b	NOUN
fumecheng-10743	142	59	t	t	PROPN
fumecheng-10743	142	60	p	p	X
fumecheng-10743	142	61	b	b	PROPN
fumecheng-10743	142	62	t	t	PROPN
fumecheng-10743	142	63	p	p	PROPN
fumecheng-10743	142	64	b	b	PROPN
fumecheng-10743	142	65	b	b	PROPN
fumecheng-10743	142	66	p	p	PROPN
fumecheng-10743	142	67	b	b	PROPN
fumecheng-10743	142	68	b	b	PROPN
fumecheng-10743	142	69	b	b	X
fumecheng-10743	142	70	ab	ab	PROPN
fumecheng-10743	142	71	bb	bb	NOUN
fumecheng-10743	142	72	t	t	PROPN
fumecheng-10743	142	73	t	t	NOUN
fumecheng-10743	142	74	t	t	PROPN
fumecheng-10743	142	75	=	=	PUNCT
fumecheng-10743	143	1	+	+	CCONJ
fumecheng-10743	143	2	−	−	NOUN
fumecheng-10743	144	1	−	−	NOUN
fumecheng-10743	144	2	−	−	NOUN
fumecheng-10743	145	1	=	=	PUNCT
fumecheng-10743	146	1	+	+	PUNCT
fumecheng-10743	146	2	+	+	CCONJ
fumecheng-10743	146	3	+	+	CCONJ
fumecheng-10743	146	4	ω	ω	PROPN
fumecheng-10743	146	5	ω	ω	PROPN
fumecheng-10743	146	6	ω	ω	PROPN
fumecheng-10743	146	7	ω	ω	PROPN
fumecheng-10743	146	8	ω	ω	PROPN
fumecheng-10743	146	9	ω	ω	PROPN
fumecheng-10743	146	10	ω	ω	PROPN
fumecheng-10743	146	11	ω	ω	PROPN
fumecheng-10743	146	12	(	(	PUNCT
fumecheng-10743	146	13	33	33	NUM
fumecheng-10743	146	14	)	)	PUNCT
fumecheng-10743	146	15	and	and	CCONJ
fumecheng-10743	146	16	the	the	DET
fumecheng-10743	146	17	residual	residual	ADJ
fumecheng-10743	146	18	integrals	integral	NOUN
fumecheng-10743	146	19	:	:	PUNCT
fumecheng-10743	146	20	1	1	NUM
fumecheng-10743	146	21	2	2	NUM
fumecheng-10743	146	22	6	6	NUM
fumecheng-10743	146	23	4	4	NUM
fumecheng-10743	146	24	2	2	NUM
fumecheng-10743	146	25	/	/	SYM
fumecheng-10743	146	26	4	4	NUM
fumecheng-10743	146	27	2	2	NUM
fumecheng-10743	146	28	1	1	NUM
fumecheng-10743	146	29	1	1	NUM
fumecheng-10743	146	30	1	1	NUM
fumecheng-10743	146	31	1	1	NUM
fumecheng-10743	146	32	0	0	NUM
fumecheng-10743	146	33	1	1	NUM
fumecheng-10743	146	34	4	4	NUM
fumecheng-10743	146	35	16	16	NUM
fumecheng-10743	146	36	28	28	NUM
fumecheng-10743	146	37	70	70	NUM
fumecheng-10743	146	38	210	210	NUM
fumecheng-10743	146	39	(	(	PUNCT
fumecheng-10743	146	40	)	)	PUNCT
fumecheng-10743	146	41	cos	cos	ADP
fumecheng-10743	146	42	3	3	NUM
fumecheng-10743	146	43	105	105	NUM
fumecheng-10743	146	44	t	t	NOUN
fumecheng-10743	146	45	b	b	X
fumecheng-10743	146	46	bb	bb	INTJ
fumecheng-10743	146	47	ab	ab	PROPN
fumecheng-10743	146	48	b	b	PROPN
fumecheng-10743	146	49	p	p	X
fumecheng-10743	146	50	b	b	NOUN
fumecheng-10743	146	51	r	r	NOUN
fumecheng-10743	146	52	r	r	NOUN
fumecheng-10743	146	53	tdt	tdt	PROPN
fumecheng-10743	146	54	t	t	PROPN
fumecheng-10743	146	55			PROPN
fumecheng-10743	146	56			PROPN
fumecheng-10743	146	57	+	+	X
fumecheng-10743	146	58	+	+	NUM
fumecheng-10743	146	59	−	−	NOUN
fumecheng-10743	146	60	=	=	SYM
fumecheng-10743	147	1	=	=	PUNCT
fumecheng-10743	147	2	+	+	ADJ
fumecheng-10743	147	3			X
fumecheng-10743	147	4	ω	ω	PROPN
fumecheng-10743	147	5	ω	ω	PROPN
fumecheng-10743	147	6	(	(	PUNCT
fumecheng-10743	147	7	34	34	NUM
fumecheng-10743	147	8	)	)	SYM
fumecheng-10743	147	9	2	2	NUM
fumecheng-10743	147	10	2	2	NUM
fumecheng-10743	147	11	6	6	NUM
fumecheng-10743	147	12	4	4	NUM
fumecheng-10743	147	13	2	2	NUM
fumecheng-10743	147	14	/	/	SYM
fumecheng-10743	147	15	4	4	NUM
fumecheng-10743	147	16	2	2	NUM
fumecheng-10743	147	17	2	2	NUM
fumecheng-10743	147	18	2	2	NUM
fumecheng-10743	147	19	2	2	NUM
fumecheng-10743	147	20	2	2	NUM
fumecheng-10743	147	21	0	0	NUM
fumecheng-10743	147	22	2	2	NUM
fumecheng-10743	147	23	4	4	NUM
fumecheng-10743	147	24	16	16	NUM
fumecheng-10743	147	25	28	28	NUM
fumecheng-10743	147	26	70	70	NUM
fumecheng-10743	147	27	210	210	NUM
fumecheng-10743	147	28	(	(	PUNCT
fumecheng-10743	147	29	)	)	PUNCT
fumecheng-10743	147	30	cos	cos	ADP
fumecheng-10743	147	31	3	3	NUM
fumecheng-10743	147	32	105	105	NUM
fumecheng-10743	147	33	t	t	NOUN
fumecheng-10743	147	34	b	b	X
fumecheng-10743	147	35	bb	bb	INTJ
fumecheng-10743	147	36	ab	ab	PROPN
fumecheng-10743	147	37	b	b	PROPN
fumecheng-10743	148	1	p	p	X
fumecheng-10743	148	2	b	b	NOUN
fumecheng-10743	148	3	r	r	NOUN
fumecheng-10743	148	4	r	r	NOUN
fumecheng-10743	148	5	tdt	tdt	PROPN
fumecheng-10743	148	6	t	t	PROPN
fumecheng-10743	148	7			PROPN
fumecheng-10743	148	8			PROPN
fumecheng-10743	149	1	+	+	X
fumecheng-10743	150	1	+	+	NUM
fumecheng-10743	150	2	−	−	NOUN
fumecheng-10743	151	1	=	=	SYM
fumecheng-10743	151	2	=	=	PUNCT
fumecheng-10743	152	1	+	+	ADJ
fumecheng-10743	152	2			X
fumecheng-10743	152	3	ω	ω	PROPN
fumecheng-10743	152	4	ω	ω	PROPN
fumecheng-10743	152	5	(	(	PUNCT
fumecheng-10743	152	6	35	35	NUM
fumecheng-10743	152	7	)	)	PUNCT
fumecheng-10743	152	8	the	the	DET
fumecheng-10743	152	9	original	original	ADJ
fumecheng-10743	152	10	hamiltonian	hamiltonian	NOUN
fumecheng-10743	152	11	-	-	PUNCT
fumecheng-10743	152	12	based	base	VERB
fumecheng-10743	152	13	frequency	frequency	NOUN
fumecheng-10743	152	14	formulation	formulation	NOUN
fumecheng-10743	152	15	gives	give	VERB
fumecheng-10743	152	16	the	the	DET
fumecheng-10743	152	17	following	follow	VERB
fumecheng-10743	152	18	result	result	NOUN
fumecheng-10743	152	19	2	2	NUM
fumecheng-10743	152	20	2	2	NUM
fumecheng-10743	152	21	2	2	NUM
fumecheng-10743	152	22	41	41	NUM
fumecheng-10743	152	23	2	2	NUM
fumecheng-10743	152	24	2	2	NUM
fumecheng-10743	152	25	1	1	NUM
fumecheng-10743	152	26	1	1	NUM
fumecheng-10743	152	27	2	2	NUM
fumecheng-10743	152	28	2	2	NUM
fumecheng-10743	152	29	7	7	NUM
fumecheng-10743	152	30	19	19	NUM
fumecheng-10743	152	31	1	1	NUM
fumecheng-10743	152	32	10	10	NUM
fumecheng-10743	152	33	35	35	NUM
fumecheng-10743	152	34	r	r	NOUN
fumecheng-10743	152	35	r	r	NOUN
fumecheng-10743	152	36	ab	ab	NOUN
fumecheng-10743	152	37	bb	bb	NOUN
fumecheng-10743	152	38	r	r	NOUN
fumecheng-10743	152	39	r	r	NOUN
fumecheng-10743	152	40	=	=	PUNCT
fumecheng-10743	152	41	=	=	SYM
fumecheng-10743	152	42	−	−	PROPN
fumecheng-10743	153	1	+	+	CCONJ
fumecheng-10743	153	2	+	+	CCONJ
fumecheng-10743	153	3	−	−	PROPN
fumecheng-10743	153	4	ω	ω	NUM
fumecheng-10743	153	5	ω	ω	PROPN
fumecheng-10743	153	6	ω	ω	PROPN
fumecheng-10743	153	7	(	(	PUNCT
fumecheng-10743	153	8	36	36	NUM
fumecheng-10743	153	9	)	)	PUNCT
fumecheng-10743	153	10	452	452	NUM
fumecheng-10743	153	11	h.	h.	PROPN
fumecheng-10743	153	12	ma	ma	PROPN
fumecheng-10743	154	1	eq	eq	PROPN
fumecheng-10743	154	2	.	.	PUNCT
fumecheng-10743	155	1	(	(	PUNCT
fumecheng-10743	155	2	16	16	NUM
fumecheng-10743	155	3	)	)	PUNCT
fumecheng-10743	155	4	gives	give	VERB
fumecheng-10743	155	5	immediately	immediately	ADV
fumecheng-10743	155	6	the	the	DET
fumecheng-10743	155	7	following	follow	VERB
fumecheng-10743	155	8	results	result	NOUN
fumecheng-10743	155	9	2	2	NUM
fumecheng-10743	155	10	4	4	NUM
fumecheng-10743	155	11	61	61	NUM
fumecheng-10743	155	12	1	1	NUM
fumecheng-10743	155	13	1	1	NUM
fumecheng-10743	155	14	(	(	PUNCT
fumecheng-10743	155	15	)	)	PUNCT
fumecheng-10743	156	1	+	+	CCONJ
fumecheng-10743	156	2	2	2	NUM
fumecheng-10743	156	3	4	4	NUM
fumecheng-10743	156	4	6	6	NUM
fumecheng-10743	156	5	p	p	NOUN
fumecheng-10743	156	6	w	w	PROPN
fumecheng-10743	156	7	w	w	NOUN
fumecheng-10743	156	8	aw	aw	INTJ
fumecheng-10743	156	9	bw=	bw=	NOUN
fumecheng-10743	156	10	+	+	CCONJ
fumecheng-10743	156	11	(	(	PUNCT
fumecheng-10743	156	12	37	37	NUM
fumecheng-10743	156	13	)	)	PUNCT
fumecheng-10743	156	14	and	and	CCONJ
fumecheng-10743	156	15	1	1	NUM
fumecheng-10743	156	16	2	2	NUM
fumecheng-10743	156	17	2	2	NUM
fumecheng-10743	156	18	0	0	NUM
fumecheng-10743	156	19	2	2	NUM
fumecheng-10743	156	20	1	1	NUM
fumecheng-10743	156	21	2	2	NUM
fumecheng-10743	156	22	4	4	NUM
fumecheng-10743	156	23	6	6	NUM
fumecheng-10743	156	24	2	2	NUM
fumecheng-10743	156	25	2	2	NUM
fumecheng-10743	156	26	4	4	NUM
fumecheng-10743	156	27	2	2	NUM
fumecheng-10743	156	28	2	2	NUM
fumecheng-10743	156	29	6	6	NUM
fumecheng-10743	156	30	2	2	NUM
fumecheng-10743	156	31	3	3	NUM
fumecheng-10743	156	32	0	0	NUM
fumecheng-10743	156	33	2	2	NUM
fumecheng-10743	156	34	2	2	NUM
fumecheng-10743	156	35	4	4	NUM
fumecheng-10743	156	36	6	6	NUM
fumecheng-10743	156	37	2	2	NUM
fumecheng-10743	156	38	4	4	NUM
fumecheng-10743	156	39	6	6	NUM
fumecheng-10743	156	40	2	2	NUM
fumecheng-10743	156	41	2	2	NUM
fumecheng-10743	156	42	4	4	NUM
fumecheng-10743	156	43	6	6	NUM
fumecheng-10743	156	44	2	2	NUM
fumecheng-10743	156	45	2	2	NUM
fumecheng-10743	156	46	4	4	NUM
fumecheng-10743	156	47	6	6	NUM
fumecheng-10743	156	48	(	(	PUNCT
fumecheng-10743	156	49	)	)	PUNCT
fumecheng-10743	156	50	6	6	NUM
fumecheng-10743	156	51	(	(	PUNCT
fumecheng-10743	156	52	1	1	NUM
fumecheng-10743	156	53	)	)	SYM
fumecheng-10743	156	54	1	1	NUM
fumecheng-10743	157	1	1	1	NUM
fumecheng-10743	157	2	1	1	NUM
fumecheng-10743	157	3	1	1	NUM
fumecheng-10743	157	4	1	1	NUM
fumecheng-10743	157	5	1	1	NUM
fumecheng-10743	157	6	6	6	NUM
fumecheng-10743	157	7	6	6	NUM
fumecheng-10743	157	8	(	(	PUNCT
fumecheng-10743	157	9	1	1	NUM
fumecheng-10743	157	10	)	)	PUNCT
fumecheng-10743	157	11	(	(	PUNCT
fumecheng-10743	157	12	1	1	X
fumecheng-10743	157	13	)	)	PUNCT
fumecheng-10743	157	14	(	(	PUNCT
fumecheng-10743	157	15	1	1	X
fumecheng-10743	157	16	)	)	SYM
fumecheng-10743	157	17	2	2	NUM
fumecheng-10743	157	18	4	4	NUM
fumecheng-10743	157	19	6	6	NUM
fumecheng-10743	157	20	2	2	NUM
fumecheng-10743	157	21	4	4	NUM
fumecheng-10743	157	22	6	6	NUM
fumecheng-10743	157	23	3	3	NUM
fumecheng-10743	157	24	4	4	NUM
fumecheng-10743	157	25	16	16	NUM
fumecheng-10743	157	26	3	3	NUM
fumecheng-10743	157	27	2	2	NUM
fumecheng-10743	157	28	2	2	NUM
fumecheng-10743	157	29	5	5	NUM
fumecheng-10743	157	30	35	35	NUM
fumecheng-10743	157	31	7	7	NUM
fumecheng-10743	157	32	19	19	NUM
fumecheng-10743	157	33	10	10	NUM
fumecheng-10743	157	34	35	35	NUM
fumecheng-10743	157	35	7	7	NUM
fumecheng-10743	157	36	19	19	NUM
fumecheng-10743	157	37	1	1	NUM
fumecheng-10743	157	38	10	10	NUM
fumecheng-10743	157	39	35	35	NUM
fumecheng-10743	157	40	p	p	NOUN
fumecheng-10743	157	41	b	b	PROPN
fumecheng-10743	157	42	p	p	X
fumecheng-10743	157	43	b	b	PROPN
fumecheng-10743	157	44	x	x	X
fumecheng-10743	157	45	dx	dx	PROPN
fumecheng-10743	157	46	b	b	PROPN
fumecheng-10743	157	47	b	b	X
fumecheng-10743	157	48	ab	ab	INTJ
fumecheng-10743	157	49	bb	bb	PROPN
fumecheng-10743	157	50	b	b	PROPN
fumecheng-10743	157	51	x	x	SYM
fumecheng-10743	157	52	b	b	X
fumecheng-10743	157	53	x	x	SYM
fumecheng-10743	157	54	bb	bb	INTJ
fumecheng-10743	157	55	x	x	PROPN
fumecheng-10743	157	56	dx	dx	PROPN
fumecheng-10743	157	57	b	b	PROPN
fumecheng-10743	157	58	b	b	X
fumecheng-10743	158	1	ab	ab	INTJ
fumecheng-10743	158	2	bb	bb	PROPN
fumecheng-10743	158	3	b	b	PROPN
fumecheng-10743	158	4	ab	ab	PROPN
fumecheng-10743	159	1	bb	bb	PROPN
fumecheng-10743	159	2	b	b	PROPN
fumecheng-10743	159	3	b	b	PROPN
fumecheng-10743	159	4	ab	ab	INTJ
fumecheng-10743	159	5	bb	bb	PROPN
fumecheng-10743	159	6	b	b	PROPN
fumecheng-10743	159	7	ab	ab	PROPN
fumecheng-10743	159	8	bb	bb	NOUN
fumecheng-10743	160	1	−	−	NOUN
fumecheng-10743	161	1	−	−	PROPN
fumecheng-10743	162	1	=	=	SYM
fumecheng-10743	163	1	+	+	PUNCT
fumecheng-10743	163	2	+	+	NUM
fumecheng-10743	163	3	−	−	ADP
fumecheng-10743	163	4	−	−	PROPN
fumecheng-10743	164	1	+	+	CCONJ
fumecheng-10743	164	2	−	−	PROPN
fumecheng-10743	165	1	+	+	CCONJ
fumecheng-10743	165	2	−	−	PROPN
fumecheng-10743	165	3	=	=	SYM
fumecheng-10743	166	1	+	+	PUNCT
fumecheng-10743	167	1	+	+	CCONJ
fumecheng-10743	167	2	−	−	X
fumecheng-10743	168	1	+	+	CCONJ
fumecheng-10743	168	2	+	+	PUNCT
fumecheng-10743	168	3	=	=	SYM
fumecheng-10743	168	4	+	+	PUNCT
fumecheng-10743	168	5	+	+	NUM
fumecheng-10743	168	6	=	=	SYM
fumecheng-10743	168	7	=	=	SYM
fumecheng-10743	169	1	+	+	PUNCT
fumecheng-10743	169	2	+	+	NUM
fumecheng-10743	169	3			NOUN
fumecheng-10743	169	4			PROPN
fumecheng-10743	169	5			NOUN
fumecheng-10743	169	6			PROPN
fumecheng-10743	169	7			PROPN
fumecheng-10743	169	8			PROPN
fumecheng-10743	170	1			PROPN
fumecheng-10743	170	2			PROPN
fumecheng-10743	171	1			ADJ
fumecheng-10743	171	2			PROPN
fumecheng-10743	171	3			PROPN
fumecheng-10743	171	4			NOUN
fumecheng-10743	172	1			NOUN
fumecheng-10743	172	2			NOUN
fumecheng-10743	172	3			NOUN
fumecheng-10743	172	4			PROPN
fumecheng-10743	172	5			PROPN
fumecheng-10743	173	1			PROPN
fumecheng-10743	174	1			PROPN
fumecheng-10743	174	2			PROPN
fumecheng-10743	175	1			ADJ
fumecheng-10743	175	2			PROPN
fumecheng-10743	175	3			PROPN
fumecheng-10743	175	4			NOUN
fumecheng-10743	175	5			PUNCT
fumecheng-10743	175	6			PUNCT
fumecheng-10743	175	7	ω	ω	PROPN
fumecheng-10743	175	8	(	(	PUNCT
fumecheng-10743	175	9	38	38	NUM
fumecheng-10743	175	10	)	)	PUNCT
fumecheng-10743	175	11	this	this	PRON
fumecheng-10743	175	12	is	be	AUX
fumecheng-10743	175	13	the	the	DET
fumecheng-10743	175	14	same	same	ADJ
fumecheng-10743	175	15	with	with	ADP
fumecheng-10743	175	16	eq	eq	NOUN
fumecheng-10743	175	17	.	.	PUNCT
fumecheng-10743	176	1	(	(	PUNCT
fumecheng-10743	176	2	36	36	NUM
fumecheng-10743	176	3	)	)	PUNCT
fumecheng-10743	176	4	.	.	PUNCT
fumecheng-10743	177	1	the	the	DET
fumecheng-10743	177	2	one	one	NUM
fumecheng-10743	177	3	-	-	PUNCT
fumecheng-10743	177	4	step	step	NOUN
fumecheng-10743	177	5	solving	solving	NOUN
fumecheng-10743	177	6	process	process	NOUN
fumecheng-10743	177	7	by	by	ADP
fumecheng-10743	177	8	eq	eq	PROPN
fumecheng-10743	177	9	.	.	PUNCT
fumecheng-10743	178	1	(	(	PUNCT
fumecheng-10743	178	2	21	21	NUM
fumecheng-10743	178	3	)	)	PUNCT
fumecheng-10743	178	4	leads	lead	VERB
fumecheng-10743	178	5	to	to	ADP
fumecheng-10743	178	6	the	the	DET
fumecheng-10743	178	7	following	follow	VERB
fumecheng-10743	178	8	result	result	NOUN
fumecheng-10743	178	9	2	2	NUM
fumecheng-10743	178	10	2	2	NUM
fumecheng-10743	178	11	2	2	NUM
fumecheng-10743	178	12	4	4	NUM
fumecheng-10743	178	13	6	6	NUM
fumecheng-10743	178	14	2	2	NUM
fumecheng-10743	178	15	4	4	NUM
fumecheng-10743	178	16	6	6	NUM
fumecheng-10743	178	17	2	2	NUM
fumecheng-10743	178	18	2	2	NUM
fumecheng-10743	178	19	4	4	NUM
fumecheng-10743	178	20	6	6	NUM
fumecheng-10743	178	21	2	2	NUM
fumecheng-10743	178	22	2	2	NUM
fumecheng-10743	178	23	4	4	NUM
fumecheng-10743	178	24	4	4	NUM
fumecheng-10743	178	25	(	(	PUNCT
fumecheng-10743	178	26	(	(	PUNCT
fumecheng-10743	178	27	)	)	PUNCT
fumecheng-10743	178	28	(	(	PUNCT
fumecheng-10743	178	29	/	/	SYM
fumecheng-10743	178	30	2	2	NUM
fumecheng-10743	178	31	)	)	PUNCT
fumecheng-10743	178	32	)	)	PUNCT
fumecheng-10743	179	1	1	1	NUM
fumecheng-10743	179	2	1	1	NUM
fumecheng-10743	179	3	1	1	NUM
fumecheng-10743	179	4	1	1	NUM
fumecheng-10743	179	5	1	1	NUM
fumecheng-10743	179	6	1	1	NUM
fumecheng-10743	179	7	4	4	NUM
fumecheng-10743	179	8	2	2	NUM
fumecheng-10743	179	9	4	4	NUM
fumecheng-10743	179	10	6	6	NUM
fumecheng-10743	179	11	4	4	NUM
fumecheng-10743	179	12	16	16	NUM
fumecheng-10743	179	13	48	48	NUM
fumecheng-10743	179	14	3	3	NUM
fumecheng-10743	179	15	7	7	NUM
fumecheng-10743	179	16	4	4	NUM
fumecheng-10743	179	17	12	12	NUM
fumecheng-10743	179	18	3	3	NUM
fumecheng-10743	179	19	7	7	NUM
fumecheng-10743	179	20	1	1	NUM
fumecheng-10743	179	21	4	4	NUM
fumecheng-10743	179	22	12	12	NUM
fumecheng-10743	179	23	p	p	NOUN
fumecheng-10743	179	24	b	b	PROPN
fumecheng-10743	179	25	p	p	X
fumecheng-10743	179	26	b	b	PROPN
fumecheng-10743	179	27	b	b	PROPN
fumecheng-10743	179	28	b	b	X
fumecheng-10743	179	29	ab	ab	PROPN
fumecheng-10743	179	30	bb	bb	PROPN
fumecheng-10743	179	31	b	b	PROPN
fumecheng-10743	179	32	ab	ab	PROPN
fumecheng-10743	179	33	bb	bb	PROPN
fumecheng-10743	179	34	b	b	PROPN
fumecheng-10743	179	35	b	b	PROPN
fumecheng-10743	179	36	ab	ab	INTJ
fumecheng-10743	180	1	bb	bb	PROPN
fumecheng-10743	180	2	b	b	PROPN
fumecheng-10743	180	3	ab	ab	PROPN
fumecheng-10743	180	4	bb	bb	NOUN
fumecheng-10743	180	5	−	−	PROPN
fumecheng-10743	180	6	=	=	NOUN
fumecheng-10743	180	7			NOUN
fumecheng-10743	180	8			NOUN
fumecheng-10743	180	9	+	+	CCONJ
fumecheng-10743	181	1	+	+	CCONJ
fumecheng-10743	181	2	−	−	PROPN
fumecheng-10743	181	3	−	−	PROPN
fumecheng-10743	181	4	−	−	PROPN
fumecheng-10743	181	5			PROPN
fumecheng-10743	181	6			PROPN
fumecheng-10743	181	7			NOUN
fumecheng-10743	181	8	=	=	PUNCT
fumecheng-10743	182	1	+	+	PUNCT
fumecheng-10743	183	1	+	+	PUNCT
fumecheng-10743	183	2	=	=	SYM
fumecheng-10743	183	3	=	=	SYM
fumecheng-10743	184	1	+	+	NUM
fumecheng-10743	184	2	+	+	NUM
fumecheng-10743	184	3	ω	ω	NUM
fumecheng-10743	184	4	(	(	PUNCT
fumecheng-10743	184	5	39	39	NUM
fumecheng-10743	184	6	)	)	PUNCT
fumecheng-10743	184	7	fig	fig	NOUN
fumecheng-10743	184	8	.	.	PUNCT
fumecheng-10743	184	9	1	1	NUM
fumecheng-10743	184	10	shows	show	VERB
fumecheng-10743	184	11	the	the	DET
fumecheng-10743	184	12	comparison	comparison	NOUN
fumecheng-10743	184	13	of	of	ADP
fumecheng-10743	184	14	approximate	approximate	ADJ
fumecheng-10743	184	15	solution	solution	NOUN
fumecheng-10743	184	16	w(t)=bcosωt	w(t)=bcosωt	PROPN
fumecheng-10743	184	17	,	,	PUNCT
fumecheng-10743	184	18	where	where	SCONJ
fumecheng-10743	184	19	the	the	DET
fumecheng-10743	184	20	frequency	frequency	NOUN
fumecheng-10743	184	21	is	be	AUX
fumecheng-10743	184	22	determined	determine	VERB
fumecheng-10743	184	23	by	by	ADP
fumecheng-10743	184	24	eq	eq	PROPN
fumecheng-10743	184	25	.	.	PUNCT
fumecheng-10743	185	1	(	(	PUNCT
fumecheng-10743	185	2	38	38	NUM
fumecheng-10743	185	3	)	)	PUNCT
fumecheng-10743	185	4	or	or	CCONJ
fumecheng-10743	185	5	eq	eq	NOUN
fumecheng-10743	185	6	.	.	PUNCT
fumecheng-10743	186	1	(	(	PUNCT
fumecheng-10743	186	2	39	39	NUM
fumecheng-10743	186	3	)	)	PUNCT
fumecheng-10743	186	4	,	,	PUNCT
fumecheng-10743	186	5	with	with	ADP
fumecheng-10743	186	6	the	the	DET
fumecheng-10743	186	7	exact	exact	ADJ
fumecheng-10743	186	8	one	one	NUM
fumecheng-10743	186	9	when	when	SCONJ
fumecheng-10743	186	10	a	a	DET
fumecheng-10743	186	11	=	=	NOUN
fumecheng-10743	186	12	b=1	b=1	NOUN
fumecheng-10743	186	13	for	for	ADP
fumecheng-10743	186	14	various	various	ADJ
fumecheng-10743	186	15	values	value	NOUN
fumecheng-10743	186	16	of	of	ADP
fumecheng-10743	186	17	amplitudes	amplitude	NOUN
fumecheng-10743	186	18	.	.	PUNCT
fumecheng-10743	187	1	4	4	X
fumecheng-10743	187	2	.	.	X
fumecheng-10743	187	3	conclusions	conclusion	NOUN
fumecheng-10743	187	4	this	this	DET
fumecheng-10743	187	5	paper	paper	NOUN
fumecheng-10743	187	6	simplifies	simplifie	NOUN
fumecheng-10743	187	7	hamiltonian	hamiltonian	NOUN
fumecheng-10743	187	8	-	-	PUNCT
fumecheng-10743	187	9	based	base	VERB
fumecheng-10743	187	10	frequency	frequency	NOUN
fumecheng-10743	187	11	formulation	formulation	NOUN
fumecheng-10743	187	12	for	for	ADP
fumecheng-10743	187	13	nonlinear	nonlinear	ADJ
fumecheng-10743	187	14	oscillators	oscillator	NOUN
fumecheng-10743	187	15	.	.	PUNCT
fumecheng-10743	188	1	all	all	DET
fumecheng-10743	188	2	the	the	DET
fumecheng-10743	188	3	intermediate	intermediate	ADJ
fumecheng-10743	188	4	steps	step	NOUN
fumecheng-10743	188	5	involved	involve	VERB
fumecheng-10743	188	6	in	in	ADP
fumecheng-10743	188	7	the	the	DET
fumecheng-10743	188	8	original	original	ADJ
fumecheng-10743	188	9	formulation	formulation	NOUN
fumecheng-10743	188	10	become	become	VERB
fumecheng-10743	188	11	totally	totally	ADV
fumecheng-10743	188	12	unnecessary	unnecessary	ADJ
fumecheng-10743	188	13	,	,	PUNCT
fumecheng-10743	188	14	making	make	VERB
fumecheng-10743	188	15	the	the	DET
fumecheng-10743	188	16	formulation	formulation	NOUN
fumecheng-10743	188	17	unprecedentedly	unprecedentedly	ADV
fumecheng-10743	188	18	simple	simple	ADJ
fumecheng-10743	188	19	.	.	PUNCT
fumecheng-10743	189	1	both	both	DET
fumecheng-10743	189	2	the	the	DET
fumecheng-10743	189	3	simplified	simplified	ADJ
fumecheng-10743	189	4	frequency	frequency	NOUN
fumecheng-10743	189	5	formulations	formulation	NOUN
fumecheng-10743	189	6	will	will	AUX
fumecheng-10743	189	7	play	play	VERB
fumecheng-10743	189	8	an	an	DET
fumecheng-10743	189	9	important	important	ADJ
fumecheng-10743	189	10	role	role	NOUN
fumecheng-10743	189	11	in	in	ADP
fumecheng-10743	189	12	the	the	DET
fumecheng-10743	189	13	nonlinear	nonlinear	ADJ
fumecheng-10743	189	14	vibration	vibration	NOUN
fumecheng-10743	189	15	theory	theory	NOUN
fumecheng-10743	189	16	for	for	ADP
fumecheng-10743	189	17	a	a	DET
fumecheng-10743	189	18	fast	fast	ADJ
fumecheng-10743	189	19	and	and	CCONJ
fumecheng-10743	189	20	reliable	reliable	ADJ
fumecheng-10743	189	21	insight	insight	NOUN
fumecheng-10743	189	22	into	into	ADP
fumecheng-10743	189	23	the	the	DET
fumecheng-10743	189	24	periodic	periodic	ADJ
fumecheng-10743	189	25	properties	property	NOUN
fumecheng-10743	189	26	of	of	ADP
fumecheng-10743	189	27	a	a	DET
fumecheng-10743	189	28	complex	complex	ADJ
fumecheng-10743	189	29	nonlinear	nonlinear	ADJ
fumecheng-10743	189	30	oscillator	oscillator	NOUN
fumecheng-10743	189	31	,	,	PUNCT
fumecheng-10743	189	32	and	and	CCONJ
fumecheng-10743	189	33	it	it	PRON
fumecheng-10743	189	34	will	will	AUX
fumecheng-10743	189	35	open	open	VERB
fumecheng-10743	189	36	up	up	ADP
fumecheng-10743	189	37	a	a	DET
fumecheng-10743	189	38	flood	flood	NOUN
fumecheng-10743	189	39	of	of	ADP
fumecheng-10743	189	40	opportunities	opportunity	NOUN
fumecheng-10743	189	41	for	for	ADP
fumecheng-10743	189	42	various	various	ADJ
fumecheng-10743	189	43	applications	application	NOUN
fumecheng-10743	189	44	.	.	PUNCT
fumecheng-10743	190	1	the	the	DET
fumecheng-10743	190	2	one	one	NUM
fumecheng-10743	190	3	-	-	PUNCT
fumecheng-10743	190	4	step	step	NOUN
fumecheng-10743	190	5	solving	solving	NOUN
fumecheng-10743	190	6	process	process	NOUN
fumecheng-10743	190	7	given	give	VERB
fumecheng-10743	190	8	in	in	ADP
fumecheng-10743	190	9	this	this	DET
fumecheng-10743	190	10	paper	paper	NOUN
fumecheng-10743	190	11	confirms	confirm	VERB
fumecheng-10743	190	12	again	again	ADV
fumecheng-10743	190	13	ji	ji	PROPN
fumecheng-10743	190	14	-	-	PROPN
fumecheng-10743	190	15	huan	huan	NOUN
fumecheng-10743	190	16	he	he	PRON
fumecheng-10743	190	17	’s	’	VERB
fumecheng-10743	190	18	famous	famous	ADJ
fumecheng-10743	190	19	saying	saying	NOUN
fumecheng-10743	190	20	:	:	PUNCT
fumecheng-10743	190	21	“	"	PUNCT
fumecheng-10743	190	22	the	the	DET
fumecheng-10743	190	23	simpler	simple	ADJ
fumecheng-10743	190	24	is	be	AUX
fumecheng-10743	190	25	the	the	DET
fumecheng-10743	190	26	better	well	ADJ
fumecheng-10743	190	27	for	for	ADP
fumecheng-10743	190	28	the	the	DET
fumecheng-10743	190	29	nonlinear	nonlinear	ADJ
fumecheng-10743	190	30	vibration	vibration	NOUN
fumecheng-10743	190	31	theory	theory	NOUN
fumecheng-10743	190	32	”	"	PUNCT
fumecheng-10743	190	33	.	.	PUNCT
fumecheng-10743	191	1	simplified	simplify	VERB
fumecheng-10743	191	2	hamiltonian	hamiltonian	NOUN
fumecheng-10743	191	3	-	-	PUNCT
fumecheng-10743	191	4	based	base	VERB
fumecheng-10743	191	5	frequency	frequency	NOUN
fumecheng-10743	191	6	-	-	PUNCT
fumecheng-10743	191	7	amplitude	amplitude	NOUN
fumecheng-10743	191	8	formulation	formulation	NOUN
fumecheng-10743	191	9	for	for	ADP
fumecheng-10743	191	10	nonlinear	nonlinear	ADJ
fumecheng-10743	191	11	vibration	vibration	NOUN
fumecheng-10743	191	12	systems	system	NOUN
fumecheng-10743	191	13	453	453	NUM
fumecheng-10743	191	14	fig	fig	NOUN
fumecheng-10743	191	15	.	.	PUNCT
fumecheng-10743	192	1	1	1	NUM
fumecheng-10743	192	2	comparison	comparison	NOUN
fumecheng-10743	192	3	of	of	ADP
fumecheng-10743	192	4	the	the	DET
fumecheng-10743	192	5	exact	exact	ADJ
fumecheng-10743	192	6	solutions	solution	NOUN
fumecheng-10743	192	7	with	with	ADP
fumecheng-10743	192	8	the	the	DET
fumecheng-10743	192	9	approximate	approximate	ADJ
fumecheng-10743	192	10	solutions	solution	NOUN
fumecheng-10743	192	11	based	base	VERB
fumecheng-10743	192	12	on	on	ADP
fumecheng-10743	192	13	eqs	eqs	PROPN
fumecheng-10743	192	14	.	.	PUNCT
fumecheng-10743	193	1	(	(	PUNCT
fumecheng-10743	193	2	38	38	NUM
fumecheng-10743	193	3	)	)	PUNCT
fumecheng-10743	193	4	and	and	CCONJ
fumecheng-10743	193	5	(	(	PUNCT
fumecheng-10743	193	6	39	39	NUM
fumecheng-10743	193	7	)	)	PUNCT
fumecheng-10743	193	8	for	for	ADP
fumecheng-10743	193	9	amplitude	amplitude	NOUN
fumecheng-10743	193	10	b	b	NOUN
fumecheng-10743	193	11	ranging	range	VERB
fumecheng-10743	193	12	from	from	ADP
fumecheng-10743	193	13	0.01	0.01	NUM
fumecheng-10743	193	14	to	to	ADP
fumecheng-10743	193	15	10000	10000	NUM
fumecheng-10743	193	16	454	454	NUM
fumecheng-10743	193	17	h.	h.	PROPN
fumecheng-10743	193	18	ma	ma	PROPN
fumecheng-10743	193	19	references	reference	NOUN
fumecheng-10743	194	1	1	1	PROPN
fumecheng-10743	194	2	.	.	PUNCT
fumecheng-10743	194	3	rama	rama	PROPN
fumecheng-10743	194	4	g.	g.	PROPN
fumecheng-10743	194	5	,	,	PUNCT
fumecheng-10743	194	6	marinkovic	marinkovic	PROPN
fumecheng-10743	194	7	d.	d.	PROPN
fumecheng-10743	194	8	,	,	PUNCT
fumecheng-10743	194	9	zehn	zehn	PROPN
fumecheng-10743	194	10	m.	m.	NOUN
fumecheng-10743	194	11	,	,	PUNCT
fumecheng-10743	194	12	2018	2018	NUM
fumecheng-10743	194	13	,	,	PUNCT
fumecheng-10743	194	14	high	high	ADJ
fumecheng-10743	194	15	performance	performance	NOUN
fumecheng-10743	194	16	3	3	NUM
fumecheng-10743	194	17	-	-	PUNCT
fumecheng-10743	194	18	node	node	ADJ
fumecheng-10743	194	19	shell	shell	NOUN
fumecheng-10743	194	20	element	element	NOUN
fumecheng-10743	194	21	for	for	ADP
fumecheng-10743	194	22	linear	linear	PROPN
fumecheng-10743	194	23	and	and	CCONJ
fumecheng-10743	194	24	geometrically	geometrically	ADV
fumecheng-10743	194	25	nonlinear	nonlinear	VERB
fumecheng-10743	194	26	analysis	analysis	NOUN
fumecheng-10743	194	27	of	of	ADP
fumecheng-10743	194	28	composite	composite	ADJ
fumecheng-10743	194	29	laminates	laminate	NOUN
fumecheng-10743	194	30	,	,	PUNCT
fumecheng-10743	194	31	composites	composite	VERB
fumecheng-10743	194	32	part	part	NOUN
fumecheng-10743	194	33	b	b	NOUN
fumecheng-10743	194	34	:	:	PUNCT
fumecheng-10743	194	35	engineering	engineering	NOUN
fumecheng-10743	194	36	,	,	PUNCT
fumecheng-10743	194	37	151	151	NUM
fumecheng-10743	194	38	,	,	PUNCT
fumecheng-10743	194	39	pp	pp	ADJ
fumecheng-10743	194	40	.	.	PUNCT
fumecheng-10743	195	1	118	118	NUM
fumecheng-10743	195	2	-	-	SYM
fumecheng-10743	195	3	126	126	NUM
fumecheng-10743	195	4	.	.	PUNCT
fumecheng-10743	196	1	2	2	NUM
fumecheng-10743	196	2	.	.	X
fumecheng-10743	196	3	wang	wang	PROPN
fumecheng-10743	196	4	,	,	PUNCT
fumecheng-10743	196	5	c.c	c.c	PROPN
fumecheng-10743	196	6	.	.	PROPN
fumecheng-10743	196	7	,	,	PUNCT
fumecheng-10743	196	8	yau	yau	PROPN
fumecheng-10743	196	9	,	,	PUNCT
fumecheng-10743	196	10	h.t	h.t	PROPN
fumecheng-10743	196	11	.	.	PROPN
fumecheng-10743	196	12	,	,	PUNCT
fumecheng-10743	196	13	jang	jang	PROPN
fumecheng-10743	196	14	,	,	PUNCT
fumecheng-10743	196	15	m.j	m.j	PROPN
fumecheng-10743	196	16	.	.	PROPN
fumecheng-10743	196	17	,	,	PUNCT
fumecheng-10743	196	18	yeh	yeh	PROPN
fumecheng-10743	196	19	,	,	PUNCT
fumecheng-10743	196	20	y.l	y.l	PROPN
fumecheng-10743	196	21	.	.	PROPN
fumecheng-10743	196	22	,	,	PUNCT
fumecheng-10743	196	23	2007	2007	NUM
fumecheng-10743	196	24	,	,	PUNCT
fumecheng-10743	196	25	theoretical	theoretical	ADJ
fumecheng-10743	196	26	analysis	analysis	NOUN
fumecheng-10743	196	27	of	of	ADP
fumecheng-10743	196	28	the	the	DET
fumecheng-10743	196	29	non	non	ADJ
fumecheng-10743	196	30	-	-	ADJ
fumecheng-10743	196	31	linear	linear	ADJ
fumecheng-10743	196	32	behavior	behavior	NOUN
fumecheng-10743	196	33	of	of	ADP
fumecheng-10743	196	34	a	a	DET
fumecheng-10743	196	35	flexible	flexible	ADJ
fumecheng-10743	196	36	rotor	rotor	NOUN
fumecheng-10743	196	37	supported	support	VERB
fumecheng-10743	196	38	by	by	ADP
fumecheng-10743	196	39	herringbone	herringbone	PROPN
fumecheng-10743	196	40	grooved	groove	VERB
fumecheng-10743	196	41	gas	gas	NOUN
fumecheng-10743	196	42	journal	journal	NOUN
fumecheng-10743	196	43	bearings	bearing	NOUN
fumecheng-10743	196	44	,	,	PUNCT
fumecheng-10743	196	45	tribology	tribology	NOUN
fumecheng-10743	196	46	international	international	NOUN
fumecheng-10743	196	47	,	,	PUNCT
fumecheng-10743	196	48	40(3	40(3	NUM
fumecheng-10743	196	49	)	)	PUNCT
fumecheng-10743	196	50	,	,	PUNCT
fumecheng-10743	196	51	pp	pp	ADP
fumecheng-10743	196	52	.	.	PUNCT
fumecheng-10743	197	1	533–541	533–541	NUM
fumecheng-10743	197	2	.	.	PUNCT
fumecheng-10743	198	1	3	3	X
fumecheng-10743	198	2	.	.	X
fumecheng-10743	198	3	wang	wang	PROPN
fumecheng-10743	198	4	,	,	PUNCT
fumecheng-10743	198	5	c.c	c.c	PROPN
fumecheng-10743	198	6	.	.	PROPN
fumecheng-10743	198	7	,	,	PUNCT
fumecheng-10743	198	8	yau	yau	PROPN
fumecheng-10743	198	9	,	,	PUNCT
fumecheng-10743	198	10	h.t	h.t	PROPN
fumecheng-10743	198	11	.	.	PROPN
fumecheng-10743	198	12	,	,	PUNCT
fumecheng-10743	198	13	2008	2008	NUM
fumecheng-10743	198	14	,	,	PUNCT
fumecheng-10743	198	15	application	application	NOUN
fumecheng-10743	198	16	of	of	ADP
fumecheng-10743	198	17	a	a	DET
fumecheng-10743	198	18	hybrid	hybrid	ADJ
fumecheng-10743	198	19	numerical	numerical	ADJ
fumecheng-10743	198	20	method	method	NOUN
fumecheng-10743	198	21	to	to	ADP
fumecheng-10743	198	22	the	the	DET
fumecheng-10743	198	23	bifurcation	bifurcation	NOUN
fumecheng-10743	198	24	analysis	analysis	NOUN
fumecheng-10743	198	25	of	of	ADP
fumecheng-10743	198	26	a	a	DET
fumecheng-10743	198	27	rigid	rigid	ADJ
fumecheng-10743	198	28	rotor	rotor	NOUN
fumecheng-10743	198	29	supported	support	VERB
fumecheng-10743	198	30	by	by	ADP
fumecheng-10743	198	31	a	a	DET
fumecheng-10743	198	32	spherical	spherical	ADJ
fumecheng-10743	198	33	gas	gas	NOUN
fumecheng-10743	198	34	journal	journal	NOUN
fumecheng-10743	198	35	bearing	bear	VERB
fumecheng-10743	198	36	system	system	NOUN
fumecheng-10743	198	37	,	,	PUNCT
fumecheng-10743	198	38	nonlinear	nonlinear	ADJ
fumecheng-10743	198	39	dynamics	dynamic	NOUN
fumecheng-10743	198	40	,	,	PUNCT
fumecheng-10743	198	41	51(4	51(4	NUM
fumecheng-10743	198	42	)	)	PUNCT
fumecheng-10743	198	43	,	,	PUNCT
fumecheng-10743	198	44	pp	pp	ADP
fumecheng-10743	198	45	.	.	PUNCT
fumecheng-10743	199	1	515–528	515–528	NUM
fumecheng-10743	199	2	.	.	PUNCT
fumecheng-10743	200	1	4	4	NUM
fumecheng-10743	200	2	.	.	X
fumecheng-10743	200	3	yau	yau	PROPN
fumecheng-10743	200	4	,	,	PUNCT
fumecheng-10743	200	5	h.t	h.t	PROPN
fumecheng-10743	200	6	.	.	PROPN
fumecheng-10743	200	7	,	,	PUNCT
fumecheng-10743	200	8	2008	2008	NUM
fumecheng-10743	200	9	,	,	PUNCT
fumecheng-10743	200	10	generalized	generalized	ADJ
fumecheng-10743	200	11	projective	projective	ADJ
fumecheng-10743	200	12	chaos	chaos	NOUN
fumecheng-10743	200	13	synchronization	synchronization	NOUN
fumecheng-10743	200	14	of	of	ADP
fumecheng-10743	200	15	gyroscope	gyroscope	NOUN
fumecheng-10743	200	16	systems	system	NOUN
fumecheng-10743	200	17	subjected	subject	VERB
fumecheng-10743	200	18	to	to	ADP
fumecheng-10743	200	19	dead	dead	ADJ
fumecheng-10743	200	20	-	-	PUNCT
fumecheng-10743	200	21	zone	zone	NOUN
fumecheng-10743	200	22	nonlinear	nonlinear	ADJ
fumecheng-10743	200	23	inputs	input	NOUN
fumecheng-10743	200	24	,	,	PUNCT
fumecheng-10743	200	25	physics	physics	NOUN
fumecheng-10743	200	26	letters	letter	NOUN
fumecheng-10743	200	27	a	a	PRON
fumecheng-10743	200	28	,	,	PUNCT
fumecheng-10743	200	29	372(14	372(14	NUM
fumecheng-10743	200	30	)	)	PUNCT
fumecheng-10743	200	31	,	,	PUNCT
fumecheng-10743	200	32	pp	pp	ADJ
fumecheng-10743	200	33	.	.	PUNCT
fumecheng-10743	201	1	2380	2380	NUM
fumecheng-10743	201	2	-	-	SYM
fumecheng-10743	201	3	2385	2385	NUM
fumecheng-10743	201	4	.	.	PUNCT
fumecheng-10743	202	1	5	5	X
fumecheng-10743	202	2	.	.	X
fumecheng-10743	202	3	yau	yau	PROPN
fumecheng-10743	202	4	,	,	PUNCT
fumecheng-10743	202	5	h.t	h.t	PROPN
fumecheng-10743	202	6	.	.	PROPN
fumecheng-10743	202	7	,	,	PUNCT
fumecheng-10743	202	8	2007	2007	NUM
fumecheng-10743	202	9	,	,	PUNCT
fumecheng-10743	202	10	nonlinear	nonlinear	ADJ
fumecheng-10743	202	11	rule	rule	NOUN
fumecheng-10743	202	12	-	-	PUNCT
fumecheng-10743	202	13	based	base	VERB
fumecheng-10743	202	14	controller	controller	NOUN
fumecheng-10743	202	15	for	for	ADP
fumecheng-10743	202	16	chaos	chaos	NOUN
fumecheng-10743	202	17	synchronization	synchronization	NOUN
fumecheng-10743	202	18	of	of	ADP
fumecheng-10743	202	19	two	two	NUM
fumecheng-10743	202	20	gyros	gyro	NOUN
fumecheng-10743	202	21	with	with	ADP
fumecheng-10743	202	22	linear	linear	ADJ
fumecheng-10743	202	23	-	-	PUNCT
fumecheng-10743	202	24	plus	plus	CCONJ
fumecheng-10743	202	25	-	-	PUNCT
fumecheng-10743	202	26	cubic	cubic	ADJ
fumecheng-10743	202	27	damping	damping	NOUN
fumecheng-10743	202	28	,	,	PUNCT
fumecheng-10743	202	29	chaos	chaos	NOUN
fumecheng-10743	202	30	,	,	PUNCT
fumecheng-10743	202	31	solitons	soliton	NOUN
fumecheng-10743	202	32	and	and	CCONJ
fumecheng-10743	202	33	fractals	fractal	NOUN
fumecheng-10743	202	34	,	,	PUNCT
fumecheng-10743	202	35	34(4	34(4	NUM
fumecheng-10743	202	36	)	)	PUNCT
fumecheng-10743	202	37	,	,	PUNCT
fumecheng-10743	202	38	pp	pp	ADP
fumecheng-10743	202	39	.	.	PUNCT
fumecheng-10743	203	1	1357	1357	NUM
fumecheng-10743	203	2	-	-	SYM
fumecheng-10743	203	3	1365	1365	NUM
fumecheng-10743	203	4	.	.	PUNCT
fumecheng-10743	204	1	6	6	NUM
fumecheng-10743	204	2	.	.	X
fumecheng-10743	204	3	skrzypacz	skrzypacz	NOUN
fumecheng-10743	204	4	,	,	PUNCT
fumecheng-10743	204	5	p.	p.	PROPN
fumecheng-10743	204	6	,	,	PUNCT
fumecheng-10743	204	7	ellis	ellis	PROPN
fumecheng-10743	204	8	,	,	PUNCT
fumecheng-10743	204	9	g.	g.	PROPN
fumecheng-10743	204	10	,	,	PUNCT
fumecheng-10743	204	11	he	he	PRON
fumecheng-10743	204	12	,	,	PUNCT
fumecheng-10743	204	13	j.h	j.h	PROPN
fumecheng-10743	204	14	.	.	PROPN
fumecheng-10743	204	15	,	,	PUNCT
fumecheng-10743	204	16	he	he	PRON
fumecheng-10743	204	17	,	,	PUNCT
fumecheng-10743	204	18	c.h	c.h	PROPN
fumecheng-10743	204	19	.	.	PROPN
fumecheng-10743	204	20	,	,	PUNCT
fumecheng-10743	204	21	2022	2022	NUM
fumecheng-10743	204	22	,	,	PUNCT
fumecheng-10743	204	23	dynamic	dynamic	ADJ
fumecheng-10743	204	24	pull	pull	NOUN
fumecheng-10743	204	25	-	-	PUNCT
fumecheng-10743	204	26	in	in	NOUN
fumecheng-10743	204	27	and	and	CCONJ
fumecheng-10743	204	28	oscillations	oscillation	NOUN
fumecheng-10743	204	29	of	of	ADP
fumecheng-10743	204	30	current	current	ADJ
fumecheng-10743	204	31	-	-	PUNCT
fumecheng-10743	204	32	carrying	carry	VERB
fumecheng-10743	204	33	filaments	filament	NOUN
fumecheng-10743	204	34	in	in	ADP
fumecheng-10743	204	35	magnetic	magnetic	ADJ
fumecheng-10743	204	36	micro	micro	ADJ
fumecheng-10743	204	37	-	-	ADJ
fumecheng-10743	204	38	electro	electro	ADJ
fumecheng-10743	204	39	-	-	PUNCT
fumecheng-10743	204	40	mechanical	mechanical	ADJ
fumecheng-10743	204	41	system	system	NOUN
fumecheng-10743	204	42	,	,	PUNCT
fumecheng-10743	204	43	communications	communication	NOUN
fumecheng-10743	204	44	in	in	ADP
fumecheng-10743	204	45	nonlinear	nonlinear	ADJ
fumecheng-10743	204	46	science	science	NOUN
fumecheng-10743	204	47	and	and	CCONJ
fumecheng-10743	204	48	numerical	numerical	PROPN
fumecheng-10743	204	49	simulation	simulation	PROPN
fumecheng-10743	204	50	,	,	PUNCT
fumecheng-10743	204	51	109	109	NUM
fumecheng-10743	204	52	,	,	PUNCT
fumecheng-10743	204	53	106350	106350	NUM
fumecheng-10743	204	54	.	.	PUNCT
fumecheng-10743	205	1	7	7	X
fumecheng-10743	205	2	.	.	X
fumecheng-10743	205	3	tian	tian	PROPN
fumecheng-10743	205	4	,	,	PUNCT
fumecheng-10743	205	5	d.	d.	PROPN
fumecheng-10743	205	6	,	,	PUNCT
fumecheng-10743	205	7	he	he	PRON
fumecheng-10743	205	8	,	,	PUNCT
fumecheng-10743	205	9	c.h	c.h	PROPN
fumecheng-10743	205	10	.	.	PROPN
fumecheng-10743	205	11	,	,	PUNCT
fumecheng-10743	205	12	2021	2021	NUM
fumecheng-10743	205	13	,	,	PUNCT
fumecheng-10743	205	14	a	a	DET
fumecheng-10743	205	15	fractal	fractal	ADJ
fumecheng-10743	205	16	micro	micro	ADJ
fumecheng-10743	205	17	-	-	ADJ
fumecheng-10743	205	18	electromechanical	electromechanical	ADJ
fumecheng-10743	205	19	system	system	NOUN
fumecheng-10743	205	20	and	and	CCONJ
fumecheng-10743	205	21	its	its	PRON
fumecheng-10743	205	22	pull	pull	NOUN
fumecheng-10743	205	23	-	-	PUNCT
fumecheng-10743	205	24	in	in	ADP
fumecheng-10743	205	25	stability	stability	NOUN
fumecheng-10743	205	26	,	,	PUNCT
fumecheng-10743	205	27	journal	journal	NOUN
fumecheng-10743	205	28	of	of	ADP
fumecheng-10743	205	29	low	low	ADJ
fumecheng-10743	205	30	frequency	frequency	NOUN
fumecheng-10743	205	31	noise	noise	NOUN
fumecheng-10743	205	32	,	,	PUNCT
fumecheng-10743	205	33	vibration	vibration	NOUN
fumecheng-10743	205	34	&	&	CCONJ
fumecheng-10743	205	35	active	active	ADJ
fumecheng-10743	205	36	control	control	NOUN
fumecheng-10743	205	37	,	,	PUNCT
fumecheng-10743	205	38	40(3	40(3	NUM
fumecheng-10743	205	39	)	)	PUNCT
fumecheng-10743	205	40	,	,	PUNCT
fumecheng-10743	205	41	pp	pp	ADP
fumecheng-10743	205	42	.	.	PUNCT
fumecheng-10743	206	1	1380	1380	NUM
fumecheng-10743	206	2	-	-	SYM
fumecheng-10743	206	3	1386	1386	NUM
fumecheng-10743	206	4	.	.	PUNCT
fumecheng-10743	207	1	8	8	NUM
fumecheng-10743	207	2	.	.	X
fumecheng-10743	208	1	ji	ji	PROPN
fumecheng-10743	208	2	,	,	PUNCT
fumecheng-10743	208	3	q.p	q.p	PROPN
fumecheng-10743	208	4	.	.	PROPN
fumecheng-10743	208	5	,	,	PUNCT
fumecheng-10743	208	6	wang	wang	PROPN
fumecheng-10743	208	7	,	,	PUNCT
fumecheng-10743	208	8	j.	j.	PROPN
fumecheng-10743	208	9	,	,	PUNCT
fumecheng-10743	208	10	lu	lu	PROPN
fumecheng-10743	208	11	,	,	PUNCT
fumecheng-10743	208	12	l.x	l.x	PROPN
fumecheng-10743	208	13	.	.	PROPN
fumecheng-10743	208	14	,	,	PUNCT
fumecheng-10743	208	15	ge	ge	PROPN
fumecheng-10743	208	16	,	,	PUNCT
fumecheng-10743	208	17	c.f	c.f	PROPN
fumecheng-10743	208	18	.	.	PROPN
fumecheng-10743	208	19	,	,	PUNCT
fumecheng-10743	208	20	2021	2021	NUM
fumecheng-10743	208	21	,	,	PUNCT
fumecheng-10743	208	22	li	li	PROPN
fumecheng-10743	208	23	-	-	PROPN
fumecheng-10743	208	24	he	he	PRON
fumecheng-10743	208	25	's	's	PART
fumecheng-10743	208	26	modified	modify	VERB
fumecheng-10743	208	27	homotopy	homotopy	NOUN
fumecheng-10743	208	28	perturbation	perturbation	NOUN
fumecheng-10743	208	29	method	method	NOUN
fumecheng-10743	208	30	coupled	couple	VERB
fumecheng-10743	208	31	with	with	ADP
fumecheng-10743	208	32	the	the	DET
fumecheng-10743	208	33	energy	energy	NOUN
fumecheng-10743	208	34	method	method	NOUN
fumecheng-10743	208	35	for	for	ADP
fumecheng-10743	208	36	the	the	DET
fumecheng-10743	208	37	dropping	drop	VERB
fumecheng-10743	208	38	shock	shock	NOUN
fumecheng-10743	208	39	response	response	NOUN
fumecheng-10743	208	40	of	of	ADP
fumecheng-10743	208	41	a	a	DET
fumecheng-10743	208	42	tangent	tangent	ADJ
fumecheng-10743	208	43	nonlinear	nonlinear	ADJ
fumecheng-10743	208	44	packaging	packaging	NOUN
fumecheng-10743	208	45	system	system	NOUN
fumecheng-10743	208	46	,	,	PUNCT
fumecheng-10743	208	47	journal	journal	NOUN
fumecheng-10743	208	48	of	of	ADP
fumecheng-10743	208	49	low	low	ADJ
fumecheng-10743	208	50	frequency	frequency	NOUN
fumecheng-10743	208	51	noise	noise	NOUN
fumecheng-10743	208	52	,	,	PUNCT
fumecheng-10743	208	53	vibration	vibration	NOUN
fumecheng-10743	208	54	&	&	CCONJ
fumecheng-10743	208	55	active	active	ADJ
fumecheng-10743	208	56	control	control	NOUN
fumecheng-10743	208	57	,	,	PUNCT
fumecheng-10743	208	58	40(2	40(2	NUM
fumecheng-10743	208	59	)	)	PUNCT
fumecheng-10743	208	60	,	,	PUNCT
fumecheng-10743	209	1	pp	pp	ADJ
fumecheng-10743	209	2	.	.	PUNCT
fumecheng-10743	210	1	675	675	NUM
fumecheng-10743	210	2	-	-	SYM
fumecheng-10743	210	3	682	682	NUM
fumecheng-10743	210	4	.	.	PUNCT
fumecheng-10743	211	1	9	9	NUM
fumecheng-10743	211	2	.	.	X
fumecheng-10743	211	3	shen	shen	PROPN
fumecheng-10743	211	4	,	,	PUNCT
fumecheng-10743	211	5	y.	y.	PROPN
fumecheng-10743	211	6	,	,	PUNCT
fumecheng-10743	211	7	el	el	PROPN
fumecheng-10743	211	8	-	-	PUNCT
fumecheng-10743	211	9	dib	dib	PROPN
fumecheng-10743	211	10	,	,	PUNCT
fumecheng-10743	211	11	y.o	y.o	PROPN
fumecheng-10743	211	12	.	.	PROPN
fumecheng-10743	211	13	,	,	PUNCT
fumecheng-10743	211	14	2021	2021	NUM
fumecheng-10743	211	15	,	,	PUNCT
fumecheng-10743	211	16	a	a	DET
fumecheng-10743	211	17	periodic	periodic	ADJ
fumecheng-10743	211	18	solution	solution	NOUN
fumecheng-10743	211	19	of	of	ADP
fumecheng-10743	211	20	the	the	DET
fumecheng-10743	211	21	fractional	fractional	ADJ
fumecheng-10743	211	22	sine	sine	NOUN
fumecheng-10743	211	23	-	-	PUNCT
fumecheng-10743	211	24	gordon	gordon	NOUN
fumecheng-10743	211	25	equation	equation	NOUN
fumecheng-10743	211	26	arising	arise	VERB
fumecheng-10743	211	27	in	in	ADP
fumecheng-10743	211	28	architectural	architectural	ADJ
fumecheng-10743	211	29	engineering	engineering	NOUN
fumecheng-10743	211	30	,	,	PUNCT
fumecheng-10743	211	31	journal	journal	NOUN
fumecheng-10743	211	32	of	of	ADP
fumecheng-10743	211	33	low	low	ADJ
fumecheng-10743	211	34	frequency	frequency	NOUN
fumecheng-10743	211	35	noise	noise	NOUN
fumecheng-10743	211	36	,	,	PUNCT
fumecheng-10743	211	37	vibration	vibration	NOUN
fumecheng-10743	211	38	&	&	CCONJ
fumecheng-10743	211	39	active	active	ADJ
fumecheng-10743	211	40	control	control	NOUN
fumecheng-10743	211	41	,	,	PUNCT
fumecheng-10743	211	42	40(2	40(2	NUM
fumecheng-10743	211	43	)	)	PUNCT
fumecheng-10743	211	44	,	,	PUNCT
fumecheng-10743	211	45	pp	pp	ADJ
fumecheng-10743	211	46	.	.	PUNCT
fumecheng-10743	212	1	683	683	NUM
fumecheng-10743	212	2	-	-	SYM
fumecheng-10743	212	3	691	691	NUM
fumecheng-10743	212	4	.	.	PUNCT
fumecheng-10743	213	1	10	10	NUM
fumecheng-10743	213	2	.	.	X
fumecheng-10743	214	1	mitrev	mitrev	PROPN
fumecheng-10743	214	2	,	,	PUNCT
fumecheng-10743	214	3	r.	r.	PROPN
fumecheng-10743	214	4	,	,	PUNCT
fumecheng-10743	214	5	janošević	janošević	PROPN
fumecheng-10743	214	6	,	,	PUNCT
fumecheng-10743	214	7	d.	d.	PROPN
fumecheng-10743	214	8	,	,	PUNCT
fumecheng-10743	214	9	marinković	marinković	PROPN
fumecheng-10743	214	10	,	,	PUNCT
fumecheng-10743	214	11	d.	d.	PROPN
fumecheng-10743	214	12	,	,	PUNCT
fumecheng-10743	214	13	2017	2017	NUM
fumecheng-10743	214	14	,	,	PUNCT
fumecheng-10743	214	15	dynamical	dynamical	ADJ
fumecheng-10743	214	16	modelling	modelling	NOUN
fumecheng-10743	214	17	of	of	ADP
fumecheng-10743	214	18	hydraulic	hydraulic	ADJ
fumecheng-10743	214	19	excavator	excavator	NOUN
fumecheng-10743	214	20	considered	consider	VERB
fumecheng-10743	214	21	as	as	ADP
fumecheng-10743	214	22	a	a	DET
fumecheng-10743	214	23	multibody	multibody	ADJ
fumecheng-10743	214	24	system	system	NOUN
fumecheng-10743	214	25	,	,	PUNCT
fumecheng-10743	214	26	tehnicki	tehnicki	NOUN
fumecheng-10743	214	27	vjesnik	vjesnik	PROPN
fumecheng-10743	214	28	,	,	PUNCT
fumecheng-10743	214	29	24	24	NUM
fumecheng-10743	214	30	,	,	PUNCT
fumecheng-10743	214	31	pp	pp	ADJ
fumecheng-10743	214	32	.	.	PUNCT
fumecheng-10743	215	1	327	327	NUM
fumecheng-10743	215	2	-	-	SYM
fumecheng-10743	215	3	338	338	NUM
fumecheng-10743	215	4	.	.	PUNCT
fumecheng-10743	216	1	11	11	NUM
fumecheng-10743	216	2	.	.	PUNCT
fumecheng-10743	217	1	he	he	PRON
fumecheng-10743	217	2	,	,	PUNCT
fumecheng-10743	217	3	j.h	j.h	PROPN
fumecheng-10743	217	4	.	.	PROPN
fumecheng-10743	217	5	,	,	PUNCT
fumecheng-10743	217	6	amer	amer	PROPN
fumecheng-10743	217	7	,	,	PUNCT
fumecheng-10743	217	8	t.s	t.s	PROPN
fumecheng-10743	217	9	.	.	PROPN
fumecheng-10743	217	10	,	,	PUNCT
fumecheng-10743	217	11	elnaggar	elnaggar	PROPN
fumecheng-10743	217	12	,	,	PUNCT
fumecheng-10743	217	13	s.	s.	PROPN
fumecheng-10743	217	14	,	,	PUNCT
fumecheng-10743	217	15	galal	galal	PROPN
fumecheng-10743	217	16	,	,	PUNCT
fumecheng-10743	217	17	a.a	a.a	PROPN
fumecheng-10743	217	18	.	.	PROPN
fumecheng-10743	217	19	,	,	PUNCT
fumecheng-10743	217	20	2021	2021	NUM
fumecheng-10743	217	21	,	,	PUNCT
fumecheng-10743	217	22	periodic	periodic	ADJ
fumecheng-10743	217	23	property	property	NOUN
fumecheng-10743	217	24	and	and	CCONJ
fumecheng-10743	217	25	instability	instability	NOUN
fumecheng-10743	217	26	of	of	ADP
fumecheng-10743	217	27	a	a	DET
fumecheng-10743	217	28	rotating	rotate	VERB
fumecheng-10743	217	29	pendulum	pendulum	NOUN
fumecheng-10743	217	30	system	system	NOUN
fumecheng-10743	217	31	,	,	PUNCT
fumecheng-10743	217	32	axioms	axiom	NOUN
fumecheng-10743	217	33	,	,	PUNCT
fumecheng-10743	217	34	10(3	10(3	NUM
fumecheng-10743	217	35	)	)	PUNCT
fumecheng-10743	217	36	,	,	PUNCT
fumecheng-10743	217	37	191	191	NUM
fumecheng-10743	217	38	.	.	NOUN
fumecheng-10743	217	39	12	12	NUM
fumecheng-10743	217	40	.	.	PUNCT
fumecheng-10743	218	1	he	he	PRON
fumecheng-10743	218	2	,	,	PUNCT
fumecheng-10743	218	3	j.h	j.h	PROPN
fumecheng-10743	218	4	.	.	PROPN
fumecheng-10743	218	5	,	,	PUNCT
fumecheng-10743	218	6	amer	amer	PROPN
fumecheng-10743	218	7	,	,	PUNCT
fumecheng-10743	218	8	t.s	t.s	PROPN
fumecheng-10743	218	9	.	.	PROPN
fumecheng-10743	218	10	,	,	PUNCT
fumecheng-10743	218	11	el	el	PROPN
fumecheng-10743	218	12	-	-	PUNCT
fumecheng-10743	218	13	kafly	kafly	NOUN
fumecheng-10743	218	14	,	,	PUNCT
fumecheng-10743	218	15	h.f	h.f	PROPN
fumecheng-10743	218	16	.	.	PROPN
fumecheng-10743	218	17	,	,	PUNCT
fumecheng-10743	218	18	galal	galal	PROPN
fumecheng-10743	218	19	,	,	PUNCT
fumecheng-10743	218	20	a.a	a.a	PROPN
fumecheng-10743	218	21	.	.	PROPN
fumecheng-10743	218	22	,	,	PUNCT
fumecheng-10743	218	23	2022	2022	NUM
fumecheng-10743	218	24	,	,	PUNCT
fumecheng-10743	218	25	modelling	modelling	NOUN
fumecheng-10743	218	26	of	of	ADP
fumecheng-10743	218	27	the	the	DET
fumecheng-10743	218	28	rotational	rotational	ADJ
fumecheng-10743	218	29	motion	motion	NOUN
fumecheng-10743	218	30	of	of	ADP
fumecheng-10743	218	31	6	6	NUM
fumecheng-10743	218	32	-	-	PUNCT
fumecheng-10743	218	33	dof	dof	ADJ
fumecheng-10743	218	34	rigid	rigid	ADJ
fumecheng-10743	218	35	body	body	NOUN
fumecheng-10743	218	36	according	accord	VERB
fumecheng-10743	218	37	to	to	ADP
fumecheng-10743	218	38	the	the	DET
fumecheng-10743	218	39	bobylev	bobylev	NOUN
fumecheng-10743	218	40	-	-	PUNCT
fumecheng-10743	218	41	steklov	steklov	NOUN
fumecheng-10743	218	42	conditions	condition	NOUN
fumecheng-10743	218	43	,	,	PUNCT
fumecheng-10743	218	44	results	result	NOUN
fumecheng-10743	218	45	in	in	ADP
fumecheng-10743	218	46	physics	physics	NOUN
fumecheng-10743	218	47	,	,	PUNCT
fumecheng-10743	218	48	35(2022	35(2022	NOUN
fumecheng-10743	218	49	)	)	PUNCT
fumecheng-10743	218	50	,	,	PUNCT
fumecheng-10743	218	51	105391	105391	NUM
fumecheng-10743	218	52	.	.	PUNCT
fumecheng-10743	219	1	13	13	NUM
fumecheng-10743	219	2	.	.	PUNCT
fumecheng-10743	220	1	he	he	PRON
fumecheng-10743	220	2	,	,	PUNCT
fumecheng-10743	220	3	c.h	c.h	PROPN
fumecheng-10743	220	4	.	.	PROPN
fumecheng-10743	220	5	,	,	PUNCT
fumecheng-10743	220	6	tian	tian	PROPN
fumecheng-10743	220	7	,	,	PUNCT
fumecheng-10743	220	8	d.	d.	PROPN
fumecheng-10743	220	9	,	,	PUNCT
fumecheng-10743	220	10	moatimid	moatimid	PROPN
fumecheng-10743	220	11	,	,	PUNCT
fumecheng-10743	220	12	g.m	g.m	PROPN
fumecheng-10743	220	13	.	.	PROPN
fumecheng-10743	220	14	,	,	PUNCT
fumecheng-10743	220	15	salman	salman	PROPN
fumecheng-10743	220	16	,	,	PUNCT
fumecheng-10743	220	17	h.f	h.f	PROPN
fumecheng-10743	220	18	.	.	PROPN
fumecheng-10743	220	19	,	,	PUNCT
fumecheng-10743	220	20	zekry	zekry	PROPN
fumecheng-10743	220	21	,	,	PUNCT
fumecheng-10743	220	22	m.h	m.h	PROPN
fumecheng-10743	220	23	.	.	PROPN
fumecheng-10743	220	24	,	,	PUNCT
fumecheng-10743	220	25	2022	2022	NUM
fumecheng-10743	220	26	,	,	PUNCT
fumecheng-10743	220	27	hybrid	hybrid	ADJ
fumecheng-10743	220	28	rayleigh	rayleigh	PROPN
fumecheng-10743	220	29	-van	-van	PROPN
fumecheng-10743	220	30	der	der	ADJ
fumecheng-10743	220	31	pol	pol	NOUN
fumecheng-10743	220	32	-	-	PUNCT
fumecheng-10743	220	33	duffing	duffe	VERB
fumecheng-10743	220	34	oscillator	oscillator	NOUN
fumecheng-10743	220	35	:	:	PUNCT
fumecheng-10743	220	36	stability	stability	NOUN
fumecheng-10743	220	37	analysis	analysis	NOUN
fumecheng-10743	220	38	and	and	CCONJ
fumecheng-10743	220	39	controller	controller	NOUN
fumecheng-10743	220	40	,	,	PUNCT
fumecheng-10743	220	41	journal	journal	NOUN
fumecheng-10743	220	42	of	of	ADP
fumecheng-10743	220	43	low	low	ADJ
fumecheng-10743	220	44	frequency	frequency	NOUN
fumecheng-10743	220	45	noise	noise	NOUN
fumecheng-10743	220	46	,	,	PUNCT
fumecheng-10743	220	47	vibration	vibration	NOUN
fumecheng-10743	220	48	&	&	CCONJ
fumecheng-10743	220	49	active	active	ADJ
fumecheng-10743	220	50	control	control	NOUN
fumecheng-10743	220	51	,	,	PUNCT
fumecheng-10743	220	52	41(1	41(1	NUM
fumecheng-10743	220	53	)	)	PUNCT
fumecheng-10743	220	54	,	,	PUNCT
fumecheng-10743	220	55	pp	pp	PROPN
fumecheng-10743	220	56	.	.	PUNCT
fumecheng-10743	221	1	244	244	NUM
fumecheng-10743	221	2	-	-	SYM
fumecheng-10743	221	3	268	268	NUM
fumecheng-10743	221	4	.	.	PUNCT
fumecheng-10743	222	1	14	14	NUM
fumecheng-10743	222	2	.	.	PUNCT
fumecheng-10743	223	1	he	he	PRON
fumecheng-10743	223	2	,	,	PUNCT
fumecheng-10743	223	3	c.h	c.h	PROPN
fumecheng-10743	223	4	.	.	PROPN
fumecheng-10743	223	5	,	,	PUNCT
fumecheng-10743	223	6	amer	amer	PROPN
fumecheng-10743	223	7	,	,	PUNCT
fumecheng-10743	223	8	t.s	t.s	PROPN
fumecheng-10743	223	9	.	.	PROPN
fumecheng-10743	223	10	,	,	PUNCT
fumecheng-10743	223	11	tian	tian	PROPN
fumecheng-10743	223	12	,	,	PUNCT
fumecheng-10743	223	13	d.	d.	PROPN
fumecheng-10743	223	14	,	,	PUNCT
fumecheng-10743	223	15	abolila	abolila	PROPN
fumecheng-10743	223	16	,	,	PUNCT
fumecheng-10743	223	17	a.f	a.f	PROPN
fumecheng-10743	223	18	.	.	PROPN
fumecheng-10743	223	19	,	,	PUNCT
fumecheng-10743	223	20	galal	galal	PROPN
fumecheng-10743	223	21	,	,	PUNCT
fumecheng-10743	223	22	a.a	a.a	PROPN
fumecheng-10743	223	23	.	.	PROPN
fumecheng-10743	223	24	,	,	PUNCT
fumecheng-10743	223	25	2022	2022	NUM
fumecheng-10743	223	26	,	,	PUNCT
fumecheng-10743	223	27	controlling	control	VERB
fumecheng-10743	223	28	the	the	DET
fumecheng-10743	223	29	kinematics	kinematic	NOUN
fumecheng-10743	223	30	of	of	ADP
fumecheng-10743	223	31	a	a	DET
fumecheng-10743	223	32	spring	spring	NOUN
fumecheng-10743	223	33	-	-	PUNCT
fumecheng-10743	223	34	pendulum	pendulum	NOUN
fumecheng-10743	223	35	system	system	NOUN
fumecheng-10743	223	36	using	use	VERB
fumecheng-10743	223	37	an	an	DET
fumecheng-10743	223	38	energy	energy	NOUN
fumecheng-10743	223	39	harvesting	harvesting	NOUN
fumecheng-10743	223	40	device	device	NOUN
fumecheng-10743	223	41	,	,	PUNCT
fumecheng-10743	223	42	journal	journal	NOUN
fumecheng-10743	223	43	of	of	ADP
fumecheng-10743	223	44	low	low	ADJ
fumecheng-10743	223	45	frequency	frequency	NOUN
fumecheng-10743	223	46	noise	noise	NOUN
fumecheng-10743	223	47	,	,	PUNCT
fumecheng-10743	223	48	vibration	vibration	NOUN
fumecheng-10743	223	49	&	&	CCONJ
fumecheng-10743	223	50	active	active	ADJ
fumecheng-10743	223	51	control	control	NOUN
fumecheng-10743	223	52	,	,	PUNCT
fumecheng-10743	223	53	doi	doi	NOUN
fumecheng-10743	223	54	:	:	PUNCT
fumecheng-10743	223	55	10.1177/14613484221077474	10.1177/14613484221077474	NUM
fumecheng-10743	223	56	.	.	PROPN
fumecheng-10743	224	1	15	15	NUM
fumecheng-10743	224	2	.	.	X
fumecheng-10743	225	1	wang	wang	PROPN
fumecheng-10743	225	2	,	,	PUNCT
fumecheng-10743	225	3	k.l	k.l	PROPN
fumecheng-10743	225	4	.	.	PROPN
fumecheng-10743	225	5	,	,	PUNCT
fumecheng-10743	225	6	wei	wei	PROPN
fumecheng-10743	225	7	,	,	PUNCT
fumecheng-10743	225	8	c.f	c.f	PROPN
fumecheng-10743	225	9	.	.	PROPN
fumecheng-10743	225	10	,	,	PUNCT
fumecheng-10743	225	11	2021	2021	NUM
fumecheng-10743	225	12	,	,	PUNCT
fumecheng-10743	225	13	a	a	DET
fumecheng-10743	225	14	powerful	powerful	ADJ
fumecheng-10743	225	15	and	and	CCONJ
fumecheng-10743	225	16	simple	simple	ADJ
fumecheng-10743	225	17	frequency	frequency	NOUN
fumecheng-10743	225	18	formula	formula	NOUN
fumecheng-10743	225	19	to	to	PART
fumecheng-10743	225	20	nonlinear	nonlinear	ADJ
fumecheng-10743	225	21	fractal	fractal	ADJ
fumecheng-10743	225	22	oscillators	oscillator	NOUN
fumecheng-10743	225	23	,	,	PUNCT
fumecheng-10743	225	24	journal	journal	NOUN
fumecheng-10743	225	25	of	of	ADP
fumecheng-10743	225	26	low	low	ADJ
fumecheng-10743	225	27	frequency	frequency	NOUN
fumecheng-10743	225	28	noise	noise	NOUN
fumecheng-10743	225	29	,	,	PUNCT
fumecheng-10743	225	30	vibration	vibration	NOUN
fumecheng-10743	225	31	&	&	CCONJ
fumecheng-10743	225	32	active	active	ADJ
fumecheng-10743	225	33	control	control	NOUN
fumecheng-10743	225	34	,	,	PUNCT
fumecheng-10743	225	35	40(3	40(3	NUM
fumecheng-10743	225	36	)	)	PUNCT
fumecheng-10743	225	37	,	,	PUNCT
fumecheng-10743	225	38	pp	pp	ADP
fumecheng-10743	225	39	.	.	PUNCT
fumecheng-10743	225	40	1373	1373	NUM
fumecheng-10743	225	41	-	-	SYM
fumecheng-10743	225	42	1379	1379	NUM
fumecheng-10743	225	43	.	.	PUNCT
fumecheng-10743	226	1	16	16	NUM
fumecheng-10743	226	2	.	.	PUNCT
fumecheng-10743	227	1	feng	feng	PROPN
fumecheng-10743	227	2	,	,	PUNCT
fumecheng-10743	227	3	g.q	g.q	PROPN
fumecheng-10743	227	4	.	.	PROPN
fumecheng-10743	227	5	,	,	PUNCT
fumecheng-10743	227	6	2021	2021	NUM
fumecheng-10743	227	7	,	,	PUNCT
fumecheng-10743	227	8	he	he	PRON
fumecheng-10743	227	9	's	's	PART
fumecheng-10743	227	10	frequency	frequency	NOUN
fumecheng-10743	227	11	formula	formula	NOUN
fumecheng-10743	227	12	to	to	ADP
fumecheng-10743	227	13	fractal	fractal	ADJ
fumecheng-10743	227	14	undamped	undampe	VERB
fumecheng-10743	227	15	duffing	duffing	NOUN
fumecheng-10743	227	16	equation	equation	NOUN
fumecheng-10743	227	17	,	,	PUNCT
fumecheng-10743	227	18	journal	journal	NOUN
fumecheng-10743	227	19	of	of	ADP
fumecheng-10743	227	20	low	low	ADJ
fumecheng-10743	227	21	frequency	frequency	NOUN
fumecheng-10743	227	22	noise	noise	NOUN
fumecheng-10743	227	23	,	,	PUNCT
fumecheng-10743	227	24	vibration	vibration	NOUN
fumecheng-10743	227	25	&	&	CCONJ
fumecheng-10743	227	26	active	active	ADJ
fumecheng-10743	227	27	control	control	NOUN
fumecheng-10743	227	28	,	,	PUNCT
fumecheng-10743	227	29	40(4	40(4	NUM
fumecheng-10743	227	30	)	)	PUNCT
fumecheng-10743	227	31	,	,	PUNCT
fumecheng-10743	227	32	pp	pp	ADP
fumecheng-10743	227	33	.	.	PUNCT
fumecheng-10743	227	34	1671	1671	NUM
fumecheng-10743	227	35	-	-	SYM
fumecheng-10743	227	36	1676	1676	NUM
fumecheng-10743	227	37	.	.	PUNCT
fumecheng-10743	228	1	17	17	NUM
fumecheng-10743	228	2	.	.	PUNCT
fumecheng-10743	229	1	tian	tian	PROPN
fumecheng-10743	229	2	,	,	PUNCT
fumecheng-10743	229	3	y.	y.	NOUN
fumecheng-10743	229	4	,	,	PUNCT
fumecheng-10743	229	5	2022	2022	NUM
fumecheng-10743	229	6	,	,	PUNCT
fumecheng-10743	229	7	frequency	frequency	NOUN
fumecheng-10743	229	8	formula	formula	NOUN
fumecheng-10743	229	9	for	for	ADP
fumecheng-10743	229	10	a	a	DET
fumecheng-10743	229	11	class	class	NOUN
fumecheng-10743	229	12	of	of	ADP
fumecheng-10743	229	13	fractal	fractal	ADJ
fumecheng-10743	229	14	vibration	vibration	NOUN
fumecheng-10743	229	15	system	system	NOUN
fumecheng-10743	229	16	,	,	PUNCT
fumecheng-10743	229	17	reports	report	NOUN
fumecheng-10743	229	18	in	in	ADP
fumecheng-10743	229	19	mechanical	mechanical	ADJ
fumecheng-10743	229	20	engineering	engineering	NOUN
fumecheng-10743	229	21	,	,	PUNCT
fumecheng-10743	229	22	3(1	3(1	NUM
fumecheng-10743	229	23	)	)	PUNCT
fumecheng-10743	229	24	,	,	PUNCT
fumecheng-10743	229	25	pp	pp	ADP
fumecheng-10743	229	26	.	.	PUNCT
fumecheng-10743	230	1	55	55	NUM
fumecheng-10743	230	2	-	-	SYM
fumecheng-10743	230	3	61	61	NUM
fumecheng-10743	230	4	.	.	PUNCT
fumecheng-10743	231	1	18	18	NUM
fumecheng-10743	231	2	.	.	PUNCT
fumecheng-10743	232	1	he	he	PRON
fumecheng-10743	232	2	,	,	PUNCT
fumecheng-10743	232	3	j.h	j.h	PROPN
fumecheng-10743	232	4	.	.	PROPN
fumecheng-10743	232	5	,	,	PUNCT
fumecheng-10743	232	6	2019	2019	NUM
fumecheng-10743	232	7	,	,	PUNCT
fumecheng-10743	232	8	the	the	PRON
fumecheng-10743	232	9	simpler	simple	ADJ
fumecheng-10743	232	10	,	,	PUNCT
fumecheng-10743	232	11	the	the	PRON
fumecheng-10743	232	12	better	well	ADJ
fumecheng-10743	232	13	:	:	PUNCT
fumecheng-10743	232	14	analytical	analytical	ADJ
fumecheng-10743	232	15	methods	method	NOUN
fumecheng-10743	232	16	for	for	ADP
fumecheng-10743	232	17	nonlinear	nonlinear	ADJ
fumecheng-10743	232	18	oscillators	oscillator	NOUN
fumecheng-10743	232	19	and	and	CCONJ
fumecheng-10743	232	20	fractional	fractional	ADJ
fumecheng-10743	232	21	oscillators	oscillator	NOUN
fumecheng-10743	232	22	,	,	PUNCT
fumecheng-10743	232	23	journal	journal	NOUN
fumecheng-10743	232	24	of	of	ADP
fumecheng-10743	232	25	low	low	ADJ
fumecheng-10743	232	26	frequency	frequency	NOUN
fumecheng-10743	232	27	noise	noise	NOUN
fumecheng-10743	232	28	,	,	PUNCT
fumecheng-10743	232	29	vibration	vibration	NOUN
fumecheng-10743	232	30	&	&	CCONJ
fumecheng-10743	232	31	active	active	ADJ
fumecheng-10743	232	32	control	control	NOUN
fumecheng-10743	232	33	,	,	PUNCT
fumecheng-10743	232	34	38(3–4	38(3–4	PROPN
fumecheng-10743	232	35	)	)	PUNCT
fumecheng-10743	232	36	,	,	PUNCT
fumecheng-10743	232	37	pp	pp	PROPN
fumecheng-10743	232	38	.	.	PUNCT
fumecheng-10743	232	39	1252–1260	1252–1260	NUM
fumecheng-10743	232	40	.	.	PUNCT
fumecheng-10743	232	41	19	19	NUM
fumecheng-10743	232	42	.	.	PUNCT
fumecheng-10743	233	1	he	he	PRON
fumecheng-10743	233	2	,	,	PUNCT
fumecheng-10743	233	3	j.h	j.h	PROPN
fumecheng-10743	233	4	.	.	PROPN
fumecheng-10743	233	5	,	,	PUNCT
fumecheng-10743	233	6	el	el	PROPN
fumecheng-10743	233	7	-	-	PUNCT
fumecheng-10743	233	8	dib	dib	PROPN
fumecheng-10743	233	9	,	,	PUNCT
fumecheng-10743	233	10	y.o	y.o	PROPN
fumecheng-10743	233	11	.	.	PROPN
fumecheng-10743	233	12	,	,	PUNCT
fumecheng-10743	233	13	2021	2021	NUM
fumecheng-10743	233	14	,	,	PUNCT
fumecheng-10743	233	15	the	the	DET
fumecheng-10743	233	16	enhanced	enhance	VERB
fumecheng-10743	233	17	homotopy	homotopy	NOUN
fumecheng-10743	233	18	perturbation	perturbation	NOUN
fumecheng-10743	233	19	method	method	NOUN
fumecheng-10743	233	20	for	for	ADP
fumecheng-10743	233	21	axial	axial	ADJ
fumecheng-10743	233	22	vibration	vibration	NOUN
fumecheng-10743	233	23	of	of	ADP
fumecheng-10743	233	24	strings	string	NOUN
fumecheng-10743	233	25	,	,	PUNCT
fumecheng-10743	233	26	facta	facta	PROPN
fumecheng-10743	233	27	universitatis	universitatis	PROPN
fumecheng-10743	233	28	-	-	PUNCT
fumecheng-10743	233	29	series	series	NOUN
fumecheng-10743	233	30	mechanical	mechanical	ADJ
fumecheng-10743	233	31	engineering	engineering	NOUN
fumecheng-10743	233	32	,	,	PUNCT
fumecheng-10743	233	33	19(4	19(4	PROPN
fumecheng-10743	233	34	)	)	PUNCT
fumecheng-10743	233	35	,	,	PUNCT
fumecheng-10743	233	36	pp	pp	PROPN
fumecheng-10743	233	37	.	.	PUNCT
fumecheng-10743	234	1	735	735	NUM
fumecheng-10743	234	2	-	-	SYM
fumecheng-10743	234	3	750	750	NUM
fumecheng-10743	234	4	.	.	PUNCT
fumecheng-10743	235	1	20	20	NUM
fumecheng-10743	235	2	.	.	PUNCT
fumecheng-10743	236	1	he	he	PRON
fumecheng-10743	236	2	,	,	PUNCT
fumecheng-10743	236	3	j.h	j.h	PROPN
fumecheng-10743	236	4	.	.	PROPN
fumecheng-10743	236	5	,	,	PUNCT
fumecheng-10743	236	6	el‐dib	el‐dib	X
fumecheng-10743	236	7	,	,	PUNCT
fumecheng-10743	236	8	y.o	y.o	PROPN
fumecheng-10743	236	9	.	.	PROPN
fumecheng-10743	236	10	,	,	PUNCT
fumecheng-10743	236	11	mady	mady	PROPN
fumecheng-10743	236	12	,	,	PUNCT
fumecheng-10743	236	13	a.a	a.a	PROPN
fumecheng-10743	236	14	.	.	PROPN
fumecheng-10743	236	15	,	,	PUNCT
fumecheng-10743	236	16	2021	2021	NUM
fumecheng-10743	236	17	,	,	PUNCT
fumecheng-10743	236	18	homotopy	homotopy	VERB
fumecheng-10743	236	19	perturbation	perturbation	NOUN
fumecheng-10743	236	20	method	method	NOUN
fumecheng-10743	236	21	for	for	ADP
fumecheng-10743	236	22	the	the	DET
fumecheng-10743	236	23	fractal	fractal	ADJ
fumecheng-10743	236	24	toda	toda	PROPN
fumecheng-10743	236	25	oscillator	oscillator	PROPN
fumecheng-10743	236	26	,	,	PUNCT
fumecheng-10743	236	27	fractal	fractal	ADJ
fumecheng-10743	236	28	and	and	CCONJ
fumecheng-10743	236	29	fractional	fractional	ADJ
fumecheng-10743	236	30	,	,	PUNCT
fumecheng-10743	236	31	5(2021	5(2021	NUM
fumecheng-10743	236	32	)	)	PUNCT
fumecheng-10743	236	33	,	,	PUNCT
fumecheng-10743	236	34	93	93	NUM
fumecheng-10743	236	35	.	.	PUNCT
fumecheng-10743	237	1	21	21	NUM
fumecheng-10743	237	2	.	.	PUNCT
fumecheng-10743	238	1	he	he	PRON
fumecheng-10743	238	2	,	,	PUNCT
fumecheng-10743	238	3	c.h	c.h	PROPN
fumecheng-10743	238	4	.	.	PROPN
fumecheng-10743	238	5	,	,	PUNCT
fumecheng-10743	238	6	el	el	PROPN
fumecheng-10743	238	7	-	-	PUNCT
fumecheng-10743	238	8	dib	dib	PROPN
fumecheng-10743	238	9	,	,	PUNCT
fumecheng-10743	238	10	y.o	y.o	PROPN
fumecheng-10743	238	11	.	.	PROPN
fumecheng-10743	238	12	,	,	PUNCT
fumecheng-10743	238	13	2022	2022	NUM
fumecheng-10743	238	14	,	,	PUNCT
fumecheng-10743	238	15	a	a	DET
fumecheng-10743	238	16	heuristic	heuristic	ADJ
fumecheng-10743	238	17	review	review	NOUN
fumecheng-10743	238	18	on	on	ADP
fumecheng-10743	238	19	the	the	DET
fumecheng-10743	238	20	homotopy	homotopy	NOUN
fumecheng-10743	238	21	perturbation	perturbation	NOUN
fumecheng-10743	238	22	method	method	NOUN
fumecheng-10743	238	23	for	for	ADP
fumecheng-10743	238	24	non	non	ADJ
fumecheng-10743	238	25	-	-	ADJ
fumecheng-10743	238	26	conservative	conservative	ADJ
fumecheng-10743	238	27	oscillators	oscillator	NOUN
fumecheng-10743	238	28	,	,	PUNCT
fumecheng-10743	238	29	journal	journal	NOUN
fumecheng-10743	238	30	of	of	ADP
fumecheng-10743	238	31	low	low	ADJ
fumecheng-10743	238	32	frequency	frequency	NOUN
fumecheng-10743	238	33	noise	noise	NOUN
fumecheng-10743	238	34	,	,	PUNCT
fumecheng-10743	238	35	vibration	vibration	NOUN
fumecheng-10743	238	36	&	&	CCONJ
fumecheng-10743	238	37	active	active	ADJ
fumecheng-10743	238	38	control	control	NOUN
fumecheng-10743	238	39	,	,	PUNCT
fumecheng-10743	238	40	doi	doi	NOUN
fumecheng-10743	238	41	:	:	PUNCT
fumecheng-10743	238	42	10.1177/14613484211059264	10.1177/14613484211059264	NUM
fumecheng-10743	238	43	.	.	X
fumecheng-10743	238	44	22	22	NUM
fumecheng-10743	238	45	.	.	PUNCT
fumecheng-10743	239	1	nadeem	nadeem	PROPN
fumecheng-10743	239	2	,	,	PUNCT
fumecheng-10743	239	3	m.	m.	NOUN
fumecheng-10743	239	4	,	,	PUNCT
fumecheng-10743	239	5	he	he	PRON
fumecheng-10743	239	6	,	,	PUNCT
fumecheng-10743	239	7	j.h	j.h	PROPN
fumecheng-10743	239	8	.	.	PROPN
fumecheng-10743	239	9	,	,	PUNCT
fumecheng-10743	239	10	2021	2021	NUM
fumecheng-10743	239	11	,	,	PUNCT
fumecheng-10743	239	12	he	he	PRON
fumecheng-10743	239	13	-	-	PUNCT
fumecheng-10743	239	14	laplace	laplace	NOUN
fumecheng-10743	239	15	variational	variational	ADJ
fumecheng-10743	239	16	iteration	iteration	NOUN
fumecheng-10743	239	17	method	method	NOUN
fumecheng-10743	239	18	for	for	ADP
fumecheng-10743	239	19	solving	solve	VERB
fumecheng-10743	239	20	the	the	DET
fumecheng-10743	239	21	nonlinear	nonlinear	ADJ
fumecheng-10743	239	22	equations	equation	NOUN
fumecheng-10743	239	23	arising	arise	VERB
fumecheng-10743	239	24	in	in	ADP
fumecheng-10743	239	25	chemical	chemical	ADJ
fumecheng-10743	239	26	kinetics	kinetic	NOUN
fumecheng-10743	239	27	and	and	CCONJ
fumecheng-10743	239	28	population	population	NOUN
fumecheng-10743	239	29	dynamics	dynamic	NOUN
fumecheng-10743	239	30	,	,	PUNCT
fumecheng-10743	239	31	journal	journal	NOUN
fumecheng-10743	239	32	of	of	ADP
fumecheng-10743	239	33	mathematical	mathematical	ADJ
fumecheng-10743	239	34	chemistry	chemistry	NOUN
fumecheng-10743	239	35	,	,	PUNCT
fumecheng-10743	239	36	59(5	59(5	NUM
fumecheng-10743	239	37	)	)	PUNCT
fumecheng-10743	239	38	,	,	PUNCT
fumecheng-10743	239	39	pp	pp	PROPN
fumecheng-10743	239	40	.	.	PUNCT
fumecheng-10743	240	1	1234	1234	NUM
fumecheng-10743	240	2	-	-	SYM
fumecheng-10743	240	3	1245	1245	NUM
fumecheng-10743	240	4	.	.	PUNCT
fumecheng-10743	241	1	23	23	NUM
fumecheng-10743	241	2	.	.	X
fumecheng-10743	242	1	anjum	anjum	PROPN
fumecheng-10743	242	2	,	,	PUNCT
fumecheng-10743	242	3	n.	n.	PROPN
fumecheng-10743	242	4	,	,	PUNCT
fumecheng-10743	242	5	he	he	PRON
fumecheng-10743	242	6	,	,	PUNCT
fumecheng-10743	242	7	j.h	j.h	PROPN
fumecheng-10743	242	8	.	.	PROPN
fumecheng-10743	242	9	,	,	PUNCT
fumecheng-10743	242	10	2020	2020	NUM
fumecheng-10743	242	11	,	,	PUNCT
fumecheng-10743	242	12	analysis	analysis	NOUN
fumecheng-10743	242	13	of	of	ADP
fumecheng-10743	242	14	nonlinear	nonlinear	ADJ
fumecheng-10743	242	15	vibration	vibration	NOUN
fumecheng-10743	242	16	of	of	ADP
fumecheng-10743	242	17	nano	nano	NOUN
fumecheng-10743	242	18	/	/	SYM
fumecheng-10743	242	19	microelectromechanical	microelectromechanical	ADJ
fumecheng-10743	242	20	system	system	NOUN
fumecheng-10743	242	21	switch	switch	NOUN
fumecheng-10743	242	22	induced	induce	VERB
fumecheng-10743	242	23	by	by	ADP
fumecheng-10743	242	24	electromagnetic	electromagnetic	ADJ
fumecheng-10743	242	25	force	force	NOUN
fumecheng-10743	242	26	under	under	ADP
fumecheng-10743	242	27	zero	zero	NUM
fumecheng-10743	242	28	initial	initial	ADJ
fumecheng-10743	242	29	conditions	condition	NOUN
fumecheng-10743	242	30	,	,	PUNCT
fumecheng-10743	242	31	alexandria	alexandria	PROPN
fumecheng-10743	242	32	engineering	engineering	PROPN
fumecheng-10743	242	33	journal	journal	PROPN
fumecheng-10743	242	34	,	,	PUNCT
fumecheng-10743	242	35	59(6	59(6	NUM
fumecheng-10743	242	36	)	)	PUNCT
fumecheng-10743	242	37	,	,	PUNCT
fumecheng-10743	242	38	pp	pp	PROPN
fumecheng-10743	242	39	.	.	PUNCT
fumecheng-10743	242	40	4343	4343	NUM
fumecheng-10743	242	41	-	-	SYM
fumecheng-10743	242	42	4352	4352	NUM
fumecheng-10743	242	43	.	.	PUNCT
fumecheng-10743	243	1	24	24	NUM
fumecheng-10743	243	2	.	.	X
fumecheng-10743	243	3	skrzypacz	skrzypacz	NOUN
fumecheng-10743	243	4	,	,	PUNCT
fumecheng-10743	243	5	p.	p.	PROPN
fumecheng-10743	243	6	,	,	PUNCT
fumecheng-10743	243	7	he	he	PRON
fumecheng-10743	243	8	,	,	PUNCT
fumecheng-10743	243	9	j.h	j.h	PROPN
fumecheng-10743	243	10	.	.	PROPN
fumecheng-10743	243	11	,	,	PUNCT
fumecheng-10743	243	12	ellis	ellis	PROPN
fumecheng-10743	243	13	,	,	PUNCT
fumecheng-10743	243	14	g.	g.	PROPN
fumecheng-10743	243	15	,	,	PUNCT
fumecheng-10743	243	16	kuanyshbay	kuanyshbay	ADJ
fumecheng-10743	243	17	,	,	PUNCT
fumecheng-10743	243	18	m.	m.	NOUN
fumecheng-10743	243	19	,	,	PUNCT
fumecheng-10743	243	20	2020	2020	NUM
fumecheng-10743	243	21	,	,	PUNCT
fumecheng-10743	243	22	a	a	DET
fumecheng-10743	243	23	simple	simple	ADJ
fumecheng-10743	243	24	approximation	approximation	NOUN
fumecheng-10743	243	25	of	of	ADP
fumecheng-10743	243	26	periodic	periodic	ADJ
fumecheng-10743	243	27	solutions	solution	NOUN
fumecheng-10743	243	28	to	to	ADP
fumecheng-10743	243	29	microelectromechanical	microelectromechanical	ADJ
fumecheng-10743	243	30	system	system	NOUN
fumecheng-10743	243	31	model	model	NOUN
fumecheng-10743	243	32	of	of	ADP
fumecheng-10743	243	33	oscillating	oscillate	VERB
fumecheng-10743	243	34	parallel	parallel	ADJ
fumecheng-10743	243	35	plate	plate	NOUN
fumecheng-10743	243	36	capacitor	capacitor	NOUN
fumecheng-10743	243	37	,	,	PUNCT
fumecheng-10743	243	38	mathematical	mathematical	ADJ
fumecheng-10743	243	39	methods	method	NOUN
fumecheng-10743	243	40	in	in	ADP
fumecheng-10743	243	41	the	the	DET
fumecheng-10743	243	42	applied	apply	VERB
fumecheng-10743	243	43	science	science	NOUN
fumecheng-10743	243	44	,	,	PUNCT
fumecheng-10743	243	45	doi	doi	NOUN
fumecheng-10743	243	46	:	:	PUNCT
fumecheng-10743	243	47	10.1002	10.1002	NUM
fumecheng-10743	243	48	/	/	SYM
fumecheng-10743	243	49	mma.6898	mma.6898	PROPN
fumecheng-10743	243	50	.	.	PUNCT
fumecheng-10743	244	1	simplified	simplify	VERB
fumecheng-10743	244	2	hamiltonian	hamiltonian	NOUN
fumecheng-10743	244	3	-	-	PUNCT
fumecheng-10743	244	4	based	base	VERB
fumecheng-10743	244	5	frequency	frequency	NOUN
fumecheng-10743	244	6	-	-	PUNCT
fumecheng-10743	244	7	amplitude	amplitude	NOUN
fumecheng-10743	244	8	formulation	formulation	NOUN
fumecheng-10743	244	9	for	for	ADP
fumecheng-10743	244	10	nonlinear	nonlinear	ADJ
fumecheng-10743	244	11	vibration	vibration	NOUN
fumecheng-10743	244	12	systems	system	NOUN
fumecheng-10743	244	13	455	455	NUM
fumecheng-10743	244	14	25	25	NUM
fumecheng-10743	244	15	.	.	PUNCT
fumecheng-10743	245	1	he	he	PRON
fumecheng-10743	245	2	,	,	PUNCT
fumecheng-10743	245	3	j.h	j.h	PROPN
fumecheng-10743	245	4	.	.	PROPN
fumecheng-10743	245	5	,	,	PUNCT
fumecheng-10743	245	6	hou	hou	PROPN
fumecheng-10743	245	7	w.f	w.f	PROPN
fumecheng-10743	245	8	.	.	PROPN
fumecheng-10743	245	9	,	,	PUNCT
fumecheng-10743	245	10	qie	qie	PROPN
fumecheng-10743	245	11	,	,	PUNCT
fumecheng-10743	245	12	n.	n.	NOUN
fumecheng-10743	245	13	,	,	PUNCT
fumecheng-10743	245	14	gepreel	gepreel	ADJ
fumecheng-10743	245	15	,	,	PUNCT
fumecheng-10743	245	16	k.a	k.a	PROPN
fumecheng-10743	245	17	.	.	PROPN
fumecheng-10743	245	18	,	,	PUNCT
fumecheng-10743	245	19	shirazi	shirazi	PROPN
fumecheng-10743	245	20	,	,	PUNCT
fumecheng-10743	245	21	a.h	a.h	PROPN
fumecheng-10743	245	22	.	.	PROPN
fumecheng-10743	245	23	,	,	PUNCT
fumecheng-10743	245	24	sedighi	sedighi	PROPN
fumecheng-10743	245	25	,	,	PUNCT
fumecheng-10743	245	26	h.m	h.m	PROPN
fumecheng-10743	245	27	.	.	PROPN
fumecheng-10743	245	28	,	,	PUNCT
fumecheng-10743	245	29	2021	2021	NUM
fumecheng-10743	245	30	,	,	PUNCT
fumecheng-10743	245	31	hamiltonian	hamiltonian	NOUN
fumecheng-10743	245	32	-	-	PUNCT
fumecheng-10743	245	33	based	base	VERB
fumecheng-10743	245	34	frequency	frequency	NOUN
fumecheng-10743	245	35	-	-	PUNCT
fumecheng-10743	245	36	amplitude	amplitude	NOUN
fumecheng-10743	245	37	formulation	formulation	NOUN
fumecheng-10743	245	38	for	for	ADP
fumecheng-10743	245	39	nonlinear	nonlinear	ADJ
fumecheng-10743	245	40	oscillators	oscillator	NOUN
fumecheng-10743	245	41	,	,	PUNCT
fumecheng-10743	245	42	facta	facta	PROPN
fumecheng-10743	245	43	universitatis	universitatis	PROPN
fumecheng-10743	245	44	-	-	PUNCT
fumecheng-10743	245	45	series	series	NOUN
fumecheng-10743	245	46	mechanical	mechanical	ADJ
fumecheng-10743	245	47	engineering	engineering	NOUN
fumecheng-10743	245	48	,	,	PUNCT
fumecheng-10743	245	49	19(2	19(2	NUM
fumecheng-10743	245	50	)	)	PUNCT
fumecheng-10743	245	51	,	,	PUNCT
fumecheng-10743	245	52	pp	pp	PROPN
fumecheng-10743	245	53	.	.	PUNCT
fumecheng-10743	245	54	199	199	NUM
fumecheng-10743	245	55	-	-	SYM
fumecheng-10743	245	56	208	208	NUM
fumecheng-10743	245	57	.	.	PUNCT
fumecheng-10743	245	58	26	26	NUM
fumecheng-10743	245	59	.	.	PUNCT
fumecheng-10743	246	1	he	he	PRON
fumecheng-10743	246	2	,	,	PUNCT
fumecheng-10743	246	3	j.h	j.h	PROPN
fumecheng-10743	246	4	.	.	PROPN
fumecheng-10743	246	5	,	,	PUNCT
fumecheng-10743	246	6	2006	2006	NUM
fumecheng-10743	246	7	,	,	PUNCT
fumecheng-10743	246	8	some	some	DET
fumecheng-10743	246	9	asymptotic	asymptotic	ADJ
fumecheng-10743	246	10	methods	method	NOUN
fumecheng-10743	246	11	for	for	ADP
fumecheng-10743	246	12	strongly	strongly	ADV
fumecheng-10743	246	13	nonlinear	nonlinear	ADJ
fumecheng-10743	246	14	equations	equation	NOUN
fumecheng-10743	246	15	,	,	PUNCT
fumecheng-10743	246	16	international	international	ADJ
fumecheng-10743	246	17	journal	journal	NOUN
fumecheng-10743	246	18	of	of	ADP
fumecheng-10743	246	19	modern	modern	ADJ
fumecheng-10743	246	20	physics	physics	PROPN
fumecheng-10743	246	21	b	b	PROPN
fumecheng-10743	246	22	,	,	PUNCT
fumecheng-10743	246	23	20(10	20(10	NUM
fumecheng-10743	246	24	)	)	PUNCT
fumecheng-10743	246	25	,	,	PUNCT
fumecheng-10743	246	26	pp	pp	ADJ
fumecheng-10743	246	27	.	.	PUNCT
fumecheng-10743	246	28	1141–1199	1141–1199	NUM
fumecheng-10743	246	29	.	.	PUNCT
fumecheng-10743	246	30	27	27	NUM
fumecheng-10743	246	31	.	.	PUNCT
fumecheng-10743	247	1	wang	wang	PROPN
fumecheng-10743	247	2	,	,	PUNCT
fumecheng-10743	247	3	k.j	k.j	PROPN
fumecheng-10743	247	4	.	.	PROPN
fumecheng-10743	247	5	,	,	PUNCT
fumecheng-10743	247	6	zhu	zhu	PROPN
fumecheng-10743	247	7	,	,	PUNCT
fumecheng-10743	247	8	h.w	h.w	PROPN
fumecheng-10743	247	9	.	.	PROPN
fumecheng-10743	247	10	,	,	PUNCT
fumecheng-10743	247	11	2021	2021	NUM
fumecheng-10743	247	12	,	,	PUNCT
fumecheng-10743	247	13	periodic	periodic	ADJ
fumecheng-10743	247	14	wave	wave	NOUN
fumecheng-10743	247	15	solution	solution	NOUN
fumecheng-10743	247	16	of	of	ADP
fumecheng-10743	247	17	the	the	DET
fumecheng-10743	247	18	kundu	kundu	NOUN
fumecheng-10743	247	19	-	-	PUNCT
fumecheng-10743	247	20	mukherjee	mukherjee	NOUN
fumecheng-10743	247	21	-	-	PUNCT
fumecheng-10743	247	22	naskar	naskar	NOUN
fumecheng-10743	247	23	equation	equation	NOUN
fumecheng-10743	247	24	in	in	ADP
fumecheng-10743	247	25	birefringent	birefringent	NOUN
fumecheng-10743	247	26	fibers	fiber	NOUN
fumecheng-10743	247	27	via	via	ADP
fumecheng-10743	247	28	the	the	DET
fumecheng-10743	247	29	hamiltonian	hamiltonian	NOUN
fumecheng-10743	247	30	-	-	PUNCT
fumecheng-10743	247	31	based	base	VERB
fumecheng-10743	247	32	algorithm	algorithm	NOUN
fumecheng-10743	247	33	,	,	PUNCT
fumecheng-10743	247	34	epl	epl	PROPN
fumecheng-10743	247	35	,	,	PUNCT
fumecheng-10743	247	36	doi	doi	PROPN
fumecheng-10743	247	37	:	:	PUNCT
fumecheng-10743	247	38	10.1209/0295	10.1209/0295	NUM
fumecheng-10743	247	39	-	-	SYM
fumecheng-10743	247	40	5075	5075	NUM
fumecheng-10743	247	41	/	/	SYM
fumecheng-10743	247	42	ac3d6b	ac3d6b	PROPN
fumecheng-10743	247	43	.	.	PUNCT
fumecheng-10743	248	1	28	28	NUM
fumecheng-10743	248	2	.	.	PUNCT
fumecheng-10743	249	1	wang	wang	PROPN
fumecheng-10743	249	2	,	,	PUNCT
fumecheng-10743	249	3	k.j	k.j	PROPN
fumecheng-10743	249	4	.	.	PROPN
fumecheng-10743	249	5	,	,	PUNCT
fumecheng-10743	249	6	wang	wang	PROPN
fumecheng-10743	249	7	,	,	PUNCT
fumecheng-10743	249	8	g.d	g.d	PROPN
fumecheng-10743	249	9	.	.	PROPN
fumecheng-10743	249	10	,	,	PUNCT
fumecheng-10743	249	11	2022	2022	NUM
fumecheng-10743	249	12	,	,	PUNCT
fumecheng-10743	249	13	study	study	NOUN
fumecheng-10743	249	14	on	on	ADP
fumecheng-10743	249	15	the	the	DET
fumecheng-10743	249	16	nonlinear	nonlinear	ADJ
fumecheng-10743	249	17	vibration	vibration	NOUN
fumecheng-10743	249	18	of	of	ADP
fumecheng-10743	249	19	embedded	embed	VERB
fumecheng-10743	249	20	carbon	carbon	NOUN
fumecheng-10743	249	21	nanotube	nanotube	NOUN
fumecheng-10743	249	22	via	via	ADP
fumecheng-10743	249	23	the	the	DET
fumecheng-10743	249	24	hamiltonian	hamiltonian	NOUN
fumecheng-10743	249	25	-	-	PUNCT
fumecheng-10743	249	26	based	base	VERB
fumecheng-10743	249	27	method	method	NOUN
fumecheng-10743	249	28	,	,	PUNCT
fumecheng-10743	249	29	journal	journal	NOUN
fumecheng-10743	249	30	of	of	ADP
fumecheng-10743	249	31	low	low	ADJ
fumecheng-10743	249	32	frequency	frequency	NOUN
fumecheng-10743	249	33	noise	noise	NOUN
fumecheng-10743	249	34	,	,	PUNCT
fumecheng-10743	249	35	vibration	vibration	NOUN
fumecheng-10743	249	36	&	&	CCONJ
fumecheng-10743	249	37	active	active	ADJ
fumecheng-10743	249	38	control	control	NOUN
fumecheng-10743	249	39	,	,	PUNCT
fumecheng-10743	249	40	41(1	41(1	NUM
fumecheng-10743	249	41	)	)	PUNCT
fumecheng-10743	249	42	,	,	PUNCT
fumecheng-10743	249	43	pp	pp	ADP
fumecheng-10743	249	44	.	.	PUNCT
fumecheng-10743	250	1	112	112	NUM
fumecheng-10743	250	2	-	-	SYM
fumecheng-10743	250	3	117	117	NUM
fumecheng-10743	250	4	.	.	PUNCT
fumecheng-10743	251	1	29	29	NUM
fumecheng-10743	251	2	.	.	PUNCT
fumecheng-10743	252	1	he	he	PRON
fumecheng-10743	252	2	,	,	PUNCT
fumecheng-10743	252	3	c.h	c.h	PROPN
fumecheng-10743	252	4	.	.	PROPN
fumecheng-10743	252	5	,	,	PUNCT
fumecheng-10743	252	6	liu	liu	PROPN
fumecheng-10743	252	7	,	,	PUNCT
fumecheng-10743	252	8	c.	c.	PROPN
fumecheng-10743	252	9	,	,	PUNCT
fumecheng-10743	252	10	2022	2022	NUM
fumecheng-10743	252	11	,	,	PUNCT
fumecheng-10743	252	12	a	a	DET
fumecheng-10743	252	13	modified	modify	VERB
fumecheng-10743	252	14	frequency	frequency	NOUN
fumecheng-10743	252	15	-	-	PUNCT
fumecheng-10743	252	16	amplitude	amplitude	NOUN
fumecheng-10743	252	17	formulation	formulation	NOUN
fumecheng-10743	252	18	for	for	ADP
fumecheng-10743	252	19	fractal	fractal	ADJ
fumecheng-10743	252	20	vibration	vibration	NOUN
fumecheng-10743	252	21	systems	system	NOUN
fumecheng-10743	252	22	,	,	PUNCT
fumecheng-10743	252	23	fractals	fractal	NOUN
fumecheng-10743	252	24	,	,	PUNCT
fumecheng-10743	252	25	doi	doi	NOUN
fumecheng-10743	252	26	:	:	PUNCT
fumecheng-10743	252	27	10.1142	10.1142	NUM
fumecheng-10743	252	28	/	/	SYM
fumecheng-10743	252	29	s0218348x22500463	s0218348x22500463	ADJ
fumecheng-10743	252	30	.	.	NOUN
fumecheng-10743	252	31	30	30	NUM
fumecheng-10743	252	32	.	.	PUNCT
fumecheng-10743	253	1	he	he	PRON
fumecheng-10743	253	2	,	,	PUNCT
fumecheng-10743	253	3	j.h	j.h	PROPN
fumecheng-10743	253	4	.	.	PROPN
fumecheng-10743	253	5	,	,	PUNCT
fumecheng-10743	253	6	el	el	PROPN
fumecheng-10743	253	7	-	-	PUNCT
fumecheng-10743	253	8	dib	dib	PROPN
fumecheng-10743	253	9	,	,	PUNCT
fumecheng-10743	253	10	y.o	y.o	PROPN
fumecheng-10743	253	11	.	.	PROPN
fumecheng-10743	253	12	,	,	PUNCT
fumecheng-10743	253	13	2021	2021	NUM
fumecheng-10743	253	14	,	,	PUNCT
fumecheng-10743	253	15	a	a	DET
fumecheng-10743	253	16	tutorial	tutorial	ADJ
fumecheng-10743	253	17	introduction	introduction	NOUN
fumecheng-10743	253	18	to	to	ADP
fumecheng-10743	253	19	the	the	DET
fumecheng-10743	253	20	two	two	NUM
fumecheng-10743	253	21	-	-	PUNCT
fumecheng-10743	253	22	scale	scale	NOUN
fumecheng-10743	253	23	fractal	fractal	ADJ
fumecheng-10743	253	24	calculus	calculus	NOUN
fumecheng-10743	253	25	and	and	CCONJ
fumecheng-10743	253	26	its	its	PRON
fumecheng-10743	253	27	application	application	NOUN
fumecheng-10743	253	28	to	to	ADP
fumecheng-10743	253	29	the	the	DET
fumecheng-10743	253	30	fractal	fractal	ADJ
fumecheng-10743	253	31	zhiber	zhiber	NOUN
fumecheng-10743	253	32	-	-	PUNCT
fumecheng-10743	253	33	shabat	shabat	PROPN
fumecheng-10743	253	34	oscillator	oscillator	NOUN
fumecheng-10743	253	35	,	,	PUNCT
fumecheng-10743	253	36	fractals	fractal	NOUN
fumecheng-10743	253	37	,	,	PUNCT
fumecheng-10743	253	38	29(08	29(08	NUM
fumecheng-10743	253	39	)	)	PUNCT
fumecheng-10743	253	40	,	,	PUNCT
fumecheng-10743	253	41	2150268	2150268	NUM
fumecheng-10743	253	42	.	.	PUNCT
fumecheng-10743	254	1	31	31	NUM
fumecheng-10743	254	2	.	.	PUNCT
fumecheng-10743	255	1	he	he	PRON
fumecheng-10743	255	2	,	,	PUNCT
fumecheng-10743	255	3	j.h	j.h	PROPN
fumecheng-10743	255	4	.	.	PROPN
fumecheng-10743	255	5	,	,	PUNCT
fumecheng-10743	255	6	yang	yang	PROPN
fumecheng-10743	255	7	,	,	PUNCT
fumecheng-10743	255	8	q.	q.	PROPN
fumecheng-10743	255	9	,	,	PUNCT
fumecheng-10743	255	10	he	he	PRON
fumecheng-10743	255	11	,	,	PUNCT
fumecheng-10743	255	12	c.h	c.h	PROPN
fumecheng-10743	255	13	.	.	PROPN
fumecheng-10743	255	14	,	,	PUNCT
fumecheng-10743	255	15	khan	khan	PROPN
fumecheng-10743	255	16	,	,	PUNCT
fumecheng-10743	255	17	y.	y.	PROPN
fumecheng-10743	255	18	,	,	PUNCT
fumecheng-10743	255	19	2021	2021	NUM
fumecheng-10743	255	20	,	,	PUNCT
fumecheng-10743	255	21	a	a	DET
fumecheng-10743	255	22	simple	simple	ADJ
fumecheng-10743	255	23	frequency	frequency	NOUN
fumecheng-10743	255	24	formulation	formulation	NOUN
fumecheng-10743	255	25	for	for	ADP
fumecheng-10743	255	26	the	the	DET
fumecheng-10743	255	27	tangent	tangent	NOUN
fumecheng-10743	255	28	oscillator	oscillator	NOUN
fumecheng-10743	255	29	,	,	PUNCT
fumecheng-10743	255	30	axioms	axiom	NOUN
fumecheng-10743	255	31	,	,	PUNCT
fumecheng-10743	255	32	10	10	NUM
fumecheng-10743	255	33	,	,	PUNCT
fumecheng-10743	255	34	320	320	NUM
fumecheng-10743	255	35	.	.	PUNCT
fumecheng-10743	255	36	32	32	NUM
fumecheng-10743	255	37	.	.	PUNCT
fumecheng-10743	256	1	he	he	PRON
fumecheng-10743	256	2	,	,	PUNCT
fumecheng-10743	256	3	j.h	j.h	PROPN
fumecheng-10743	256	4	.	.	PROPN
fumecheng-10743	256	5	,	,	PUNCT
fumecheng-10743	256	6	qie	qie	PROPN
fumecheng-10743	256	7	,	,	PUNCT
fumecheng-10743	256	8	n.	n.	PROPN
fumecheng-10743	256	9	,	,	PUNCT
fumecheng-10743	256	10	he	he	PRON
fumecheng-10743	256	11	,	,	PUNCT
fumecheng-10743	256	12	c.h	c.h	PROPN
fumecheng-10743	256	13	.	.	PROPN
fumecheng-10743	256	14	,	,	PUNCT
fumecheng-10743	256	15	gepreel	gepreel	PROPN
fumecheng-10743	256	16	,	,	PUNCT
fumecheng-10743	256	17	k.	k.	PROPN
fumecheng-10743	256	18	,	,	PUNCT
fumecheng-10743	256	19	2022	2022	NUM
fumecheng-10743	256	20	,	,	PUNCT
fumecheng-10743	256	21	fast	fast	ADJ
fumecheng-10743	256	22	identification	identification	NOUN
fumecheng-10743	256	23	of	of	ADP
fumecheng-10743	256	24	the	the	DET
fumecheng-10743	256	25	pull	pull	NOUN
fumecheng-10743	256	26	-	-	PUNCT
fumecheng-10743	256	27	in	in	ADP
fumecheng-10743	256	28	voltage	voltage	NOUN
fumecheng-10743	256	29	of	of	ADP
fumecheng-10743	256	30	a	a	DET
fumecheng-10743	256	31	nano	nano	NOUN
fumecheng-10743	256	32	/	/	SYM
fumecheng-10743	256	33	micro	micro	ADJ
fumecheng-10743	256	34	-	-	ADJ
fumecheng-10743	256	35	electromechanical	electromechanical	ADJ
fumecheng-10743	256	36	system	system	NOUN
fumecheng-10743	256	37	,	,	PUNCT
fumecheng-10743	256	38	journal	journal	NOUN
fumecheng-10743	256	39	of	of	ADP
fumecheng-10743	256	40	low	low	ADJ
fumecheng-10743	256	41	frequency	frequency	NOUN
fumecheng-10743	256	42	noise	noise	NOUN
fumecheng-10743	256	43	,	,	PUNCT
fumecheng-10743	256	44	vibration	vibration	NOUN
fumecheng-10743	256	45	&	&	CCONJ
fumecheng-10743	256	46	active	active	ADJ
fumecheng-10743	256	47	control	control	NOUN
fumecheng-10743	256	48	,	,	PUNCT
fumecheng-10743	256	49	2022	2022	NUM
fumecheng-10743	256	50	,	,	PUNCT
fumecheng-10743	256	51	doi	doi	NOUN
fumecheng-10743	256	52	:	:	PUNCT
fumecheng-10743	256	53	10.1177/14613484211068252	10.1177/14613484211068252	NUM
fumecheng-10743	256	54	.	.	PUNCT
fumecheng-10743	257	1	33	33	NUM
fumecheng-10743	257	2	.	.	PUNCT
fumecheng-10743	258	1	he	he	PRON
fumecheng-10743	258	2	,	,	PUNCT
fumecheng-10743	258	3	j.h	j.h	PROPN
fumecheng-10743	258	4	.	.	PROPN
fumecheng-10743	258	5	,	,	PUNCT
fumecheng-10743	258	6	hou	hou	PROPN
fumecheng-10743	258	7	,	,	PUNCT
fumecheng-10743	258	8	w.f	w.f	PROPN
fumecheng-10743	258	9	.	.	PROPN
fumecheng-10743	258	10	,	,	PUNCT
fumecheng-10743	258	11	he	he	PRON
fumecheng-10743	258	12	,	,	PUNCT
fumecheng-10743	258	13	c.h	c.h	PROPN
fumecheng-10743	258	14	.	.	PROPN
fumecheng-10743	258	15	,	,	PUNCT
fumecheng-10743	258	16	saeed	saeed	PROPN
fumecheng-10743	258	17	,	,	PUNCT
fumecheng-10743	258	18	t.	t.	PROPN
fumecheng-10743	258	19	,	,	PUNCT
fumecheng-10743	258	20	hayat	hayat	PROPN
fumecheng-10743	258	21	,	,	PUNCT
fumecheng-10743	258	22	t.	t.	PROPN
fumecheng-10743	258	23	,	,	PUNCT
fumecheng-10743	258	24	2021	2021	NUM
fumecheng-10743	258	25	,	,	PUNCT
fumecheng-10743	258	26	variational	variational	ADJ
fumecheng-10743	258	27	approach	approach	NOUN
fumecheng-10743	258	28	to	to	ADP
fumecheng-10743	258	29	fractal	fractal	ADJ
fumecheng-10743	258	30	solitary	solitary	ADJ
fumecheng-10743	258	31	waves	wave	NOUN
fumecheng-10743	258	32	,	,	PUNCT
fumecheng-10743	258	33	fractals	fractal	NOUN
fumecheng-10743	258	34	,	,	PUNCT
fumecheng-10743	258	35	29(07	29(07	NUM
fumecheng-10743	258	36	)	)	PUNCT
fumecheng-10743	258	37	,	,	PUNCT
fumecheng-10743	258	38	2150199	2150199	NUM
fumecheng-10743	258	39	.	.	PUNCT
fumecheng-10743	259	1	34	34	NUM
fumecheng-10743	259	2	.	.	PUNCT
fumecheng-10743	260	1	he	he	PRON
fumecheng-10743	260	2	,	,	PUNCT
fumecheng-10743	260	3	c.h	c.h	PROPN
fumecheng-10743	260	4	.	.	PROPN
fumecheng-10743	260	5	,	,	PUNCT
fumecheng-10743	260	6	2016	2016	NUM
fumecheng-10743	260	7	,	,	PUNCT
fumecheng-10743	260	8	an	an	DET
fumecheng-10743	260	9	introduction	introduction	NOUN
fumecheng-10743	260	10	to	to	ADP
fumecheng-10743	260	11	an	an	DET
fumecheng-10743	260	12	ancient	ancient	ADJ
fumecheng-10743	260	13	chinese	chinese	ADJ
fumecheng-10743	260	14	algorithm	algorithm	NOUN
fumecheng-10743	260	15	and	and	CCONJ
fumecheng-10743	260	16	its	its	PRON
fumecheng-10743	260	17	modification	modification	NOUN
fumecheng-10743	260	18	,	,	PUNCT
fumecheng-10743	260	19	international	international	ADJ
fumecheng-10743	260	20	journal	journal	NOUN
fumecheng-10743	260	21	of	of	ADP
fumecheng-10743	260	22	numerical	numerical	ADJ
fumecheng-10743	260	23	methods	method	NOUN
fumecheng-10743	260	24	for	for	ADP
fumecheng-10743	260	25	heat	heat	NOUN
fumecheng-10743	260	26	&	&	CCONJ
fumecheng-10743	260	27	fluid	fluid	ADJ
fumecheng-10743	260	28	flow	flow	NOUN
fumecheng-10743	260	29	,	,	PUNCT
fumecheng-10743	260	30	26(8	26(8	NUM
fumecheng-10743	260	31	)	)	PUNCT
fumecheng-10743	260	32	,	,	PUNCT
fumecheng-10743	260	33	pp	pp	PROPN
fumecheng-10743	260	34	.	.	PUNCT
fumecheng-10743	260	35	2486	2486	NUM
fumecheng-10743	260	36	-	-	SYM
fumecheng-10743	260	37	2491	2491	NUM
fumecheng-10743	260	38	.	.	PUNCT
fumecheng-10743	261	1	35	35	NUM
fumecheng-10743	261	2	.	.	PUNCT
fumecheng-10743	262	1	khan	khan	PROPN
fumecheng-10743	262	2	,	,	PUNCT
fumecheng-10743	262	3	w.a	w.a	PROPN
fumecheng-10743	262	4	.	.	PROPN
fumecheng-10743	262	5	,	,	PUNCT
fumecheng-10743	262	6	2022	2022	NUM
fumecheng-10743	262	7	,	,	PUNCT
fumecheng-10743	262	8	numerical	numerical	PROPN
fumecheng-10743	262	9	simulation	simulation	NOUN
fumecheng-10743	262	10	of	of	ADP
fumecheng-10743	262	11	chun	chun	PROPN
fumecheng-10743	262	12	-	-	PUNCT
fumecheng-10743	262	13	hui	hui	PROPN
fumecheng-10743	263	1	he	he	PRON
fumecheng-10743	263	2	's	be	AUX
fumecheng-10743	263	3	iteration	iteration	NOUN
fumecheng-10743	263	4	method	method	NOUN
fumecheng-10743	263	5	with	with	ADP
fumecheng-10743	263	6	applications	application	NOUN
fumecheng-10743	263	7	in	in	ADP
fumecheng-10743	263	8	engineering	engineering	NOUN
fumecheng-10743	263	9	,	,	PUNCT
fumecheng-10743	263	10	international	international	ADJ
fumecheng-10743	263	11	journal	journal	NOUN
fumecheng-10743	263	12	of	of	ADP
fumecheng-10743	263	13	numerical	numerical	ADJ
fumecheng-10743	263	14	methods	method	NOUN
fumecheng-10743	263	15	for	for	ADP
fumecheng-10743	263	16	heat	heat	NOUN
fumecheng-10743	263	17	&	&	CCONJ
fumecheng-10743	263	18	fluid	fluid	ADJ
fumecheng-10743	263	19	flow	flow	NOUN
fumecheng-10743	263	20	,	,	PUNCT
fumecheng-10743	263	21	32(3	32(3	NUM
fumecheng-10743	263	22	)	)	PUNCT
fumecheng-10743	263	23	,	,	PUNCT
fumecheng-10743	263	24	pp	pp	PROPN
fumecheng-10743	263	25	.	.	PUNCT
fumecheng-10743	264	1	944	944	NUM
fumecheng-10743	264	2	-	-	SYM
fumecheng-10743	264	3	955	955	NUM
fumecheng-10743	264	4	.	.	PUNCT
fumecheng-10743	265	1	https://doi.org/10.1209/0295-5075/ac3d6b	https://doi.org/10.1209/0295-5075/ac3d6b	PROPN
fumecheng-10743	265	2	https://doi.org/10.1142/s0218348x22500463	https://doi.org/10.1142/s0218348x22500463	PROPN