id	sid	tid	token	lemma	pos
fumecheng-11687	1	1	11687	11687	NUM
fumecheng-11687	1	2	facta	facta	PROPN
fumecheng-11687	1	3	universitatis	universitatis	PROPN
fumecheng-11687	1	4	series	series	NOUN
fumecheng-11687	1	5	:	:	PUNCT
fumecheng-11687	1	6	mechanical	mechanical	ADJ
fumecheng-11687	1	7	engineering	engineering	NOUN
fumecheng-11687	1	8	vol	vol	NOUN
fumecheng-11687	1	9	.	.	PUNCT
fumecheng-11687	1	10	22	22	NUM
fumecheng-11687	1	11	,	,	PUNCT
fumecheng-11687	1	12	no	no	DET
fumecheng-11687	1	13	2	2	NUM
fumecheng-11687	1	14	,	,	PUNCT
fumecheng-11687	1	15	2024	2024	NUM
fumecheng-11687	1	16	,	,	PUNCT
fumecheng-11687	1	17	pp	pp	ADV
fumecheng-11687	1	18	.	.	PUNCT
fumecheng-11687	2	1	199	199	NUM
fumecheng-11687	2	2	216	216	NUM
fumecheng-11687	2	3	https://doi.org/10.22190/fume230605035e	https://doi.org/10.22190/fume230605035e	PROPN
fumecheng-11687	2	4	©	©	PROPN
fumecheng-11687	2	5	2024	2024	NUM
fumecheng-11687	2	6	by	by	ADP
fumecheng-11687	2	7	university	university	PROPN
fumecheng-11687	2	8	of	of	ADP
fumecheng-11687	2	9	niš	niš	PROPN
fumecheng-11687	2	10	,	,	PUNCT
fumecheng-11687	2	11	serbia	serbia	PROPN
fumecheng-11687	2	12	|	|	ADV
fumecheng-11687	2	13	creative	creative	ADJ
fumecheng-11687	2	14	commons	common	NOUN
fumecheng-11687	2	15	license	license	NOUN
fumecheng-11687	2	16	:	:	PUNCT
fumecheng-11687	2	17	cc	cc	VERB
fumecheng-11687	2	18	by	by	ADP
fumecheng-11687	2	19	-	-	PUNCT
fumecheng-11687	2	20	nc	nc	VERB
fumecheng-11687	2	21	-	-	PUNCT
fumecheng-11687	2	22	nd	nd	ADV
fumecheng-11687	2	23	original	original	ADJ
fumecheng-11687	2	24	scientific	scientific	NOUN
fumecheng-11687	2	25	paper	paper	VERB
fumecheng-11687	2	26	the	the	DET
fumecheng-11687	2	27	up	up	ADV
fumecheng-11687	2	28	-	-	PUNCT
fumecheng-11687	2	29	grating	grate	VERB
fumecheng-11687	2	30	rank	rank	NOUN
fumecheng-11687	2	31	approach	approach	NOUN
fumecheng-11687	2	32	to	to	PART
fumecheng-11687	2	33	solve	solve	VERB
fumecheng-11687	2	34	the	the	DET
fumecheng-11687	2	35	forced	force	VERB
fumecheng-11687	2	36	fractal	fractal	ADJ
fumecheng-11687	2	37	duffing	duffing	NOUN
fumecheng-11687	2	38	oscillator	oscillator	NOUN
fumecheng-11687	2	39	by	by	ADP
fumecheng-11687	2	40	nonperturbative	nonperturbative	ADJ
fumecheng-11687	2	41	technique	technique	NOUN
fumecheng-11687	2	42	yusry	yusry	PROPN
fumecheng-11687	2	43	o.	o.	PROPN
fumecheng-11687	2	44	el	el	PROPN
fumecheng-11687	2	45	-	-	PROPN
fumecheng-11687	2	46	dib1	dib1	PROPN
fumecheng-11687	2	47	,	,	PUNCT
fumecheng-11687	2	48	nasser	nasser	PROPN
fumecheng-11687	2	49	s.	s.	PROPN
fumecheng-11687	2	50	elgazery1	elgazery1	PROPN
fumecheng-11687	2	51	,	,	PUNCT
fumecheng-11687	2	52	haifa	haifa	PROPN
fumecheng-11687	2	53	a.	a.	NOUN
fumecheng-11687	2	54	alyousef2	alyousef2	PROPN
fumecheng-11687	3	1	1department	1department	NUM
fumecheng-11687	3	2	of	of	ADP
fumecheng-11687	3	3	mathematics	mathematic	NOUN
fumecheng-11687	3	4	,	,	PUNCT
fumecheng-11687	3	5	faculty	faculty	NOUN
fumecheng-11687	3	6	of	of	ADP
fumecheng-11687	3	7	education	education	NOUN
fumecheng-11687	3	8	,	,	PUNCT
fumecheng-11687	3	9	ain	ain	PROPN
fumecheng-11687	3	10	shams	shams	PROPN
fumecheng-11687	3	11	university	university	PROPN
fumecheng-11687	3	12	,	,	PUNCT
fumecheng-11687	3	13	roxy	roxy	PROPN
fumecheng-11687	3	14	,	,	PUNCT
fumecheng-11687	3	15	cairo	cairo	PROPN
fumecheng-11687	3	16	,	,	PUNCT
fumecheng-11687	3	17	egypt	egypt	PROPN
fumecheng-11687	3	18	2department	2department	NUM
fumecheng-11687	3	19	of	of	ADP
fumecheng-11687	3	20	physics	physics	PROPN
fumecheng-11687	3	21	,	,	PUNCT
fumecheng-11687	3	22	college	college	NOUN
fumecheng-11687	3	23	of	of	ADP
fumecheng-11687	3	24	science	science	NOUN
fumecheng-11687	3	25	,	,	PUNCT
fumecheng-11687	3	26	princess	princess	PROPN
fumecheng-11687	3	27	nourah	nourah	PROPN
fumecheng-11687	3	28	bint	bint	PROPN
fumecheng-11687	3	29	abdulrahman	abdulrahman	PROPN
fumecheng-11687	3	30	university	university	PROPN
fumecheng-11687	3	31	,	,	PUNCT
fumecheng-11687	3	32	riyadh	riyadh	PROPN
fumecheng-11687	3	33	,	,	PUNCT
fumecheng-11687	3	34	saudi	saudi	PROPN
fumecheng-11687	3	35	arabia	arabia	PROPN
fumecheng-11687	3	36	orcid	orcid	PROPN
fumecheng-11687	3	37	ids	ids	PROPN
fumecheng-11687	3	38	:	:	PUNCT
fumecheng-11687	3	39	yusry	yusry	PROPN
fumecheng-11687	3	40	o.	o.	PROPN
fumecheng-11687	4	1	el	el	PROPN
fumecheng-11687	4	2	-	-	PROPN
fumecheng-11687	4	3	dib	dib	PROPN
fumecheng-11687	4	4	https://orcid.org/0000-0001-6381-5918	https://orcid.org/0000-0001-6381-5918	PROPN
fumecheng-11687	4	5	nasser	nasser	PROPN
fumecheng-11687	4	6	s.	s.	PROPN
fumecheng-11687	4	7	elgazery	elgazery	PROPN
fumecheng-11687	5	1	https://orcid.org/0000-0003-4691-2526	https://orcid.org/0000-0003-4691-2526	PROPN
fumecheng-11687	5	2	haifa	haifa	PROPN
fumecheng-11687	5	3	a.	a.	PROPN
fumecheng-11687	5	4	alyousef	alyousef	PROPN
fumecheng-11687	5	5	https://orcid.org/0000-0003-1727-0958	https://orcid.org/0000-0003-1727-0958	PROPN
fumecheng-11687	5	6	abstract	abstract	NOUN
fumecheng-11687	5	7	.	.	PUNCT
fumecheng-11687	6	1	the	the	DET
fumecheng-11687	6	2	current	current	ADJ
fumecheng-11687	6	3	research	research	NOUN
fumecheng-11687	6	4	studies	study	NOUN
fumecheng-11687	6	5	a	a	DET
fumecheng-11687	6	6	fractal	fractal	ADJ
fumecheng-11687	6	7	duffing	duffing	NOUN
fumecheng-11687	6	8	oscillator	oscillator	NOUN
fumecheng-11687	6	9	in	in	ADP
fumecheng-11687	6	10	the	the	DET
fumecheng-11687	6	11	presence	presence	NOUN
fumecheng-11687	6	12	of	of	ADP
fumecheng-11687	6	13	periodic	periodic	ADJ
fumecheng-11687	6	14	force	force	NOUN
fumecheng-11687	6	15	.	.	PUNCT
fumecheng-11687	7	1	to	to	PART
fumecheng-11687	7	2	find	find	VERB
fumecheng-11687	7	3	an	an	DET
fumecheng-11687	7	4	analytic	analytic	ADJ
fumecheng-11687	7	5	solution	solution	NOUN
fumecheng-11687	7	6	for	for	ADP
fumecheng-11687	7	7	this	this	DET
fumecheng-11687	7	8	oscillator	oscillator	NOUN
fumecheng-11687	7	9	,	,	PUNCT
fumecheng-11687	7	10	the	the	DET
fumecheng-11687	7	11	aspects	aspect	NOUN
fumecheng-11687	7	12	explained	explain	VERB
fumecheng-11687	7	13	in	in	ADP
fumecheng-11687	7	14	the	the	DET
fumecheng-11687	7	15	following	following	NOUN
fumecheng-11687	7	16	are	be	AUX
fumecheng-11687	7	17	considered	consider	VERB
fumecheng-11687	7	18	.	.	PUNCT
fumecheng-11687	8	1	first	first	ADV
fumecheng-11687	8	2	,	,	PUNCT
fumecheng-11687	8	3	we	we	PRON
fumecheng-11687	8	4	obtain	obtain	VERB
fumecheng-11687	8	5	an	an	DET
fumecheng-11687	8	6	alternative	alternative	ADJ
fumecheng-11687	8	7	unforced	unforced	ADJ
fumecheng-11687	8	8	fractal	fractal	ADJ
fumecheng-11687	8	9	fourthorder	fourthorder	NOUN
fumecheng-11687	8	10	equation	equation	NOUN
fumecheng-11687	8	11	and	and	CCONJ
fumecheng-11687	8	12	then	then	ADV
fumecheng-11687	8	13	convert	convert	VERB
fumecheng-11687	8	14	it	it	PRON
fumecheng-11687	8	15	into	into	ADP
fumecheng-11687	8	16	a	a	DET
fumecheng-11687	8	17	continuous	continuous	ADJ
fumecheng-11687	8	18	space	space	NOUN
fumecheng-11687	8	19	.	.	PUNCT
fumecheng-11687	9	1	therefore	therefore	ADV
fumecheng-11687	9	2	,	,	PUNCT
fumecheng-11687	9	3	the	the	DET
fumecheng-11687	9	4	nonperturbative	nonperturbative	ADJ
fumecheng-11687	9	5	(	(	PUNCT
fumecheng-11687	9	6	np	np	NOUN
fumecheng-11687	9	7	)	)	PUNCT
fumecheng-11687	9	8	approach	approach	NOUN
fumecheng-11687	9	9	is	be	AUX
fumecheng-11687	9	10	used	use	VERB
fumecheng-11687	9	11	to	to	PART
fumecheng-11687	9	12	calculate	calculate	VERB
fumecheng-11687	9	13	the	the	DET
fumecheng-11687	9	14	analytic	analytic	ADJ
fumecheng-11687	9	15	solution	solution	NOUN
fumecheng-11687	9	16	for	for	ADP
fumecheng-11687	9	17	the	the	DET
fumecheng-11687	9	18	alternate	alternate	ADJ
fumecheng-11687	9	19	equation	equation	NOUN
fumecheng-11687	9	20	in	in	ADP
fumecheng-11687	9	21	the	the	DET
fumecheng-11687	9	22	second	second	ADJ
fumecheng-11687	9	23	-	-	PUNCT
fumecheng-11687	9	24	order	order	NOUN
fumecheng-11687	9	25	form	form	NOUN
fumecheng-11687	9	26	after	after	ADP
fumecheng-11687	9	27	reducing	reduce	VERB
fumecheng-11687	9	28	its	its	PRON
fumecheng-11687	9	29	rank	rank	NOUN
fumecheng-11687	9	30	.	.	PUNCT
fumecheng-11687	10	1	it	it	PRON
fumecheng-11687	10	2	is	be	AUX
fumecheng-11687	10	3	seen	see	VERB
fumecheng-11687	10	4	that	that	SCONJ
fumecheng-11687	10	5	the	the	DET
fumecheng-11687	10	6	analytical	analytical	ADJ
fumecheng-11687	10	7	and	and	CCONJ
fumecheng-11687	10	8	numerical	numerical	ADJ
fumecheng-11687	10	9	solutions	solution	NOUN
fumecheng-11687	10	10	agree	agree	VERB
fumecheng-11687	10	11	very	very	ADV
fumecheng-11687	10	12	well	well	ADV
fumecheng-11687	10	13	.	.	PUNCT
fumecheng-11687	11	1	the	the	DET
fumecheng-11687	11	2	computations	computation	NOUN
fumecheng-11687	11	3	reveal	reveal	VERB
fumecheng-11687	11	4	that	that	SCONJ
fumecheng-11687	11	5	for	for	ADP
fumecheng-11687	11	6	every	every	DET
fumecheng-11687	11	7	value	value	NOUN
fumecheng-11687	11	8	of	of	ADP
fumecheng-11687	11	9	the	the	DET
fumecheng-11687	11	10	fraction	fraction	NOUN
fumecheng-11687	11	11	parameter	parameter	NOUN
fumecheng-11687	11	12	,	,	PUNCT
fumecheng-11687	11	13	the	the	DET
fumecheng-11687	11	14	approximation	approximation	NOUN
fumecheng-11687	11	15	and	and	CCONJ
fumecheng-11687	11	16	numerical	numerical	ADJ
fumecheng-11687	11	17	solutions	solution	NOUN
fumecheng-11687	11	18	are	be	AUX
fumecheng-11687	11	19	identical	identical	ADJ
fumecheng-11687	11	20	.	.	PUNCT
fumecheng-11687	12	1	the	the	DET
fumecheng-11687	12	2	present	present	ADJ
fumecheng-11687	12	3	study	study	NOUN
fumecheng-11687	12	4	gives	give	VERB
fumecheng-11687	12	5	reliability	reliability	NOUN
fumecheng-11687	12	6	in	in	ADP
fumecheng-11687	12	7	the	the	DET
fumecheng-11687	12	8	technique	technique	NOUN
fumecheng-11687	12	9	of	of	ADP
fumecheng-11687	12	10	reducing	reduce	VERB
fumecheng-11687	12	11	the	the	DET
fumecheng-11687	12	12	order	order	NOUN
fumecheng-11687	12	13	of	of	ADP
fumecheng-11687	12	14	differential	differential	ADJ
fumecheng-11687	12	15	equations	equation	NOUN
fumecheng-11687	12	16	.	.	PUNCT
fumecheng-11687	13	1	furthermore	furthermore	ADV
fumecheng-11687	13	2	,	,	PUNCT
fumecheng-11687	13	3	the	the	DET
fumecheng-11687	13	4	required	require	VERB
fumecheng-11687	13	5	periodic	periodic	ADJ
fumecheng-11687	13	6	solution	solution	NOUN
fumecheng-11687	13	7	is	be	AUX
fumecheng-11687	13	8	also	also	ADV
fumecheng-11687	13	9	obtained	obtain	VERB
fumecheng-11687	13	10	by	by	ADP
fumecheng-11687	13	11	galerkin	galerkin	PROPN
fumecheng-11687	13	12	’s	’s	PART
fumecheng-11687	13	13	technique	technique	NOUN
fumecheng-11687	13	14	.	.	PUNCT
fumecheng-11687	14	1	in	in	ADP
fumecheng-11687	14	2	contrast	contrast	NOUN
fumecheng-11687	14	3	to	to	ADP
fumecheng-11687	14	4	the	the	DET
fumecheng-11687	14	5	traditional	traditional	ADJ
fumecheng-11687	14	6	technique	technique	NOUN
fumecheng-11687	14	7	,	,	PUNCT
fumecheng-11687	14	8	which	which	PRON
fumecheng-11687	14	9	works	work	VERB
fumecheng-11687	14	10	to	to	PART
fumecheng-11687	14	11	transform	transform	VERB
fumecheng-11687	14	12	the	the	DET
fumecheng-11687	14	13	variable	variable	NOUN
fumecheng-11687	14	14	and	and	CCONJ
fumecheng-11687	14	15	is	be	AUX
fumecheng-11687	14	16	valid	valid	ADJ
fumecheng-11687	14	17	only	only	ADV
fumecheng-11687	14	18	in	in	ADP
fumecheng-11687	14	19	the	the	DET
fumecheng-11687	14	20	absence	absence	NOUN
fumecheng-11687	14	21	of	of	ADP
fumecheng-11687	14	22	external	external	ADJ
fumecheng-11687	14	23	forces	force	NOUN
fumecheng-11687	14	24	,	,	PUNCT
fumecheng-11687	14	25	if	if	SCONJ
fumecheng-11687	14	26	there	there	PRON
fumecheng-11687	14	27	is	be	VERB
fumecheng-11687	14	28	an	an	DET
fumecheng-11687	14	29	external	external	ADJ
fumecheng-11687	14	30	force	force	NOUN
fumecheng-11687	14	31	,	,	PUNCT
fumecheng-11687	14	32	it	it	PRON
fumecheng-11687	14	33	leads	lead	VERB
fumecheng-11687	14	34	to	to	ADP
fumecheng-11687	14	35	significant	significant	ADJ
fumecheng-11687	14	36	mathematical	mathematical	ADJ
fumecheng-11687	14	37	difficulties	difficulty	NOUN
fumecheng-11687	14	38	.	.	PUNCT
fumecheng-11687	15	1	the	the	DET
fumecheng-11687	15	2	current	current	ADJ
fumecheng-11687	15	3	technique	technique	NOUN
fumecheng-11687	15	4	works	work	VERB
fumecheng-11687	15	5	on	on	ADP
fumecheng-11687	15	6	the	the	DET
fumecheng-11687	15	7	operator	operator	NOUN
fumecheng-11687	15	8	,	,	PUNCT
fumecheng-11687	15	9	which	which	PRON
fumecheng-11687	15	10	is	be	AUX
fumecheng-11687	15	11	simple	simple	ADJ
fumecheng-11687	15	12	and	and	CCONJ
fumecheng-11687	15	13	effective	effective	ADJ
fumecheng-11687	15	14	when	when	SCONJ
fumecheng-11687	15	15	investigating	investigate	VERB
fumecheng-11687	15	16	fractal	fractal	ADJ
fumecheng-11687	15	17	oscillators	oscillator	NOUN
fumecheng-11687	15	18	with	with	ADP
fumecheng-11687	15	19	external	external	ADJ
fumecheng-11687	15	20	forces	force	NOUN
fumecheng-11687	15	21	,	,	PUNCT
fumecheng-11687	15	22	easy	easy	ADJ
fumecheng-11687	15	23	to	to	PART
fumecheng-11687	15	24	obtain	obtain	VERB
fumecheng-11687	15	25	analytic	analytic	ADJ
fumecheng-11687	15	26	solutions	solution	NOUN
fumecheng-11687	15	27	,	,	PUNCT
fumecheng-11687	15	28	and	and	CCONJ
fumecheng-11687	15	29	does	do	AUX
fumecheng-11687	15	30	n't	not	PART
fumecheng-11687	15	31	lead	lead	VERB
fumecheng-11687	15	32	to	to	ADP
fumecheng-11687	15	33	any	any	DET
fumecheng-11687	15	34	mathematical	mathematical	ADJ
fumecheng-11687	15	35	difficulties	difficulty	NOUN
fumecheng-11687	15	36	.	.	PUNCT
fumecheng-11687	16	1	key	key	ADJ
fumecheng-11687	16	2	words	word	NOUN
fumecheng-11687	16	3	:	:	PUNCT
fumecheng-11687	16	4	forced	force	VERB
fumecheng-11687	16	5	fractal	fractal	ADJ
fumecheng-11687	16	6	duffing	duffing	NOUN
fumecheng-11687	16	7	oscillator	oscillator	NOUN
fumecheng-11687	16	8	,	,	PUNCT
fumecheng-11687	16	9	non	non	ADJ
fumecheng-11687	16	10	-	-	ADJ
fumecheng-11687	16	11	perturbative	perturbative	ADJ
fumecheng-11687	16	12	(	(	PUNCT
fumecheng-11687	16	13	np	np	NOUN
fumecheng-11687	16	14	)	)	PUNCT
fumecheng-11687	16	15	technique	technique	NOUN
fumecheng-11687	16	16	,	,	PUNCT
fumecheng-11687	16	17	fractal	fractal	ADJ
fumecheng-11687	16	18	space	space	NOUN
fumecheng-11687	16	19	,	,	PUNCT
fumecheng-11687	16	20	galerkin	galerkin	PROPN
fumecheng-11687	16	21	’s	’s	PART
fumecheng-11687	16	22	approach	approach	NOUN
fumecheng-11687	16	23	received	receive	VERB
fumecheng-11687	16	24	:	:	PUNCT
fumecheng-11687	16	25	june	june	PROPN
fumecheng-11687	16	26	05	05	NUM
fumecheng-11687	16	27	,	,	PUNCT
fumecheng-11687	16	28	2023	2023	NUM
fumecheng-11687	16	29	/	/	PUNCT
fumecheng-11687	16	30	accepted	accept	VERB
fumecheng-11687	16	31	october	october	PROPN
fumecheng-11687	16	32	07	07	NUM
fumecheng-11687	16	33	,	,	PUNCT
fumecheng-11687	16	34	2023	2023	NUM
fumecheng-11687	16	35	corresponding	correspond	VERB
fumecheng-11687	16	36	author	author	NOUN
fumecheng-11687	16	37	:	:	PUNCT
fumecheng-11687	16	38	nasser	nasser	PROPN
fumecheng-11687	16	39	s.	s.	PROPN
fumecheng-11687	16	40	elgazery	elgazery	PROPN
fumecheng-11687	16	41	department	department	PROPN
fumecheng-11687	16	42	of	of	ADP
fumecheng-11687	16	43	mathematics	mathematic	NOUN
fumecheng-11687	16	44	,	,	PUNCT
fumecheng-11687	16	45	faculty	faculty	NOUN
fumecheng-11687	16	46	of	of	ADP
fumecheng-11687	16	47	education	education	NOUN
fumecheng-11687	16	48	,	,	PUNCT
fumecheng-11687	16	49	ain	ain	PROPN
fumecheng-11687	16	50	shams	shams	PROPN
fumecheng-11687	16	51	university	university	PROPN
fumecheng-11687	16	52	,	,	PUNCT
fumecheng-11687	16	53	el	el	PROPN
fumecheng-11687	16	54	makrizy	makrizy	PROPN
fumecheng-11687	16	55	street	street	PROPN
fumecheng-11687	16	56	,	,	PUNCT
fumecheng-11687	16	57	roxy	roxy	PROPN
fumecheng-11687	16	58	,	,	PUNCT
fumecheng-11687	16	59	heliopolis	heliopolis	PROPN
fumecheng-11687	16	60	:	:	PUNCT
fumecheng-11687	16	61	11566	11566	NUM
fumecheng-11687	16	62	,	,	PUNCT
fumecheng-11687	16	63	cairo	cairo	PROPN
fumecheng-11687	16	64	,	,	PUNCT
fumecheng-11687	16	65	egypt	egypt	PROPN
fumecheng-11687	16	66	e	e	PROPN
fumecheng-11687	16	67	-	-	NOUN
fumecheng-11687	16	68	mail	mail	NOUN
fumecheng-11687	16	69	:	:	PUNCT
fumecheng-11687	16	70	nasersaleh@edu.asu.edu.eg	nasersaleh@edu.asu.edu.eg	PROPN
fumecheng-11687	16	71	https://orcid.org/0000-0001-6381-5918	https://orcid.org/0000-0001-6381-5918	PRON
fumecheng-11687	17	1	https://orcid.org/0000-0003-4691-2526	https://orcid.org/0000-0003-4691-2526	PROPN
fumecheng-11687	17	2	https://orcid.org/0000-0003-1727-0958	https://orcid.org/0000-0003-1727-0958	PROPN
fumecheng-11687	17	3	mailto:nasersaleh@edu.asu.edu.eg	mailto:nasersaleh@edu.asu.edu.eg	ADP
fumecheng-11687	17	4	200	200	NUM
fumecheng-11687	17	5	y.o	y.o	PROPN
fumecheng-11687	17	6	.	.	PROPN
fumecheng-11687	17	7	el	el	PROPN
fumecheng-11687	17	8	-	-	PUNCT
fumecheng-11687	17	9	dib	dib	PROPN
fumecheng-11687	17	10	,	,	PUNCT
fumecheng-11687	17	11	n.s	n.s	PROPN
fumecheng-11687	17	12	.	.	PROPN
fumecheng-11687	17	13	elgazery	elgazery	PROPN
fumecheng-11687	17	14	,	,	PUNCT
fumecheng-11687	17	15	h.a	h.a	PROPN
fumecheng-11687	17	16	.	.	PROPN
fumecheng-11687	17	17	alyousef	alyousef	PROPN
fumecheng-11687	17	18	1	1	NUM
fumecheng-11687	17	19	.	.	PUNCT
fumecheng-11687	18	1	introduction	introduction	NOUN
fumecheng-11687	18	2	fractals	fractal	NOUN
fumecheng-11687	18	3	have	have	AUX
fumecheng-11687	18	4	been	be	AUX
fumecheng-11687	18	5	a	a	DET
fumecheng-11687	18	6	fascinating	fascinating	ADJ
fumecheng-11687	18	7	characteristic	characteristic	NOUN
fumecheng-11687	18	8	of	of	ADP
fumecheng-11687	18	9	many	many	ADJ
fumecheng-11687	18	10	natural	natural	ADJ
fumecheng-11687	18	11	occurrences	occurrence	NOUN
fumecheng-11687	18	12	since	since	SCONJ
fumecheng-11687	18	13	the	the	DET
fumecheng-11687	18	14	seventeenth	seventeenth	ADJ
fumecheng-11687	18	15	century	century	NOUN
fumecheng-11687	18	16	,	,	PUNCT
fumecheng-11687	18	17	and	and	CCONJ
fumecheng-11687	18	18	they	they	PRON
fumecheng-11687	18	19	have	have	VERB
fumecheng-11687	18	20	a	a	DET
fumecheng-11687	18	21	significant	significant	ADJ
fumecheng-11687	18	22	impact	impact	NOUN
fumecheng-11687	18	23	on	on	ADP
fumecheng-11687	18	24	a	a	DET
fumecheng-11687	18	25	wide	wide	ADJ
fumecheng-11687	18	26	range	range	NOUN
fumecheng-11687	18	27	of	of	ADP
fumecheng-11687	18	28	applications	application	NOUN
fumecheng-11687	18	29	[	[	X
fumecheng-11687	18	30	1,2	1,2	NUM
fumecheng-11687	18	31	]	]	PUNCT
fumecheng-11687	18	32	.	.	PUNCT
fumecheng-11687	19	1	fractals	fractal	NOUN
fumecheng-11687	19	2	have	have	AUX
fumecheng-11687	19	3	been	be	AUX
fumecheng-11687	19	4	widely	widely	ADV
fumecheng-11687	19	5	applied	apply	VERB
fumecheng-11687	19	6	in	in	ADP
fumecheng-11687	19	7	many	many	ADJ
fumecheng-11687	19	8	fields	field	NOUN
fumecheng-11687	19	9	,	,	PUNCT
fumecheng-11687	19	10	such	such	ADJ
fumecheng-11687	19	11	as	as	ADP
fumecheng-11687	19	12	fluid	fluid	ADJ
fumecheng-11687	19	13	mechanics	mechanic	NOUN
fumecheng-11687	19	14	,	,	PUNCT
fumecheng-11687	19	15	materials	material	NOUN
fumecheng-11687	19	16	design	design	NOUN
fumecheng-11687	19	17	,	,	PUNCT
fumecheng-11687	19	18	and	and	CCONJ
fumecheng-11687	19	19	petroleum	petroleum	NOUN
fumecheng-11687	19	20	engineering	engineering	NOUN
fumecheng-11687	19	21	,	,	PUNCT
fumecheng-11687	19	22	as	as	ADV
fumecheng-11687	19	23	well	well	ADV
fumecheng-11687	19	24	as	as	ADP
fumecheng-11687	19	25	in	in	ADP
fumecheng-11687	19	26	other	other	ADJ
fumecheng-11687	19	27	engineering	engineering	NOUN
fumecheng-11687	19	28	problems	problem	NOUN
fumecheng-11687	19	29	to	to	PART
fumecheng-11687	19	30	describe	describe	VERB
fumecheng-11687	19	31	and	and	CCONJ
fumecheng-11687	19	32	express	express	VERB
fumecheng-11687	19	33	them	they	PRON
fumecheng-11687	19	34	clearly	clearly	ADV
fumecheng-11687	19	35	and	and	CCONJ
fumecheng-11687	19	36	effectively	effectively	ADV
fumecheng-11687	19	37	[	[	X
fumecheng-11687	19	38	3,4	3,4	NUM
fumecheng-11687	19	39	]	]	PUNCT
fumecheng-11687	19	40	.	.	PUNCT
fumecheng-11687	20	1	this	this	PRON
fumecheng-11687	20	2	also	also	ADV
fumecheng-11687	20	3	appears	appear	VERB
fumecheng-11687	20	4	clearly	clearly	ADV
fumecheng-11687	20	5	in	in	ADP
fumecheng-11687	20	6	the	the	DET
fumecheng-11687	20	7	application	application	NOUN
fumecheng-11687	20	8	of	of	ADP
fumecheng-11687	20	9	the	the	DET
fumecheng-11687	20	10	theory	theory	NOUN
fumecheng-11687	20	11	of	of	ADP
fumecheng-11687	20	12	fractals	fractal	NOUN
fumecheng-11687	20	13	in	in	ADP
fumecheng-11687	20	14	the	the	DET
fumecheng-11687	20	15	investigation	investigation	NOUN
fumecheng-11687	20	16	within	within	ADP
fumecheng-11687	20	17	the	the	DET
fumecheng-11687	20	18	branched	branched	ADJ
fumecheng-11687	20	19	networks	network	NOUN
fumecheng-11687	20	20	to	to	PART
fumecheng-11687	20	21	study	study	VERB
fumecheng-11687	20	22	thermal	thermal	ADJ
fumecheng-11687	20	23	conductivity	conductivity	NOUN
fumecheng-11687	20	24	[	[	X
fumecheng-11687	20	25	5,6	5,6	NUM
fumecheng-11687	20	26	]	]	X
fumecheng-11687	20	27	.	.	PUNCT
fumecheng-11687	21	1	for	for	ADP
fumecheng-11687	21	2	the	the	DET
fumecheng-11687	21	3	electrical	electrical	ADJ
fumecheng-11687	21	4	and	and	CCONJ
fumecheng-11687	21	5	mechanical	mechanical	ADJ
fumecheng-11687	21	6	properties	property	NOUN
fumecheng-11687	21	7	of	of	ADP
fumecheng-11687	21	8	composite	composite	ADJ
fumecheng-11687	21	9	materials	material	NOUN
fumecheng-11687	21	10	,	,	PUNCT
fumecheng-11687	21	11	the	the	DET
fumecheng-11687	21	12	fractal	fractal	ADJ
fumecheng-11687	21	13	approach	approach	NOUN
fumecheng-11687	21	14	offers	offer	VERB
fumecheng-11687	21	15	straightforward	straightforward	ADJ
fumecheng-11687	21	16	and	and	CCONJ
fumecheng-11687	21	17	effective	effective	ADJ
fumecheng-11687	21	18	tools	tool	NOUN
fumecheng-11687	21	19	[	[	X
fumecheng-11687	21	20	7	7	NUM
fumecheng-11687	21	21	]	]	PUNCT
fumecheng-11687	21	22	.	.	PUNCT
fumecheng-11687	22	1	moreover	moreover	ADV
fumecheng-11687	22	2	,	,	PUNCT
fumecheng-11687	22	3	the	the	DET
fumecheng-11687	22	4	fractal	fractal	ADJ
fumecheng-11687	22	5	rheological	rheological	ADJ
fumecheng-11687	22	6	models	model	NOUN
fumecheng-11687	22	7	provide	provide	VERB
fumecheng-11687	22	8	a	a	DET
fumecheng-11687	22	9	fast	fast	ADJ
fumecheng-11687	22	10	physical	physical	ADJ
fumecheng-11687	22	11	understanding	understanding	NOUN
fumecheng-11687	22	12	of	of	ADP
fumecheng-11687	22	13	the	the	DET
fumecheng-11687	22	14	rheological	rheological	ADJ
fumecheng-11687	22	15	characteristics	characteristic	NOUN
fumecheng-11687	22	16	of	of	ADP
fumecheng-11687	22	17	the	the	DET
fumecheng-11687	22	18	fluids	fluid	NOUN
fumecheng-11687	22	19	[	[	X
fumecheng-11687	22	20	8	8	NUM
fumecheng-11687	22	21	]	]	PUNCT
fumecheng-11687	22	22	.	.	PUNCT
fumecheng-11687	23	1	due	due	ADP
fumecheng-11687	23	2	to	to	ADP
fumecheng-11687	23	3	its	its	PRON
fumecheng-11687	23	4	numerous	numerous	ADJ
fumecheng-11687	23	5	large	large	ADJ
fumecheng-11687	23	6	-	-	PUNCT
fumecheng-11687	23	7	scale	scale	NOUN
fumecheng-11687	23	8	applications	application	NOUN
fumecheng-11687	23	9	for	for	ADP
fumecheng-11687	23	10	modeling	model	VERB
fumecheng-11687	23	11	a	a	DET
fumecheng-11687	23	12	variety	variety	NOUN
fumecheng-11687	23	13	of	of	ADP
fumecheng-11687	23	14	phenomena	phenomenon	NOUN
fumecheng-11687	23	15	that	that	PRON
fumecheng-11687	23	16	emerge	emerge	VERB
fumecheng-11687	23	17	in	in	ADP
fumecheng-11687	23	18	most	most	ADJ
fumecheng-11687	23	19	domains	domain	NOUN
fumecheng-11687	23	20	,	,	PUNCT
fumecheng-11687	23	21	the	the	DET
fumecheng-11687	23	22	idea	idea	NOUN
fumecheng-11687	23	23	of	of	ADP
fumecheng-11687	23	24	two	two	NUM
fumecheng-11687	23	25	-	-	PUNCT
fumecheng-11687	23	26	scale	scale	NOUN
fumecheng-11687	23	27	fractals	fractal	NOUN
fumecheng-11687	23	28	theory	theory	NOUN
fumecheng-11687	23	29	has	have	AUX
fumecheng-11687	23	30	recently	recently	ADV
fumecheng-11687	23	31	drawn	draw	VERB
fumecheng-11687	23	32	significant	significant	ADJ
fumecheng-11687	23	33	attention	attention	NOUN
fumecheng-11687	23	34	from	from	ADP
fumecheng-11687	23	35	scientists	scientist	NOUN
fumecheng-11687	23	36	[	[	X
fumecheng-11687	23	37	9	9	NUM
fumecheng-11687	23	38	]	]	PUNCT
fumecheng-11687	23	39	.	.	PUNCT
fumecheng-11687	24	1	where	where	SCONJ
fumecheng-11687	24	2	this	this	DET
fumecheng-11687	24	3	theory	theory	NOUN
fumecheng-11687	24	4	enables	enable	VERB
fumecheng-11687	24	5	each	each	DET
fumecheng-11687	24	6	problem	problem	NOUN
fumecheng-11687	24	7	to	to	PART
fumecheng-11687	24	8	be	be	AUX
fumecheng-11687	24	9	observed	observe	VERB
fumecheng-11687	24	10	on	on	ADP
fumecheng-11687	24	11	two	two	NUM
fumecheng-11687	24	12	different	different	ADJ
fumecheng-11687	24	13	scales	scale	NOUN
fumecheng-11687	24	14	,	,	PUNCT
fumecheng-11687	24	15	one	one	NUM
fumecheng-11687	24	16	of	of	ADP
fumecheng-11687	24	17	which	which	PRON
fumecheng-11687	24	18	is	be	AUX
fumecheng-11687	24	19	related	relate	VERB
fumecheng-11687	24	20	to	to	ADP
fumecheng-11687	24	21	a	a	DET
fumecheng-11687	24	22	continuous	continuous	ADJ
fumecheng-11687	24	23	problem	problem	NOUN
fumecheng-11687	24	24	and	and	CCONJ
fumecheng-11687	24	25	the	the	DET
fumecheng-11687	24	26	other	other	ADJ
fumecheng-11687	24	27	to	to	ADP
fumecheng-11687	24	28	a	a	DET
fumecheng-11687	24	29	discrete	discrete	ADJ
fumecheng-11687	24	30	problem	problem	NOUN
fumecheng-11687	24	31	.	.	PUNCT
fumecheng-11687	25	1	the	the	DET
fumecheng-11687	25	2	hidden	hidden	ADJ
fumecheng-11687	25	3	qualities	quality	NOUN
fumecheng-11687	25	4	of	of	ADP
fumecheng-11687	25	5	a	a	DET
fumecheng-11687	25	6	polymer	polymer	NOUN
fumecheng-11687	25	7	procedure	procedure	NOUN
fumecheng-11687	25	8	that	that	PRON
fumecheng-11687	25	9	can	can	AUX
fumecheng-11687	25	10	not	not	PART
fumecheng-11687	25	11	be	be	AUX
fumecheng-11687	25	12	exposed	expose	VERB
fumecheng-11687	25	13	by	by	ADP
fumecheng-11687	25	14	other	other	ADJ
fumecheng-11687	25	15	models	model	NOUN
fumecheng-11687	25	16	can	can	AUX
fumecheng-11687	25	17	be	be	AUX
fumecheng-11687	25	18	determined	determine	VERB
fumecheng-11687	25	19	using	use	VERB
fumecheng-11687	25	20	the	the	DET
fumecheng-11687	25	21	fractal	fractal	ADJ
fumecheng-11687	25	22	two	two	NUM
fumecheng-11687	25	23	-	-	PUNCT
fumecheng-11687	25	24	phase	phase	NOUN
fumecheng-11687	25	25	flow	flow	NOUN
fumecheng-11687	25	26	model	model	NOUN
fumecheng-11687	26	1	[	[	X
fumecheng-11687	26	2	1012	1012	NUM
fumecheng-11687	26	3	]	]	PUNCT
fumecheng-11687	26	4	.	.	PUNCT
fumecheng-11687	27	1	he	he	PRON
fumecheng-11687	27	2	et	et	PROPN
fumecheng-11687	27	3	al	al	PROPN
fumecheng-11687	27	4	.	.	PUNCT
fumecheng-11687	28	1	[	[	X
fumecheng-11687	28	2	13	13	NUM
fumecheng-11687	28	3	]	]	PUNCT
fumecheng-11687	28	4	used	use	VERB
fumecheng-11687	28	5	a	a	DET
fumecheng-11687	28	6	novel	novel	ADJ
fumecheng-11687	28	7	fractal	fractal	ADJ
fumecheng-11687	28	8	vibration	vibration	NOUN
fumecheng-11687	28	9	architecture	architecture	NOUN
fumecheng-11687	28	10	model	model	NOUN
fumecheng-11687	28	11	using	use	VERB
fumecheng-11687	28	12	the	the	DET
fumecheng-11687	28	13	two	two	NUM
fumecheng-11687	28	14	-	-	PUNCT
fumecheng-11687	28	15	scale	scale	NOUN
fumecheng-11687	28	16	fractals	fractal	NOUN
fumecheng-11687	28	17	theory	theory	NOUN
fumecheng-11687	28	18	.	.	PUNCT
fumecheng-11687	29	1	anjum	anjum	PROPN
fumecheng-11687	29	2	et	et	PROPN
fumecheng-11687	29	3	al	al	PROPN
fumecheng-11687	29	4	.	.	PUNCT
fumecheng-11687	30	1	[	[	X
fumecheng-11687	30	2	14,15	14,15	NUM
fumecheng-11687	30	3	]	]	PUNCT
fumecheng-11687	30	4	also	also	ADV
fumecheng-11687	30	5	investigate	investigate	VERB
fumecheng-11687	30	6	two	two	NUM
fumecheng-11687	30	7	different	different	ADJ
fumecheng-11687	30	8	fractional	fractional	ADJ
fumecheng-11687	30	9	models	model	NOUN
fumecheng-11687	30	10	with	with	ADP
fumecheng-11687	30	11	two	two	NUM
fumecheng-11687	30	12	-	-	PUNCT
fumecheng-11687	30	13	scale	scale	NOUN
fumecheng-11687	30	14	for	for	ADP
fumecheng-11687	30	15	population	population	NOUN
fumecheng-11687	30	16	expansion	expansion	NOUN
fumecheng-11687	30	17	and	and	CCONJ
fumecheng-11687	30	18	tsunami	tsunami	NOUN
fumecheng-11687	30	19	waves	wave	NOUN
fumecheng-11687	30	20	,	,	PUNCT
fumecheng-11687	30	21	respectively	respectively	ADV
fumecheng-11687	30	22	.	.	PUNCT
fumecheng-11687	31	1	an	an	DET
fumecheng-11687	31	2	interesting	interesting	ADJ
fumecheng-11687	31	3	topic	topic	NOUN
fumecheng-11687	31	4	in	in	ADP
fumecheng-11687	31	5	mechanical	mechanical	ADJ
fumecheng-11687	31	6	engineering	engineering	NOUN
fumecheng-11687	31	7	sciences	sciences	PROPN
fumecheng-11687	31	8	and	and	CCONJ
fumecheng-11687	31	9	physics	physics	NOUN
fumecheng-11687	31	10	is	be	AUX
fumecheng-11687	31	11	nonlinear	nonlinear	ADJ
fumecheng-11687	31	12	oscillations	oscillation	NOUN
fumecheng-11687	31	13	.	.	PUNCT
fumecheng-11687	32	1	one	one	NUM
fumecheng-11687	32	2	of	of	ADP
fumecheng-11687	32	3	the	the	DET
fumecheng-11687	32	4	most	most	ADV
fumecheng-11687	32	5	well	well	ADV
fumecheng-11687	32	6	-	-	PUNCT
fumecheng-11687	32	7	liked	like	VERB
fumecheng-11687	32	8	nonlinear	nonlinear	ADJ
fumecheng-11687	32	9	oscillators	oscillator	NOUN
fumecheng-11687	32	10	in	in	ADP
fumecheng-11687	32	11	engineering	engineering	NOUN
fumecheng-11687	32	12	,	,	PUNCT
fumecheng-11687	32	13	physics	physics	NOUN
fumecheng-11687	32	14	,	,	PUNCT
fumecheng-11687	32	15	and	and	CCONJ
fumecheng-11687	32	16	biology	biology	NOUN
fumecheng-11687	32	17	was	be	AUX
fumecheng-11687	32	18	first	first	ADV
fumecheng-11687	32	19	introduced	introduce	VERB
fumecheng-11687	32	20	in	in	ADP
fumecheng-11687	32	21	1918	1918	NUM
fumecheng-11687	32	22	by	by	ADP
fumecheng-11687	32	23	the	the	DET
fumecheng-11687	32	24	german	german	ADJ
fumecheng-11687	32	25	electrical	electrical	ADJ
fumecheng-11687	32	26	engineer	engineer	NOUN
fumecheng-11687	32	27	"	"	PUNCT
fumecheng-11687	32	28	georg	georg	NOUN
fumecheng-11687	32	29	duffing	duffing	NOUN
fumecheng-11687	32	30	"	"	PUNCT
fumecheng-11687	32	31	.	.	PUNCT
fumecheng-11687	33	1	since	since	SCONJ
fumecheng-11687	33	2	then	then	ADV
fumecheng-11687	33	3	,	,	PUNCT
fumecheng-11687	33	4	duffing	duffe	VERB
fumecheng-11687	33	5	oscillators	oscillator	NOUN
fumecheng-11687	33	6	have	have	AUX
fumecheng-11687	33	7	been	be	AUX
fumecheng-11687	33	8	widely	widely	ADV
fumecheng-11687	33	9	applied	apply	VERB
fumecheng-11687	33	10	in	in	ADP
fumecheng-11687	33	11	nature	nature	NOUN
fumecheng-11687	33	12	.	.	PUNCT
fumecheng-11687	34	1	using	use	VERB
fumecheng-11687	34	2	a	a	DET
fumecheng-11687	34	3	traditional	traditional	ADJ
fumecheng-11687	34	4	perturbation	perturbation	NOUN
fumecheng-11687	34	5	method	method	NOUN
fumecheng-11687	34	6	,	,	PUNCT
fumecheng-11687	34	7	nayfeh	nayfeh	NOUN
fumecheng-11687	34	8	and	and	CCONJ
fumecheng-11687	34	9	mook	mook	NOUN
fumecheng-11687	34	10	derived	derive	VERB
fumecheng-11687	34	11	a	a	DET
fumecheng-11687	34	12	periodic	periodic	ADJ
fumecheng-11687	34	13	solution	solution	NOUN
fumecheng-11687	34	14	for	for	ADP
fumecheng-11687	34	15	the	the	DET
fumecheng-11687	34	16	duffing	duffing	NOUN
fumecheng-11687	34	17	oscillator	oscillator	NOUN
fumecheng-11687	34	18	,	,	PUNCT
fumecheng-11687	34	19	which	which	PRON
fumecheng-11687	34	20	simulates	simulate	VERB
fumecheng-11687	34	21	a	a	DET
fumecheng-11687	34	22	nonlinear	nonlinear	ADJ
fumecheng-11687	34	23	structural	structural	ADJ
fumecheng-11687	34	24	vibration	vibration	NOUN
fumecheng-11687	34	25	.	.	PUNCT
fumecheng-11687	35	1	moreover	moreover	ADV
fumecheng-11687	35	2	,	,	PUNCT
fumecheng-11687	35	3	nayfeh	nayfeh	PROPN
fumecheng-11687	35	4	used	use	VERB
fumecheng-11687	35	5	the	the	DET
fumecheng-11687	35	6	multiple	multiple	ADJ
fumecheng-11687	35	7	-	-	PUNCT
fumecheng-11687	35	8	scale	scale	NOUN
fumecheng-11687	35	9	methodology	methodology	NOUN
fumecheng-11687	35	10	to	to	PART
fumecheng-11687	35	11	produce	produce	VERB
fumecheng-11687	35	12	a	a	DET
fumecheng-11687	35	13	periodic	periodic	ADJ
fumecheng-11687	35	14	analytical	analytical	ADJ
fumecheng-11687	35	15	solution	solution	NOUN
fumecheng-11687	35	16	for	for	ADP
fumecheng-11687	35	17	a	a	DET
fumecheng-11687	35	18	duffing	duffing	NOUN
fumecheng-11687	35	19	oscillator	oscillator	NOUN
fumecheng-11687	35	20	in	in	ADP
fumecheng-11687	35	21	the	the	DET
fumecheng-11687	35	22	presence	presence	NOUN
fumecheng-11687	35	23	of	of	ADP
fumecheng-11687	35	24	a	a	DET
fumecheng-11687	35	25	damping	damp	VERB
fumecheng-11687	35	26	coefficient	coefficient	NOUN
fumecheng-11687	35	27	[	[	X
fumecheng-11687	35	28	16	16	NUM
fumecheng-11687	35	29	]	]	PUNCT
fumecheng-11687	35	30	.	.	PUNCT
fumecheng-11687	36	1	the	the	DET
fumecheng-11687	36	2	homotopy	homotopy	NOUN
fumecheng-11687	36	3	perturbation	perturbation	NOUN
fumecheng-11687	36	4	technique	technique	NOUN
fumecheng-11687	36	5	was	be	AUX
fumecheng-11687	36	6	later	later	ADV
fumecheng-11687	36	7	developed	develop	VERB
fumecheng-11687	36	8	by	by	ADP
fumecheng-11687	36	9	renowned	renowned	ADJ
fumecheng-11687	36	10	chinese	chinese	ADJ
fumecheng-11687	36	11	scientist	scientist	NOUN
fumecheng-11687	36	12	ji	ji	PROPN
fumecheng-11687	36	13	-	-	PROPN
fumecheng-11687	36	14	huan	huan	PROPN
fumecheng-11687	36	15	he	he	PRON
fumecheng-11687	37	1	[	[	X
fumecheng-11687	37	2	17	17	NUM
fumecheng-11687	37	3	]	]	PUNCT
fumecheng-11687	37	4	and	and	CCONJ
fumecheng-11687	37	5	utilized	utilize	VERB
fumecheng-11687	37	6	in	in	ADP
fumecheng-11687	37	7	several	several	ADJ
fumecheng-11687	37	8	engineering	engineering	NOUN
fumecheng-11687	37	9	and	and	CCONJ
fumecheng-11687	37	10	physics	physics	NOUN
fumecheng-11687	37	11	investigations	investigation	NOUN
fumecheng-11687	37	12	to	to	PART
fumecheng-11687	37	13	determine	determine	VERB
fumecheng-11687	37	14	analytical	analytical	ADJ
fumecheng-11687	37	15	solutions	solution	NOUN
fumecheng-11687	37	16	for	for	ADP
fumecheng-11687	37	17	the	the	DET
fumecheng-11687	37	18	duffing	duffing	NOUN
fumecheng-11687	37	19	oscillator	oscillator	NOUN
fumecheng-11687	37	20	and	and	CCONJ
fumecheng-11687	37	21	other	other	ADJ
fumecheng-11687	37	22	mechanical	mechanical	ADJ
fumecheng-11687	37	23	vibrations	vibration	NOUN
fumecheng-11687	37	24	.	.	PUNCT
fumecheng-11687	38	1	on	on	ADP
fumecheng-11687	38	2	the	the	DET
fumecheng-11687	38	3	other	other	ADJ
fumecheng-11687	38	4	hand	hand	NOUN
fumecheng-11687	38	5	,	,	PUNCT
fumecheng-11687	38	6	recent	recent	ADJ
fumecheng-11687	38	7	years	year	NOUN
fumecheng-11687	38	8	have	have	AUX
fumecheng-11687	38	9	seen	see	VERB
fumecheng-11687	38	10	an	an	DET
fumecheng-11687	38	11	increase	increase	NOUN
fumecheng-11687	38	12	in	in	ADP
fumecheng-11687	38	13	interest	interest	NOUN
fumecheng-11687	38	14	in	in	ADP
fumecheng-11687	38	15	mechanical	mechanical	ADJ
fumecheng-11687	38	16	engineering	engineering	NOUN
fumecheng-11687	38	17	applications	application	NOUN
fumecheng-11687	38	18	for	for	ADP
fumecheng-11687	38	19	fractal	fractal	ADJ
fumecheng-11687	38	20	oscillators	oscillator	NOUN
fumecheng-11687	38	21	,	,	PUNCT
fumecheng-11687	38	22	as	as	ADP
fumecheng-11687	38	23	a	a	DET
fumecheng-11687	38	24	subfield	subfield	NOUN
fumecheng-11687	38	25	of	of	ADP
fumecheng-11687	38	26	vibration	vibration	NOUN
fumecheng-11687	38	27	theory	theory	NOUN
fumecheng-11687	38	28	.	.	PUNCT
fumecheng-11687	39	1	wang	wang	PROPN
fumecheng-11687	40	1	[	[	X
fumecheng-11687	40	2	18	18	NUM
fumecheng-11687	40	3	]	]	PUNCT
fumecheng-11687	40	4	used	use	VERB
fumecheng-11687	40	5	a	a	DET
fumecheng-11687	40	6	novel	novel	ADJ
fumecheng-11687	40	7	frequency	frequency	NOUN
fumecheng-11687	40	8	formulation	formulation	NOUN
fumecheng-11687	40	9	to	to	PART
fumecheng-11687	40	10	study	study	VERB
fumecheng-11687	40	11	a	a	DET
fumecheng-11687	40	12	fractal	fractal	ADJ
fumecheng-11687	40	13	nonlinear	nonlinear	ADJ
fumecheng-11687	40	14	oscillator	oscillator	NOUN
fumecheng-11687	40	15	.	.	PUNCT
fumecheng-11687	41	1	the	the	DET
fumecheng-11687	41	2	same	same	ADJ
fumecheng-11687	41	3	author	author	NOUN
fumecheng-11687	41	4	also	also	ADV
fumecheng-11687	41	5	found	find	VERB
fumecheng-11687	41	6	an	an	DET
fumecheng-11687	41	7	analytical	analytical	ADJ
fumecheng-11687	41	8	solution	solution	NOUN
fumecheng-11687	41	9	for	for	ADP
fumecheng-11687	41	10	a	a	DET
fumecheng-11687	41	11	fractal	fractal	ADJ
fumecheng-11687	41	12	nonlinear	nonlinear	ADJ
fumecheng-11687	41	13	oscillator	oscillator	NOUN
fumecheng-11687	41	14	in	in	ADP
fumecheng-11687	41	15	[	[	X
fumecheng-11687	41	16	19	19	NUM
fumecheng-11687	41	17	]	]	PUNCT
fumecheng-11687	41	18	by	by	ADP
fumecheng-11687	41	19	employing	employ	VERB
fumecheng-11687	41	20	the	the	DET
fumecheng-11687	41	21	effective	effective	ADJ
fumecheng-11687	41	22	he	he	PRON
fumecheng-11687	41	23	's	's	PART
fumecheng-11687	41	24	frequency	frequency	NOUN
fumecheng-11687	41	25	formulation	formulation	NOUN
fumecheng-11687	41	26	.	.	PUNCT
fumecheng-11687	42	1	further	far	ADV
fumecheng-11687	42	2	,	,	PUNCT
fumecheng-11687	42	3	wang	wang	PROPN
fumecheng-11687	42	4	and	and	CCONJ
fumecheng-11687	42	5	wei	wei	PROPN
fumecheng-11687	43	1	[	[	X
fumecheng-11687	43	2	20	20	NUM
fumecheng-11687	43	3	]	]	PUNCT
fumecheng-11687	43	4	have	have	AUX
fumecheng-11687	43	5	presented	present	VERB
fumecheng-11687	43	6	a	a	DET
fumecheng-11687	43	7	newfangled	newfangled	ADJ
fumecheng-11687	43	8	,	,	PUNCT
fumecheng-11687	43	9	straightforward	straightforward	ADJ
fumecheng-11687	43	10	,	,	PUNCT
fumecheng-11687	43	11	and	and	CCONJ
fumecheng-11687	43	12	effective	effective	ADJ
fumecheng-11687	43	13	frequency	frequency	NOUN
fumecheng-11687	43	14	formula	formula	NOUN
fumecheng-11687	43	15	to	to	PART
fumecheng-11687	43	16	deal	deal	VERB
fumecheng-11687	43	17	with	with	ADP
fumecheng-11687	43	18	fractal	fractal	ADJ
fumecheng-11687	43	19	nonlinear	nonlinear	ADJ
fumecheng-11687	43	20	oscillators	oscillator	NOUN
fumecheng-11687	43	21	.	.	PUNCT
fumecheng-11687	44	1	also	also	ADV
fumecheng-11687	44	2	,	,	PUNCT
fumecheng-11687	44	3	two	two	NUM
fumecheng-11687	44	4	approximate	approximate	ADJ
fumecheng-11687	44	5	solutions	solution	NOUN
fumecheng-11687	44	6	for	for	ADP
fumecheng-11687	44	7	the	the	DET
fumecheng-11687	44	8	fractal	fractal	ADJ
fumecheng-11687	44	9	yao	yao	PROPN
fumecheng-11687	44	10	-	-	PUNCT
fumecheng-11687	44	11	cheng	cheng	PROPN
fumecheng-11687	44	12	and	and	CCONJ
fumecheng-11687	44	13	duffing	duffe	VERB
fumecheng-11687	44	14	oscillators	oscillator	NOUN
fumecheng-11687	44	15	have	have	AUX
fumecheng-11687	44	16	been	be	AUX
fumecheng-11687	44	17	introduced	introduce	VERB
fumecheng-11687	44	18	in	in	ADP
fumecheng-11687	44	19	[	[	PUNCT
fumecheng-11687	44	20	21	21	NUM
fumecheng-11687	44	21	-	-	SYM
fumecheng-11687	44	22	23	23	NUM
fumecheng-11687	44	23	]	]	PUNCT
fumecheng-11687	44	24	,	,	PUNCT
fumecheng-11687	44	25	built	build	VERB
fumecheng-11687	44	26	on	on	ADP
fumecheng-11687	44	27	the	the	DET
fumecheng-11687	44	28	harmonic	harmonic	ADJ
fumecheng-11687	44	29	balance	balance	NOUN
fumecheng-11687	44	30	and	and	CCONJ
fumecheng-11687	44	31	antiquated	antiquate	VERB
fumecheng-11687	44	32	chinese	chinese	ADJ
fumecheng-11687	44	33	approaches	approach	NOUN
fumecheng-11687	44	34	.	.	PUNCT
fumecheng-11687	45	1	since	since	SCONJ
fumecheng-11687	45	2	the	the	DET
fumecheng-11687	45	3	solution	solution	NOUN
fumecheng-11687	45	4	of	of	ADP
fumecheng-11687	45	5	systems	system	NOUN
fumecheng-11687	45	6	related	relate	VERB
fumecheng-11687	45	7	to	to	ADP
fumecheng-11687	45	8	the	the	DET
fumecheng-11687	45	9	study	study	NOUN
fumecheng-11687	45	10	of	of	ADP
fumecheng-11687	45	11	fractal	fractal	ADJ
fumecheng-11687	45	12	oscillators	oscillator	NOUN
fumecheng-11687	45	13	plays	play	VERB
fumecheng-11687	45	14	an	an	DET
fumecheng-11687	45	15	important	important	ADJ
fumecheng-11687	45	16	and	and	CCONJ
fumecheng-11687	45	17	useful	useful	ADJ
fumecheng-11687	45	18	role	role	NOUN
fumecheng-11687	45	19	in	in	ADP
fumecheng-11687	45	20	describing	describe	VERB
fumecheng-11687	45	21	and	and	CCONJ
fumecheng-11687	45	22	explaining	explain	VERB
fumecheng-11687	45	23	many	many	ADJ
fumecheng-11687	45	24	phenomena	phenomenon	NOUN
fumecheng-11687	45	25	that	that	PRON
fumecheng-11687	45	26	occur	occur	VERB
fumecheng-11687	45	27	on	on	ADP
fumecheng-11687	45	28	irregular	irregular	ADJ
fumecheng-11687	45	29	boundaries	boundary	NOUN
fumecheng-11687	45	30	or	or	CCONJ
fumecheng-11687	45	31	in	in	ADP
fumecheng-11687	45	32	porous	porous	ADJ
fumecheng-11687	45	33	media	medium	NOUN
fumecheng-11687	45	34	.	.	PUNCT
fumecheng-11687	46	1	essentially	essentially	ADV
fumecheng-11687	46	2	,	,	PUNCT
fumecheng-11687	46	3	it	it	PRON
fumecheng-11687	46	4	is	be	AUX
fumecheng-11687	46	5	usually	usually	ADV
fumecheng-11687	46	6	impossible	impossible	ADJ
fumecheng-11687	46	7	to	to	PART
fumecheng-11687	46	8	find	find	VERB
fumecheng-11687	46	9	exact	exact	ADJ
fumecheng-11687	46	10	solutions	solution	NOUN
fumecheng-11687	46	11	for	for	ADP
fumecheng-11687	46	12	these	these	DET
fumecheng-11687	46	13	nonlinear	nonlinear	ADJ
fumecheng-11687	46	14	oscillators	oscillator	NOUN
fumecheng-11687	46	15	.	.	PUNCT
fumecheng-11687	47	1	as	as	ADP
fumecheng-11687	47	2	a	a	DET
fumecheng-11687	47	3	result	result	NOUN
fumecheng-11687	47	4	,	,	PUNCT
fumecheng-11687	47	5	mathematicians	mathematician	NOUN
fumecheng-11687	47	6	have	have	AUX
fumecheng-11687	47	7	been	be	AUX
fumecheng-11687	47	8	developing	develop	VERB
fumecheng-11687	47	9	different	different	ADJ
fumecheng-11687	47	10	analytical	analytical	ADJ
fumecheng-11687	47	11	methods	method	NOUN
fumecheng-11687	47	12	to	to	PART
fumecheng-11687	47	13	solve	solve	VERB
fumecheng-11687	47	14	this	this	DET
fumecheng-11687	47	15	type	type	NOUN
fumecheng-11687	47	16	of	of	ADP
fumecheng-11687	47	17	nonlinear	nonlinear	ADJ
fumecheng-11687	47	18	fractal	fractal	ADJ
fumecheng-11687	47	19	problem	problem	NOUN
fumecheng-11687	47	20	,	,	PUNCT
fumecheng-11687	47	21	such	such	ADJ
fumecheng-11687	47	22	as	as	ADP
fumecheng-11687	47	23	using	use	VERB
fumecheng-11687	47	24	extended	extended	ADJ
fumecheng-11687	47	25	approximation	approximation	NOUN
fumecheng-11687	47	26	approaches	approach	NOUN
fumecheng-11687	47	27	.	.	PUNCT
fumecheng-11687	48	1	the	the	DET
fumecheng-11687	48	2	most	most	ADV
fumecheng-11687	48	3	prominent	prominent	ADJ
fumecheng-11687	48	4	of	of	ADP
fumecheng-11687	48	5	these	these	DET
fumecheng-11687	48	6	methods	method	NOUN
fumecheng-11687	48	7	are	be	AUX
fumecheng-11687	48	8	perturbation	perturbation	NOUN
fumecheng-11687	48	9	and	and	CCONJ
fumecheng-11687	48	10	multiplescale	multiplescale	NOUN
fumecheng-11687	48	11	techniques	technique	NOUN
fumecheng-11687	48	12	[	[	X
fumecheng-11687	48	13	16	16	NUM
fumecheng-11687	48	14	]	]	PUNCT
fumecheng-11687	48	15	.	.	PUNCT
fumecheng-11687	49	1	sheng	sheng	PROPN
fumecheng-11687	49	2	et	et	PROPN
fumecheng-11687	49	3	al	al	PROPN
fumecheng-11687	49	4	.	.	PUNCT
fumecheng-11687	50	1	[	[	X
fumecheng-11687	50	2	24	24	NUM
fumecheng-11687	50	3	]	]	PUNCT
fumecheng-11687	50	4	have	have	AUX
fumecheng-11687	50	5	presented	present	VERB
fumecheng-11687	50	6	a	a	DET
fumecheng-11687	50	7	fractal	fractal	ADJ
fumecheng-11687	50	8	model	model	NOUN
fumecheng-11687	50	9	for	for	ADP
fumecheng-11687	50	10	a	a	DET
fumecheng-11687	50	11	shale	shale	NOUN
fumecheng-11687	50	12	matrix	matrix	NOUN
fumecheng-11687	50	13	the	the	DET
fumecheng-11687	50	14	up	up	ADV
fumecheng-11687	50	15	-	-	PUNCT
fumecheng-11687	50	16	grating	grate	VERB
fumecheng-11687	50	17	rank	rank	NOUN
fumecheng-11687	50	18	approach	approach	NOUN
fumecheng-11687	50	19	to	to	PART
fumecheng-11687	50	20	solve	solve	VERB
fumecheng-11687	50	21	a	a	DET
fumecheng-11687	50	22	forced	force	VERB
fumecheng-11687	50	23	fractal	fractal	ADJ
fumecheng-11687	50	24	duffing	duffing	NOUN
fumecheng-11687	50	25	oscillator	oscillator	NOUN
fumecheng-11687	50	26	by	by	ADP
fumecheng-11687	50	27	the	the	DET
fumecheng-11687	50	28	np	np	PROPN
fumecheng-11687	50	29	technique	technique	NOUN
fumecheng-11687	50	30	201	201	NUM
fumecheng-11687	50	31	using	use	VERB
fumecheng-11687	50	32	a	a	DET
fumecheng-11687	50	33	multi	multi	ADJ
fumecheng-11687	50	34	-	-	ADJ
fumecheng-11687	50	35	scale	scale	ADJ
fumecheng-11687	50	36	porous	porous	ADJ
fumecheng-11687	50	37	structure	structure	NOUN
fumecheng-11687	50	38	.	.	PUNCT
fumecheng-11687	51	1	miao	miao	NOUN
fumecheng-11687	51	2	et	et	PROPN
fumecheng-11687	51	3	al	al	PROPN
fumecheng-11687	51	4	.	.	PUNCT
fumecheng-11687	52	1	[	[	X
fumecheng-11687	52	2	25	25	NUM
fumecheng-11687	52	3	]	]	PUNCT
fumecheng-11687	52	4	investigated	investigate	VERB
fumecheng-11687	52	5	another	another	DET
fumecheng-11687	52	6	fractal	fractal	ADJ
fumecheng-11687	52	7	model	model	NOUN
fumecheng-11687	52	8	for	for	ADP
fumecheng-11687	52	9	a	a	DET
fumecheng-11687	52	10	fractured	fractured	ADJ
fumecheng-11687	52	11	porous	porous	ADJ
fumecheng-11687	52	12	medium	medium	NOUN
fumecheng-11687	52	13	.	.	PUNCT
fumecheng-11687	53	1	furthermore	furthermore	ADV
fumecheng-11687	53	2	,	,	PUNCT
fumecheng-11687	53	3	other	other	ADJ
fumecheng-11687	53	4	fractal	fractal	ADJ
fumecheng-11687	53	5	models	model	NOUN
fumecheng-11687	53	6	for	for	ADP
fumecheng-11687	53	7	describing	describe	VERB
fumecheng-11687	53	8	the	the	DET
fumecheng-11687	53	9	gas	gas	NOUN
fumecheng-11687	53	10	flow	flow	NOUN
fumecheng-11687	53	11	inside	inside	ADP
fumecheng-11687	53	12	microfractures	microfracture	NOUN
fumecheng-11687	53	13	in	in	ADP
fumecheng-11687	53	14	layers	layer	NOUN
fumecheng-11687	53	15	of	of	ADP
fumecheng-11687	53	16	rocks	rock	NOUN
fumecheng-11687	53	17	in	in	ADP
fumecheng-11687	53	18	the	the	DET
fumecheng-11687	53	19	depths	depth	NOUN
fumecheng-11687	53	20	of	of	ADP
fumecheng-11687	53	21	the	the	DET
fumecheng-11687	53	22	oceans	ocean	NOUN
fumecheng-11687	53	23	and	and	CCONJ
fumecheng-11687	53	24	underground	underground	NOUN
fumecheng-11687	53	25	have	have	AUX
fumecheng-11687	53	26	been	be	AUX
fumecheng-11687	53	27	mentioned	mention	VERB
fumecheng-11687	53	28	in	in	ADP
fumecheng-11687	53	29	the	the	DET
fumecheng-11687	53	30	literature	literature	NOUN
fumecheng-11687	53	31	[	[	X
fumecheng-11687	53	32	26	26	NUM
fumecheng-11687	53	33	-	-	SYM
fumecheng-11687	53	34	28	28	NUM
fumecheng-11687	53	35	]	]	PUNCT
fumecheng-11687	53	36	.	.	PUNCT
fumecheng-11687	54	1	on	on	ADP
fumecheng-11687	54	2	the	the	DET
fumecheng-11687	54	3	other	other	ADJ
fumecheng-11687	54	4	hand	hand	NOUN
fumecheng-11687	54	5	,	,	PUNCT
fumecheng-11687	54	6	yang	yang	PROPN
fumecheng-11687	54	7	et	et	PROPN
fumecheng-11687	54	8	al	al	PROPN
fumecheng-11687	54	9	.	.	PUNCT
fumecheng-11687	55	1	[	[	X
fumecheng-11687	55	2	29	29	NUM
fumecheng-11687	55	3	]	]	PUNCT
fumecheng-11687	55	4	used	use	VERB
fumecheng-11687	55	5	the	the	DET
fumecheng-11687	55	6	local	local	ADJ
fumecheng-11687	55	7	fractional	fractional	ADJ
fumecheng-11687	55	8	differential	differential	NOUN
fumecheng-11687	55	9	transform	transform	NOUN
fumecheng-11687	55	10	approach	approach	NOUN
fumecheng-11687	55	11	to	to	PART
fumecheng-11687	55	12	get	get	VERB
fumecheng-11687	55	13	the	the	DET
fumecheng-11687	55	14	precise	precise	ADJ
fumecheng-11687	55	15	solutions	solution	NOUN
fumecheng-11687	55	16	in	in	ADP
fumecheng-11687	55	17	a	a	DET
fumecheng-11687	55	18	fractal	fractal	ADJ
fumecheng-11687	55	19	heat	heat	NOUN
fumecheng-11687	55	20	transfer	transfer	NOUN
fumecheng-11687	55	21	.	.	PUNCT
fumecheng-11687	56	1	additionally	additionally	ADV
fumecheng-11687	56	2	,	,	PUNCT
fumecheng-11687	56	3	several	several	ADJ
fumecheng-11687	56	4	efforts	effort	NOUN
fumecheng-11687	56	5	have	have	AUX
fumecheng-11687	56	6	been	be	AUX
fumecheng-11687	56	7	established	establish	VERB
fumecheng-11687	56	8	to	to	PART
fumecheng-11687	56	9	analyze	analyze	VERB
fumecheng-11687	56	10	these	these	DET
fumecheng-11687	56	11	phenomena	phenomenon	NOUN
fumecheng-11687	56	12	using	use	VERB
fumecheng-11687	56	13	the	the	DET
fumecheng-11687	56	14	non	non	ADJ
fumecheng-11687	56	15	-	-	ADJ
fumecheng-11687	56	16	perturbative	perturbative	ADJ
fumecheng-11687	56	17	method	method	NOUN
fumecheng-11687	56	18	.	.	PUNCT
fumecheng-11687	57	1	by	by	ADP
fumecheng-11687	57	2	using	use	VERB
fumecheng-11687	57	3	the	the	DET
fumecheng-11687	57	4	non	non	ADJ
fumecheng-11687	57	5	-	-	ADJ
fumecheng-11687	57	6	perturbative	perturbative	ADJ
fumecheng-11687	57	7	method	method	NOUN
fumecheng-11687	57	8	,	,	PUNCT
fumecheng-11687	57	9	el	el	PROPN
fumecheng-11687	57	10	-	-	PROPN
fumecheng-11687	57	11	dib	dib	PROPN
fumecheng-11687	57	12	and	and	CCONJ
fumecheng-11687	57	13	elgazery	elgazery	NOUN
fumecheng-11687	58	1	[	[	X
fumecheng-11687	58	2	30,31	30,31	NUM
fumecheng-11687	58	3	]	]	PUNCT
fumecheng-11687	58	4	established	establish	VERB
fumecheng-11687	58	5	a	a	DET
fumecheng-11687	58	6	practical	practical	ADJ
fumecheng-11687	58	7	method	method	NOUN
fumecheng-11687	58	8	for	for	ADP
fumecheng-11687	58	9	solving	solve	VERB
fumecheng-11687	58	10	fractal	fractal	ADJ
fumecheng-11687	58	11	models	model	NOUN
fumecheng-11687	58	12	with	with	ADP
fumecheng-11687	58	13	damping	damp	VERB
fumecheng-11687	58	14	forces	force	NOUN
fumecheng-11687	58	15	.	.	PUNCT
fumecheng-11687	59	1	on	on	ADP
fumecheng-11687	59	2	the	the	DET
fumecheng-11687	59	3	other	other	ADJ
fumecheng-11687	59	4	hand	hand	NOUN
fumecheng-11687	59	5	for	for	ADP
fumecheng-11687	59	6	more	more	ADV
fumecheng-11687	59	7	relevant	relevant	ADJ
fumecheng-11687	59	8	works	work	NOUN
fumecheng-11687	59	9	focusing	focus	VERB
fumecheng-11687	59	10	on	on	ADP
fumecheng-11687	59	11	different	different	ADJ
fumecheng-11687	59	12	methods	method	NOUN
fumecheng-11687	59	13	and	and	CCONJ
fumecheng-11687	59	14	models	model	NOUN
fumecheng-11687	59	15	in	in	ADP
fumecheng-11687	59	16	the	the	DET
fumecheng-11687	59	17	literature	literature	NOUN
fumecheng-11687	59	18	,	,	PUNCT
fumecheng-11687	59	19	the	the	DET
fumecheng-11687	59	20	semi	semi	ADJ
fumecheng-11687	59	21	-	-	ADJ
fumecheng-11687	59	22	analytical	analytical	ADJ
fumecheng-11687	59	23	technique	technique	NOUN
fumecheng-11687	59	24	is	be	AUX
fumecheng-11687	59	25	one	one	NUM
fumecheng-11687	59	26	of	of	ADP
fumecheng-11687	59	27	the	the	DET
fumecheng-11687	59	28	methods	method	NOUN
fumecheng-11687	59	29	that	that	PRON
fumecheng-11687	59	30	play	play	VERB
fumecheng-11687	59	31	an	an	DET
fumecheng-11687	59	32	important	important	ADJ
fumecheng-11687	59	33	role	role	NOUN
fumecheng-11687	59	34	in	in	ADP
fumecheng-11687	59	35	finding	find	VERB
fumecheng-11687	59	36	solutions	solution	NOUN
fumecheng-11687	59	37	of	of	ADP
fumecheng-11687	59	38	physical	physical	ADJ
fumecheng-11687	59	39	problems	problem	NOUN
fumecheng-11687	59	40	[	[	X
fumecheng-11687	59	41	32,33	32,33	NUM
fumecheng-11687	59	42	]	]	PUNCT
fumecheng-11687	59	43	.	.	PUNCT
fumecheng-11687	60	1	furthermore	furthermore	ADV
fumecheng-11687	60	2	,	,	PUNCT
fumecheng-11687	60	3	for	for	ADP
fumecheng-11687	60	4	some	some	DET
fumecheng-11687	60	5	numerical	numerical	ADJ
fumecheng-11687	60	6	solutions	solution	NOUN
fumecheng-11687	60	7	see	see	VERB
fumecheng-11687	60	8	sinc	sinc	ADJ
fumecheng-11687	60	9	-	-	PUNCT
fumecheng-11687	60	10	bernoulli	bernoulli	NOUN
fumecheng-11687	60	11	collocation	collocation	NOUN
fumecheng-11687	60	12	procedure	procedure	NOUN
fumecheng-11687	60	13	[	[	X
fumecheng-11687	60	14	34	34	NUM
fumecheng-11687	60	15	]	]	PUNCT
fumecheng-11687	60	16	.	.	PUNCT
fumecheng-11687	61	1	fractal	fractal	PROPN
fumecheng-11687	61	2	oscillators	oscillator	NOUN
fumecheng-11687	61	3	have	have	AUX
fumecheng-11687	61	4	recently	recently	ADV
fumecheng-11687	61	5	attracted	attract	VERB
fumecheng-11687	61	6	more	more	ADJ
fumecheng-11687	61	7	attention	attention	NOUN
fumecheng-11687	61	8	in	in	ADP
fumecheng-11687	61	9	mechanical	mechanical	ADJ
fumecheng-11687	61	10	engineering	engineering	NOUN
fumecheng-11687	61	11	and	and	CCONJ
fumecheng-11687	61	12	physics	physics	NOUN
fumecheng-11687	61	13	.	.	PUNCT
fumecheng-11687	62	1	despite	despite	SCONJ
fumecheng-11687	62	2	this	this	PRON
fumecheng-11687	62	3	,	,	PUNCT
fumecheng-11687	62	4	all	all	DET
fumecheng-11687	62	5	previous	previous	ADJ
fumecheng-11687	62	6	studies	study	NOUN
fumecheng-11687	62	7	depended	depend	VERB
fumecheng-11687	62	8	on	on	ADP
fumecheng-11687	62	9	a	a	DET
fumecheng-11687	62	10	classical	classical	ADJ
fumecheng-11687	62	11	technique	technique	NOUN
fumecheng-11687	62	12	that	that	PRON
fumecheng-11687	62	13	works	work	VERB
fumecheng-11687	62	14	to	to	PART
fumecheng-11687	62	15	transform	transform	VERB
fumecheng-11687	62	16	the	the	DET
fumecheng-11687	62	17	variable	variable	NOUN
fumecheng-11687	62	18	.	.	PUNCT
fumecheng-11687	63	1	this	this	DET
fumecheng-11687	63	2	traditional	traditional	ADJ
fumecheng-11687	63	3	technique	technique	NOUN
fumecheng-11687	63	4	is	be	AUX
fumecheng-11687	63	5	limited	limit	VERB
fumecheng-11687	63	6	only	only	ADV
fumecheng-11687	63	7	by	by	ADP
fumecheng-11687	63	8	the	the	DET
fumecheng-11687	63	9	absence	absence	NOUN
fumecheng-11687	63	10	of	of	ADP
fumecheng-11687	63	11	external	external	ADJ
fumecheng-11687	63	12	forces	force	NOUN
fumecheng-11687	63	13	.	.	PUNCT
fumecheng-11687	64	1	here	here	ADV
fumecheng-11687	64	2	it	it	PRON
fumecheng-11687	64	3	should	should	AUX
fumecheng-11687	64	4	be	be	AUX
fumecheng-11687	64	5	noted	note	VERB
fumecheng-11687	64	6	that	that	SCONJ
fumecheng-11687	64	7	there	there	PRON
fumecheng-11687	64	8	were	be	VERB
fumecheng-11687	64	9	some	some	DET
fumecheng-11687	64	10	timid	timid	ADJ
fumecheng-11687	64	11	attempts	attempt	NOUN
fumecheng-11687	64	12	to	to	PART
fumecheng-11687	64	13	deal	deal	VERB
fumecheng-11687	64	14	with	with	ADP
fumecheng-11687	64	15	fractal	fractal	ADJ
fumecheng-11687	64	16	oscillators	oscillator	NOUN
fumecheng-11687	64	17	under	under	ADP
fumecheng-11687	64	18	external	external	ADJ
fumecheng-11687	64	19	forces	force	NOUN
fumecheng-11687	64	20	,	,	PUNCT
fumecheng-11687	64	21	such	such	ADJ
fumecheng-11687	64	22	as	as	ADP
fumecheng-11687	64	23	the	the	DET
fumecheng-11687	64	24	attempt	attempt	NOUN
fumecheng-11687	64	25	of	of	ADP
fumecheng-11687	64	26	elías	elías	NOUN
fumecheng-11687	64	27	-	-	PUNCT
fumecheng-11687	64	28	zúñiga	zúñiga	PROPN
fumecheng-11687	64	29	et	et	PROPN
fumecheng-11687	64	30	al	al	PROPN
fumecheng-11687	64	31	.	.	PUNCT
fumecheng-11687	65	1	[	[	X
fumecheng-11687	65	2	35	35	NUM
fumecheng-11687	65	3	]	]	SYM
fumecheng-11687	65	4	,	,	PUNCT
fumecheng-11687	65	5	where	where	SCONJ
fumecheng-11687	65	6	they	they	PRON
fumecheng-11687	65	7	faced	face	VERB
fumecheng-11687	65	8	many	many	ADJ
fumecheng-11687	65	9	mathematical	mathematical	ADJ
fumecheng-11687	65	10	difficulties	difficulty	NOUN
fumecheng-11687	65	11	.	.	PUNCT
fumecheng-11687	66	1	regarding	regard	VERB
fumecheng-11687	66	2	our	our	PRON
fumecheng-11687	66	3	new	new	ADJ
fumecheng-11687	66	4	technique	technique	NOUN
fumecheng-11687	66	5	,	,	PUNCT
fumecheng-11687	66	6	it	it	PRON
fumecheng-11687	66	7	is	be	AUX
fumecheng-11687	66	8	a	a	DET
fumecheng-11687	66	9	different	different	ADJ
fumecheng-11687	66	10	and	and	CCONJ
fumecheng-11687	66	11	distinct	distinct	ADJ
fumecheng-11687	66	12	technique	technique	NOUN
fumecheng-11687	66	13	from	from	ADP
fumecheng-11687	66	14	its	its	PRON
fumecheng-11687	66	15	predecessor	predecessor	NOUN
fumecheng-11687	66	16	,	,	PUNCT
fumecheng-11687	66	17	as	as	SCONJ
fumecheng-11687	66	18	it	it	PRON
fumecheng-11687	66	19	works	work	VERB
fumecheng-11687	66	20	on	on	ADP
fumecheng-11687	66	21	the	the	DET
fumecheng-11687	66	22	operator	operator	NOUN
fumecheng-11687	66	23	.	.	PUNCT
fumecheng-11687	67	1	it	it	PRON
fumecheng-11687	67	2	is	be	AUX
fumecheng-11687	67	3	also	also	ADV
fumecheng-11687	67	4	simple	simple	ADJ
fumecheng-11687	67	5	and	and	CCONJ
fumecheng-11687	67	6	effective	effective	ADJ
fumecheng-11687	67	7	when	when	SCONJ
fumecheng-11687	67	8	investigating	investigate	VERB
fumecheng-11687	67	9	fractal	fractal	ADJ
fumecheng-11687	67	10	oscillators	oscillator	NOUN
fumecheng-11687	67	11	with	with	ADP
fumecheng-11687	67	12	external	external	ADJ
fumecheng-11687	67	13	forces	force	NOUN
fumecheng-11687	67	14	,	,	PUNCT
fumecheng-11687	67	15	easy	easy	ADJ
fumecheng-11687	67	16	to	to	PART
fumecheng-11687	67	17	obtain	obtain	VERB
fumecheng-11687	67	18	analytic	analytic	ADJ
fumecheng-11687	67	19	solutions	solution	NOUN
fumecheng-11687	67	20	,	,	PUNCT
fumecheng-11687	67	21	and	and	CCONJ
fumecheng-11687	67	22	does	do	AUX
fumecheng-11687	67	23	n't	not	PART
fumecheng-11687	67	24	lead	lead	VERB
fumecheng-11687	67	25	to	to	ADP
fumecheng-11687	67	26	any	any	DET
fumecheng-11687	67	27	mathematical	mathematical	ADJ
fumecheng-11687	67	28	difficulties	difficulty	NOUN
fumecheng-11687	67	29	.	.	PUNCT
fumecheng-11687	68	1	the	the	DET
fumecheng-11687	68	2	aforementioned	aforementione	VERB
fumecheng-11687	68	3	factors	factor	NOUN
fumecheng-11687	68	4	serve	serve	VERB
fumecheng-11687	68	5	as	as	ADP
fumecheng-11687	68	6	an	an	DET
fumecheng-11687	68	7	inspiration	inspiration	NOUN
fumecheng-11687	68	8	for	for	ADP
fumecheng-11687	68	9	this	this	DET
fumecheng-11687	68	10	investigation	investigation	NOUN
fumecheng-11687	68	11	goal	goal	NOUN
fumecheng-11687	68	12	,	,	PUNCT
fumecheng-11687	68	13	which	which	PRON
fumecheng-11687	68	14	is	be	AUX
fumecheng-11687	68	15	to	to	PART
fumecheng-11687	68	16	look	look	VERB
fumecheng-11687	68	17	into	into	ADP
fumecheng-11687	68	18	the	the	DET
fumecheng-11687	68	19	fractal	fractal	ADJ
fumecheng-11687	68	20	duffing	duffing	NOUN
fumecheng-11687	68	21	oscillator	oscillator	NOUN
fumecheng-11687	68	22	in	in	ADP
fumecheng-11687	68	23	the	the	DET
fumecheng-11687	68	24	presence	presence	NOUN
fumecheng-11687	68	25	of	of	ADP
fumecheng-11687	68	26	a	a	DET
fumecheng-11687	68	27	periodic	periodic	ADJ
fumecheng-11687	68	28	force	force	NOUN
fumecheng-11687	68	29	via	via	ADP
fumecheng-11687	68	30	the	the	DET
fumecheng-11687	68	31	nonperturbative	nonperturbative	ADJ
fumecheng-11687	68	32	technique	technique	NOUN
fumecheng-11687	68	33	.	.	PUNCT
fumecheng-11687	69	1	as	as	SCONJ
fumecheng-11687	69	2	opposed	oppose	VERB
fumecheng-11687	69	3	to	to	ADP
fumecheng-11687	69	4	earlier	early	ADJ
fumecheng-11687	69	5	works	work	NOUN
fumecheng-11687	69	6	,	,	PUNCT
fumecheng-11687	69	7	with	with	ADP
fumecheng-11687	69	8	direct	direct	ADJ
fumecheng-11687	69	9	handling	handling	NOUN
fumecheng-11687	69	10	of	of	ADP
fumecheng-11687	69	11	the	the	DET
fumecheng-11687	69	12	operator	operator	NOUN
fumecheng-11687	69	13	,	,	PUNCT
fumecheng-11687	69	14	the	the	DET
fumecheng-11687	69	15	present	present	ADJ
fumecheng-11687	69	16	technique	technique	NOUN
fumecheng-11687	69	17	is	be	AUX
fumecheng-11687	69	18	simple	simple	ADJ
fumecheng-11687	69	19	to	to	PART
fumecheng-11687	69	20	deal	deal	VERB
fumecheng-11687	69	21	with	with	ADP
fumecheng-11687	69	22	forced	force	VERB
fumecheng-11687	69	23	fractal	fractal	ADJ
fumecheng-11687	69	24	problems	problem	NOUN
fumecheng-11687	69	25	and	and	CCONJ
fumecheng-11687	69	26	easy	easy	ADJ
fumecheng-11687	69	27	to	to	PART
fumecheng-11687	69	28	obtain	obtain	VERB
fumecheng-11687	69	29	analytic	analytic	ADJ
fumecheng-11687	69	30	solutions	solution	NOUN
fumecheng-11687	69	31	.	.	PUNCT
fumecheng-11687	70	1	2	2	X
fumecheng-11687	70	2	.	.	X
fumecheng-11687	70	3	problem	problem	NOUN
fumecheng-11687	70	4	statement	statement	NOUN
fumecheng-11687	70	5	indeed	indeed	ADV
fumecheng-11687	70	6	,	,	PUNCT
fumecheng-11687	70	7	ji	ji	PROPN
fumecheng-11687	70	8	-	-	PROPN
fumecheng-11687	70	9	huan	huan	NOUN
fumecheng-11687	70	10	he	he	PRON
fumecheng-11687	70	11	’s	’	VERB
fumecheng-11687	70	12	publications	publication	NOUN
fumecheng-11687	71	1	[	[	X
fumecheng-11687	71	2	36,37	36,37	X
fumecheng-11687	71	3	]	]	PUNCT
fumecheng-11687	71	4	aiming	aim	VERB
fumecheng-11687	71	5	to	to	PART
fumecheng-11687	71	6	formulate	formulate	VERB
fumecheng-11687	71	7	the	the	DET
fumecheng-11687	71	8	oscillation	oscillation	NOUN
fumecheng-11687	71	9	frequency	frequency	NOUN
fumecheng-11687	71	10	have	have	AUX
fumecheng-11687	71	11	considered	consider	VERB
fumecheng-11687	71	12	the	the	DET
fumecheng-11687	71	13	conservative	conservative	ADJ
fumecheng-11687	71	14	nonlinear	nonlinear	ADJ
fumecheng-11687	71	15	oscillator	oscillator	NOUN
fumecheng-11687	71	16	:	:	PUNCT
fumecheng-11687	71	17	(	(	PUNCT
fumecheng-11687	71	18	)	)	PUNCT
fumecheng-11687	71	19	0	0	NUM
fumecheng-11687	71	20	;	;	PUNCT
fumecheng-11687	71	21	(	(	PUNCT
fumecheng-11687	71	22	0	0	NUM
fumecheng-11687	71	23	)	)	PUNCT
fumecheng-11687	71	24	and	and	CCONJ
fumecheng-11687	71	25	(	(	PUNCT
fumecheng-11687	71	26	0	0	X
fumecheng-11687	71	27	)	)	PUNCT
fumecheng-11687	71	28	0u	0u	ADJ
fumecheng-11687	72	1	f	f	X
fumecheng-11687	72	2	u	u	NOUN
fumecheng-11687	72	3	u	u	NOUN
fumecheng-11687	72	4	a	a	DET
fumecheng-11687	72	5	u+	u+	NOUN
fumecheng-11687	72	6	=	=	PUNCT
fumecheng-11687	72	7	=	=	SYM
fumecheng-11687	72	8	=	=	SYM
fumecheng-11687	72	9	(	(	PUNCT
fumecheng-11687	72	10	1	1	NUM
fumecheng-11687	72	11	)	)	PUNCT
fumecheng-11687	72	12	here	here	ADV
fumecheng-11687	72	13	,	,	PUNCT
fumecheng-11687	72	14	f(u	f(u	PROPN
fumecheng-11687	72	15	)	)	PUNCT
fumecheng-11687	72	16	represents	represent	VERB
fumecheng-11687	72	17	the	the	DET
fumecheng-11687	72	18	nonlinear	nonlinear	ADJ
fumecheng-11687	72	19	restoring	restore	VERB
fumecheng-11687	72	20	force	force	NOUN
fumecheng-11687	72	21	,	,	PUNCT
fumecheng-11687	72	22	u	u	NOUN
fumecheng-11687	72	23	is	be	AUX
fumecheng-11687	72	24	the	the	DET
fumecheng-11687	72	25	displacement	displacement	NOUN
fumecheng-11687	72	26	,	,	PUNCT
fumecheng-11687	72	27	and	and	CCONJ
fumecheng-11687	72	28	a	a	PRON
fumecheng-11687	72	29	is	be	AUX
fumecheng-11687	72	30	a	a	DET
fumecheng-11687	72	31	constant	constant	ADJ
fumecheng-11687	72	32	.	.	PUNCT
fumecheng-11687	73	1	in	in	ADP
fumecheng-11687	73	2	the	the	DET
fumecheng-11687	73	3	mentioned	mention	VERB
fumecheng-11687	73	4	publications	publication	NOUN
fumecheng-11687	73	5	,	,	PUNCT
fumecheng-11687	73	6	ji	ji	PROPN
fumecheng-11687	73	7	-	-	PROPN
fumecheng-11687	73	8	huan	huan	PROPN
fumecheng-11687	73	9	he	he	PRON
fumecheng-11687	73	10	has	have	AUX
fumecheng-11687	73	11	used	use	VERB
fumecheng-11687	73	12	the	the	DET
fumecheng-11687	73	13	function	function	NOUN
fumecheng-11687	73	14	f	f	PROPN
fumecheng-11687	73	15	(	(	PUNCT
fumecheng-11687	73	16	u	u	NOUN
fumecheng-11687	73	17	)	)	PUNCT
fumecheng-11687	73	18	to	to	PART
fumecheng-11687	73	19	established	establish	VERB
fumecheng-11687	73	20	the	the	DET
fumecheng-11687	73	21	oscillation	oscillation	NOUN
fumecheng-11687	73	22	frequency	frequency	NOUN
fumecheng-11687	73	23	2(	2(	NOUN
fumecheng-11687	73	24	)	)	PUNCT
fumecheng-11687	73	25	,	,	PUNCT
fumecheng-11687	73	26	where	where	SCONJ
fumecheng-11687	73	27			PROPN
fumecheng-11687	73	28	is	be	AUX
fumecheng-11687	73	29	the	the	DET
fumecheng-11687	73	30	total	total	ADJ
fumecheng-11687	73	31	frequency	frequency	NOUN
fumecheng-11687	73	32	,	,	PUNCT
fumecheng-11687	73	33	in	in	ADP
fumecheng-11687	73	34	the	the	DET
fumecheng-11687	73	35	form	form	NOUN
fumecheng-11687	73	36	2	2	NUM
fumecheng-11687	73	37	1	1	NUM
fumecheng-11687	73	38	2	2	NUM
fumecheng-11687	73	39	(	(	PUNCT
fumecheng-11687	73	40	)	)	PUNCT
fumecheng-11687	73	41	(	(	PUNCT
fumecheng-11687	73	42	)	)	PUNCT
fumecheng-11687	73	43	lim	lim	PROPN
fumecheng-11687	73	44	u	u	PROPN
fumecheng-11687	73	45	a	a	DET
fumecheng-11687	73	46	df	df	PROPN
fumecheng-11687	73	47	u	u	X
fumecheng-11687	73	48	du	du	X
fumecheng-11687	73	49			X
fumecheng-11687	73	50	→	→	SYM
fumecheng-11687	73	51			PROPN
fumecheng-11687	73	52	=	=	SYM
fumecheng-11687	73	53	(	(	PUNCT
fumecheng-11687	73	54	2	2	X
fumecheng-11687	73	55	)	)	PUNCT
fumecheng-11687	73	56	this	this	DET
fumecheng-11687	73	57	formula	formula	NOUN
fumecheng-11687	73	58	has	have	AUX
fumecheng-11687	73	59	been	be	AUX
fumecheng-11687	73	60	well	well	ADV
fumecheng-11687	73	61	worked	work	VERB
fumecheng-11687	73	62	for	for	ADP
fumecheng-11687	73	63	the	the	DET
fumecheng-11687	73	64	cubic	cubic	ADJ
fumecheng-11687	73	65	polynomial	polynomial	NOUN
fumecheng-11687	73	66	of	of	ADP
fumecheng-11687	73	67	the	the	DET
fumecheng-11687	73	68	function	function	NOUN
fumecheng-11687	73	69	f	f	PROPN
fumecheng-11687	73	70	(	(	PUNCT
fumecheng-11687	73	71	u	u	NOUN
fumecheng-11687	73	72	)	)	PUNCT
fumecheng-11687	73	73	provided	provide	VERB
fumecheng-11687	73	74	that	that	SCONJ
fumecheng-11687	73	75	this	this	DET
fumecheng-11687	73	76	function	function	NOUN
fumecheng-11687	73	77	does	do	AUX
fumecheng-11687	73	78	not	not	PART
fumecheng-11687	73	79	contain	contain	VERB
fumecheng-11687	73	80	the	the	DET
fumecheng-11687	73	81	velocity	velocity	NOUN
fumecheng-11687	73	82	�	�	NOUN
fumecheng-11687	73	83	̇	̇	VERB
fumecheng-11687	73	84	�	�	PROPN
fumecheng-11687	73	85	or	or	CCONJ
fumecheng-11687	73	86	ü	ü	PROPN
fumecheng-11687	73	87	and	and	CCONJ
fumecheng-11687	73	88	the	the	DET
fumecheng-11687	73	89	combination	combination	NOUN
fumecheng-11687	73	90	of	of	ADP
fumecheng-11687	73	91	them	they	PRON
fumecheng-11687	73	92	.	.	PUNCT
fumecheng-11687	74	1	for	for	ADP
fumecheng-11687	74	2	these	these	DET
fumecheng-11687	74	3	shortcomings	shortcoming	NOUN
fumecheng-11687	74	4	,	,	PUNCT
fumecheng-11687	74	5	the	the	DET
fumecheng-11687	74	6	superior	superior	ADJ
fumecheng-11687	74	7	and	and	CCONJ
fumecheng-11687	74	8	most	most	ADV
fumecheng-11687	74	9	effective	effective	ADJ
fumecheng-11687	74	10	formula	formula	NOUN
fumecheng-11687	74	11	was	be	AUX
fumecheng-11687	74	12	developed	develop	VERB
fumecheng-11687	74	13	by	by	ADP
fumecheng-11687	74	14	el	el	PROPN
fumecheng-11687	74	15	-	-	PROPN
fumecheng-11687	74	16	dib	dib	PROPN
fumecheng-11687	74	17	[	[	X
fumecheng-11687	74	18	38	38	NUM
fumecheng-11687	74	19	]	]	PUNCT
fumecheng-11687	74	20	,	,	PUNCT
fumecheng-11687	74	21	and	and	CCONJ
fumecheng-11687	74	22	it	it	PRON
fumecheng-11687	74	23	can	can	AUX
fumecheng-11687	74	24	be	be	AUX
fumecheng-11687	74	25	used	use	VERB
fumecheng-11687	74	26	to	to	PART
fumecheng-11687	74	27	produce	produce	VERB
fumecheng-11687	74	28	successive	successive	ADJ
fumecheng-11687	74	29	approximations	approximation	NOUN
fumecheng-11687	74	30	to	to	ADP
fumecheng-11687	74	31	the	the	DET
fumecheng-11687	74	32	solutions	solution	NOUN
fumecheng-11687	74	33	for	for	ADP
fumecheng-11687	74	34	non	non	ADJ
fumecheng-11687	74	35	-	-	ADJ
fumecheng-11687	74	36	linear	linear	ADJ
fumecheng-11687	74	37	202	202	NUM
fumecheng-11687	74	38	y.o	y.o	PROPN
fumecheng-11687	74	39	.	.	PROPN
fumecheng-11687	74	40	el	el	PROPN
fumecheng-11687	74	41	-	-	PUNCT
fumecheng-11687	74	42	dib	dib	PROPN
fumecheng-11687	74	43	,	,	PUNCT
fumecheng-11687	74	44	n.s	n.s	PROPN
fumecheng-11687	74	45	.	.	PROPN
fumecheng-11687	74	46	elgazery	elgazery	PROPN
fumecheng-11687	74	47	,	,	PUNCT
fumecheng-11687	74	48	h.a	h.a	PROPN
fumecheng-11687	74	49	.	.	PROPN
fumecheng-11687	74	50	alyousef	alyousef	PROPN
fumecheng-11687	74	51	oscillations	oscillation	NOUN
fumecheng-11687	75	1	[	[	X
fumecheng-11687	75	2	39	39	NUM
fumecheng-11687	75	3	]	]	PUNCT
fumecheng-11687	75	4	.	.	PUNCT
fumecheng-11687	76	1	it	it	PRON
fumecheng-11687	76	2	is	be	AUX
fumecheng-11687	76	3	better	well	ADJ
fumecheng-11687	76	4	to	to	PART
fumecheng-11687	76	5	elongate	elongate	VERB
fumecheng-11687	76	6	this	this	DET
fumecheng-11687	76	7	method	method	NOUN
fumecheng-11687	76	8	to	to	ADP
fumecheng-11687	76	9	equations	equation	NOUN
fumecheng-11687	76	10	having	have	VERB
fumecheng-11687	76	11	damping	damp	VERB
fumecheng-11687	76	12	forces	force	NOUN
fumecheng-11687	76	13	such	such	ADJ
fumecheng-11687	76	14	that	that	PRON
fumecheng-11687	76	15	(	(	PUNCT
fumecheng-11687	76	16	)	)	PUNCT
fumecheng-11687	76	17	(	(	PUNCT
fumecheng-11687	76	18	,	,	PUNCT
fumecheng-11687	76	19	,	,	PUNCT
fumecheng-11687	76	20	)	)	PUNCT
fumecheng-11687	77	1	0u	0u	ADJ
fumecheng-11687	77	2	g	g	PROPN
fumecheng-11687	77	3	u	u	NOUN
fumecheng-11687	77	4	u	u	X
fumecheng-11687	77	5	f	f	PROPN
fumecheng-11687	77	6	u	u	X
fumecheng-11687	77	7	u	u	X
fumecheng-11687	77	8	u	u	NOUN
fumecheng-11687	77	9	u+	u+	VERB
fumecheng-11687	77	10	+	+	X
fumecheng-11687	77	11	=	=	SYM
fumecheng-11687	77	12	(	(	PUNCT
fumecheng-11687	77	13	3	3	NUM
fumecheng-11687	77	14	)	)	PUNCT
fumecheng-11687	77	15	if	if	SCONJ
fumecheng-11687	77	16			PROPN
fumecheng-11687	77	17	is	be	AUX
fumecheng-11687	77	18	the	the	DET
fumecheng-11687	77	19	total	total	ADJ
fumecheng-11687	77	20	frequency	frequency	NOUN
fumecheng-11687	77	21	to	to	ADP
fumecheng-11687	77	22	the	the	DET
fumecheng-11687	77	23	above	above	ADJ
fumecheng-11687	77	24	oscillator	oscillator	NOUN
fumecheng-11687	77	25	then	then	ADV
fumecheng-11687	77	26	it	it	PRON
fumecheng-11687	77	27	useful	useful	ADJ
fumecheng-11687	77	28	to	to	PART
fumecheng-11687	77	29	write	write	VERB
fumecheng-11687	77	30	2	2	NUM
fumecheng-11687	77	31	(	(	PUNCT
fumecheng-11687	77	32	)	)	PUNCT
fumecheng-11687	77	33	(	(	PUNCT
fumecheng-11687	77	34	)	)	PUNCT
fumecheng-11687	77	35	0u	0u	ADJ
fumecheng-11687	77	36	u	u	NOUN
fumecheng-11687	77	37	u	u	PROPN
fumecheng-11687	78	1	+	+	NOUN
fumecheng-11687	78	2			PROPN
fumecheng-11687	79	1	+	+	CCONJ
fumecheng-11687	79	2			PROPN
fumecheng-11687	79	3	=	=	PUNCT
fumecheng-11687	79	4	(	(	PUNCT
fumecheng-11687	79	5	4	4	X
fumecheng-11687	79	6	)	)	PUNCT
fumecheng-11687	79	7	the	the	DET
fumecheng-11687	79	8	following	follow	VERB
fumecheng-11687	79	9	procedure	procedure	NOUN
fumecheng-11687	79	10	is	be	AUX
fumecheng-11687	79	11	used	use	VERB
fumecheng-11687	79	12	to	to	PART
fumecheng-11687	79	13	estimate	estimate	VERB
fumecheng-11687	79	14	(	(	NOUN
fumecheng-11687	79	15	)	)	PUNCT
fumecheng-11687	79	16	and	and	CCONJ
fumecheng-11687	79	17	2(	2(	NOUN
fumecheng-11687	79	18	):	):	PUNCT
fumecheng-11687	79	19	the	the	DET
fumecheng-11687	79	20	comparison	comparison	NOUN
fumecheng-11687	79	21	of	of	ADP
fumecheng-11687	79	22	eqs	eqs	PROPN
fumecheng-11687	79	23	.	.	PUNCT
fumecheng-11687	80	1	(	(	PUNCT
fumecheng-11687	80	2	3	3	X
fumecheng-11687	80	3	)	)	PUNCT
fumecheng-11687	80	4	and	and	CCONJ
fumecheng-11687	80	5	(	(	PUNCT
fumecheng-11687	80	6	4	4	X
fumecheng-11687	80	7	)	)	PUNCT
fumecheng-11687	80	8	leads	lead	VERB
fumecheng-11687	80	9	to	to	ADP
fumecheng-11687	80	10	the	the	DET
fumecheng-11687	80	11	following	following	ADJ
fumecheng-11687	80	12	error	error	NOUN
fumecheng-11687	80	13	:	:	PUNCT
fumecheng-11687	80	14	2	2	NUM
fumecheng-11687	80	15	2	2	NUM
fumecheng-11687	80	16	(	(	PUNCT
fumecheng-11687	80	17	,	,	PUNCT
fumecheng-11687	80	18	)	)	PUNCT
fumecheng-11687	80	19	(	(	PUNCT
fumecheng-11687	80	20	(	(	PUNCT
fumecheng-11687	80	21	,	,	PUNCT
fumecheng-11687	80	22	,	,	PUNCT
fumecheng-11687	80	23	)	)	PUNCT
fumecheng-11687	80	24	)	)	PUNCT
fumecheng-11687	81	1	(	(	PUNCT
fumecheng-11687	81	2	)	)	PUNCT
fumecheng-11687	81	3	(	(	PUNCT
fumecheng-11687	81	4	(	(	PUNCT
fumecheng-11687	81	5	)	)	PUNCT
fumecheng-11687	81	6	)	)	PUNCT
fumecheng-11687	81	7	(	(	PUNCT
fumecheng-11687	81	8	)	)	PUNCT
fumecheng-11687	81	9	e	e	X
fumecheng-11687	81	10	f	f	X
fumecheng-11687	81	11	u	u	VERB
fumecheng-11687	81	12	u	u	VERB
fumecheng-11687	81	13	u	u	X
fumecheng-11687	81	14	u	u	NOUN
fumecheng-11687	81	15	t	t	NOUN
fumecheng-11687	81	16	g	g	X
fumecheng-11687	81	17	u	u	X
fumecheng-11687	81	18	u	u	NOUN
fumecheng-11687	81	19	t=	t=	NOUN
fumecheng-11687	81	20	−	−	PROPN
fumecheng-11687	82	1	+	+	CCONJ
fumecheng-11687	82	2	−	−	ADJ
fumecheng-11687	82	3			X
fumecheng-11687	82	4			X
fumecheng-11687	82	5			NOUN
fumecheng-11687	82	6	(	(	PUNCT
fumecheng-11687	82	7	5	5	NUM
fumecheng-11687	82	8	)	)	PUNCT
fumecheng-11687	82	9	the	the	DET
fumecheng-11687	82	10	mean	mean	ADJ
fumecheng-11687	82	11	square	square	ADJ
fumecheng-11687	82	12	error	error	NOUN
fumecheng-11687	82	13	is	be	AUX
fumecheng-11687	82	14	defined	define	VERB
fumecheng-11687	82	15	as	as	ADP
fumecheng-11687	82	16	(	(	PUNCT
fumecheng-11687	82	17	)	)	PUNCT
fumecheng-11687	82	18	2	2	NUM
fumecheng-11687	82	19	2	2	NUM
fumecheng-11687	82	20	2	2	NUM
fumecheng-11687	82	21	2	2	NUM
fumecheng-11687	82	22	0	0	NUM
fumecheng-11687	82	23	(	(	PUNCT
fumecheng-11687	82	24	,	,	PUNCT
fumecheng-11687	82	25	)	)	PUNCT
fumecheng-11687	82	26	(	(	PUNCT
fumecheng-11687	82	27	(	(	PUNCT
fumecheng-11687	82	28	,	,	PUNCT
fumecheng-11687	82	29	,	,	PUNCT
fumecheng-11687	82	30	)	)	PUNCT
fumecheng-11687	82	31	)	)	PUNCT
fumecheng-11687	83	1	(	(	PUNCT
fumecheng-11687	83	2	)	)	PUNCT
fumecheng-11687	83	3	(	(	PUNCT
fumecheng-11687	83	4	(	(	PUNCT
fumecheng-11687	83	5	)	)	PUNCT
fumecheng-11687	83	6	)	)	PUNCT
fumecheng-11687	83	7	(	(	PUNCT
fumecheng-11687	83	8	)	)	PUNCT
fumecheng-11687	83	9	;	;	PUNCT
fumecheng-11687	83	10	2	2	NUM
fumecheng-11687	83	11	t	t	NOUN
fumecheng-11687	83	12	e	e	X
fumecheng-11687	83	13	f	f	X
fumecheng-11687	83	14	u	u	X
fumecheng-11687	83	15	u	u	VERB
fumecheng-11687	83	16	u	u	X
fumecheng-11687	83	17	u	u	NOUN
fumecheng-11687	83	18	t	t	NOUN
fumecheng-11687	83	19	g	g	X
fumecheng-11687	83	20	u	u	X
fumecheng-11687	83	21	u	u	X
fumecheng-11687	83	22	t	t	NOUN
fumecheng-11687	83	23	dt	dt	NOUN
fumecheng-11687	83	24	t=	t=	PROPN
fumecheng-11687	83	25	−	−	PROPN
fumecheng-11687	84	1	+	+	CCONJ
fumecheng-11687	84	2	−	−	PROPN
fumecheng-11687	84	3	=	=	NOUN
fumecheng-11687	84	4			X
fumecheng-11687	84	5			ADJ
fumecheng-11687	84	6			NOUN
fumecheng-11687	84	7			X
fumecheng-11687	84	8			PUNCT
fumecheng-11687	84	9			NOUN
fumecheng-11687	84	10			X
fumecheng-11687	84	11	(	(	PUNCT
fumecheng-11687	84	12	6	6	NUM
fumecheng-11687	84	13	)	)	PUNCT
fumecheng-11687	84	14	the	the	DET
fumecheng-11687	84	15	minimum	minimum	ADJ
fumecheng-11687	84	16	value	value	NOUN
fumecheng-11687	84	17	requires	require	VERB
fumecheng-11687	84	18	that	that	SCONJ
fumecheng-11687	84	19	2	2	NUM
fumecheng-11687	84	20	2	2	NUM
fumecheng-11687	84	21	2	2	NUM
fumecheng-11687	84	22	2	2	NUM
fumecheng-11687	84	23	2	2	NUM
fumecheng-11687	84	24	2	2	NUM
fumecheng-11687	84	25	2	2	NUM
fumecheng-11687	84	26	0	0	NUM
fumecheng-11687	84	27	(	(	PUNCT
fumecheng-11687	84	28	(	(	PUNCT
fumecheng-11687	84	29	(	(	PUNCT
fumecheng-11687	84	30	,	,	PUNCT
fumecheng-11687	84	31	,	,	PUNCT
fumecheng-11687	84	32	)	)	PUNCT
fumecheng-11687	84	33	)	)	PUNCT
fumecheng-11687	84	34	(	(	PUNCT
fumecheng-11687	84	35	)	)	PUNCT
fumecheng-11687	84	36	2	2	NUM
fumecheng-11687	84	37	(	(	PUNCT
fumecheng-11687	84	38	(	(	PUNCT
fumecheng-11687	84	39	,	,	PUNCT
fumecheng-11687	84	40	,	,	PUNCT
fumecheng-11687	84	41	)	)	PUNCT
fumecheng-11687	84	42	)	)	PUNCT
fumecheng-11687	84	43	(	(	PUNCT
fumecheng-11687	84	44	(	(	PUNCT
fumecheng-11687	84	45	)	)	PUNCT
fumecheng-11687	84	46	)	)	PUNCT
fumecheng-11687	84	47	)	)	PUNCT
fumecheng-11687	84	48	0	0	PUNCT
fumecheng-11687	85	1	(	(	PUNCT
fumecheng-11687	85	2	)	)	PUNCT
fumecheng-11687	85	3	(	(	PUNCT
fumecheng-11687	85	4	)	)	PUNCT
fumecheng-11687	85	5	tde	tde	PROPN
fumecheng-11687	85	6	d	d	X
fumecheng-11687	85	7	f	f	X
fumecheng-11687	85	8	u	u	X
fumecheng-11687	85	9	u	u	X
fumecheng-11687	85	10	u	u	X
fumecheng-11687	85	11	u	u	NOUN
fumecheng-11687	85	12	t	t	NOUN
fumecheng-11687	85	13	f	f	PROPN
fumecheng-11687	85	14	u	u	NOUN
fumecheng-11687	85	15	u	u	VERB
fumecheng-11687	85	16	u	u	NOUN
fumecheng-11687	85	17	g	g	PROPN
fumecheng-11687	85	18	u	u	X
fumecheng-11687	85	19	uu	uu	PRON
fumecheng-11687	85	20	dt	dt	X
fumecheng-11687	86	1	d	d	X
fumecheng-11687	86	2	d	d	PROPN
fumecheng-11687	86	3	=	=	PUNCT
fumecheng-11687	86	4	−	−	PROPN
fumecheng-11687	87	1	+	+	CCONJ
fumecheng-11687	87	2	−	−	PROPN
fumecheng-11687	87	3	−	−	PROPN
fumecheng-11687	88	1	=	=	SYM
fumecheng-11687	88	2			X
fumecheng-11687	88	3			X
fumecheng-11687	88	4			X
fumecheng-11687	88	5			NOUN
fumecheng-11687	89	1			X
fumecheng-11687	89	2			X
fumecheng-11687	89	3	(	(	PUNCT
fumecheng-11687	89	4	7	7	NUM
fumecheng-11687	89	5	)	)	SYM
fumecheng-11687	89	6	2	2	NUM
fumecheng-11687	89	7	2	2	NUM
fumecheng-11687	89	8	2	2	NUM
fumecheng-11687	89	9	2	2	NUM
fumecheng-11687	89	10	0	0	NUM
fumecheng-11687	89	11	(	(	PUNCT
fumecheng-11687	89	12	(	(	PUNCT
fumecheng-11687	89	13	(	(	PUNCT
fumecheng-11687	89	14	)	)	PUNCT
fumecheng-11687	89	15	)	)	PUNCT
fumecheng-11687	89	16	(	(	PUNCT
fumecheng-11687	89	17	)	)	PUNCT
fumecheng-11687	89	18	2	2	NUM
fumecheng-11687	89	19	(	(	PUNCT
fumecheng-11687	89	20	(	(	PUNCT
fumecheng-11687	89	21	,	,	PUNCT
fumecheng-11687	89	22	,	,	PUNCT
fumecheng-11687	89	23	)	)	PUNCT
fumecheng-11687	89	24	)	)	PUNCT
fumecheng-11687	89	25	(	(	PUNCT
fumecheng-11687	89	26	(	(	PUNCT
fumecheng-11687	89	27	)	)	PUNCT
fumecheng-11687	89	28	)	)	PUNCT
fumecheng-11687	89	29	)	)	PUNCT
fumecheng-11687	89	30	0	0	PUNCT
fumecheng-11687	90	1	tde	tde	NOUN
fumecheng-11687	90	2	d	d	X
fumecheng-11687	90	3	g	g	X
fumecheng-11687	90	4	u	u	X
fumecheng-11687	90	5	u	u	NOUN
fumecheng-11687	90	6	t	t	NOUN
fumecheng-11687	90	7	f	f	PROPN
fumecheng-11687	90	8	u	u	NOUN
fumecheng-11687	90	9	u	u	VERB
fumecheng-11687	90	10	u	u	NOUN
fumecheng-11687	90	11	g	g	PROPN
fumecheng-11687	90	12	u	u	X
fumecheng-11687	90	13	uu	uu	PRON
fumecheng-11687	90	14	dt	dt	X
fumecheng-11687	91	1	d	d	X
fumecheng-11687	91	2	d	d	PROPN
fumecheng-11687	91	3	=	=	PUNCT
fumecheng-11687	91	4	−	−	PROPN
fumecheng-11687	92	1	+	+	CCONJ
fumecheng-11687	93	1	−	−	PROPN
fumecheng-11687	93	2	−	−	NOUN
fumecheng-11687	93	3	=	=	NOUN
fumecheng-11687	93	4			NOUN
fumecheng-11687	93	5			NOUN
fumecheng-11687	93	6			NOUN
fumecheng-11687	93	7			NOUN
fumecheng-11687	93	8			NOUN
fumecheng-11687	93	9			NOUN
fumecheng-11687	93	10	(	(	PUNCT
fumecheng-11687	93	11	8)	8)	NUM
fumecheng-11687	93	12	by	by	ADP
fumecheng-11687	93	13	suitable	suitable	ADJ
fumecheng-11687	93	14	introducing	introduce	VERB
fumecheng-11687	93	15	trial	trial	NOUN
fumecheng-11687	93	16	solution	solution	NOUN
fumecheng-11687	93	17	in	in	ADP
fumecheng-11687	93	18	terms	term	NOUN
fumecheng-11687	93	19	of	of	ADP
fumecheng-11687	93	20	the	the	DET
fumecheng-11687	93	21	total	total	ADJ
fumecheng-11687	93	22	frequency	frequency	NOUN
fumecheng-11687	93	23			PROPN
fumecheng-11687	93	24	,	,	PUNCT
fumecheng-11687	93	25	the	the	DET
fumecheng-11687	93	26	simplification	simplification	NOUN
fumecheng-11687	93	27	leads	lead	VERB
fumecheng-11687	93	28	to	to	ADP
fumecheng-11687	93	29	2	2	NUM
fumecheng-11687	93	30	2	2	NUM
fumecheng-11687	93	31	2	2	NUM
fumecheng-11687	93	32	0	0	NUM
fumecheng-11687	93	33	0	0	NUM
fumecheng-11687	93	34	(	(	PUNCT
fumecheng-11687	93	35	)	)	PUNCT
fumecheng-11687	93	36	(	(	PUNCT
fumecheng-11687	93	37	)	)	PUNCT
fumecheng-11687	93	38	(	(	PUNCT
fumecheng-11687	93	39	,	,	PUNCT
fumecheng-11687	93	40	,	,	PUNCT
fumecheng-11687	93	41	)	)	PUNCT
fumecheng-11687	93	42	0	0	NUM
fumecheng-11687	94	1	t	t	NOUN
fumecheng-11687	94	2	t	t	X
fumecheng-11687	94	3	u	u	NOUN
fumecheng-11687	94	4	t	t	PROPN
fumecheng-11687	94	5	dt	dt	X
fumecheng-11687	94	6	u	u	NOUN
fumecheng-11687	95	1	t	t	PROPN
fumecheng-11687	95	2	f	f	PROPN
fumecheng-11687	95	3	u	u	PROPN
fumecheng-11687	95	4	u	u	X
fumecheng-11687	95	5	u	u	NOUN
fumecheng-11687	95	6	dt	dt	NOUN
fumecheng-11687	95	7	−	−	PROPN
fumecheng-11687	96	1	=	=	NOUN
fumecheng-11687	96	2			NOUN
fumecheng-11687	96	3			X
fumecheng-11687	96	4	(	(	PUNCT
fumecheng-11687	96	5	9	9	NUM
fumecheng-11687	96	6	)	)	SYM
fumecheng-11687	97	1	2	2	NUM
fumecheng-11687	97	2	2	2	NUM
fumecheng-11687	97	3	0	0	NUM
fumecheng-11687	97	4	0	0	NUM
fumecheng-11687	97	5	(	(	PUNCT
fumecheng-11687	97	6	)	)	PUNCT
fumecheng-11687	97	7	(	(	PUNCT
fumecheng-11687	97	8	)	)	PUNCT
fumecheng-11687	97	9	(	(	PUNCT
fumecheng-11687	97	10	)	)	PUNCT
fumecheng-11687	97	11	0	0	NUM
fumecheng-11687	98	1	t	t	NOUN
fumecheng-11687	98	2	t	t	X
fumecheng-11687	98	3	u	u	NOUN
fumecheng-11687	98	4	t	t	PROPN
fumecheng-11687	98	5	dt	dt	X
fumecheng-11687	98	6	u	u	NOUN
fumecheng-11687	98	7	t	t	PROPN
fumecheng-11687	98	8	g	g	X
fumecheng-11687	98	9	u	u	PRON
fumecheng-11687	98	10	dt	dt	VERB
fumecheng-11687	98	11	−	−	PROPN
fumecheng-11687	99	1	=	=	NOUN
fumecheng-11687	99	2			NOUN
fumecheng-11687	99	3			X
fumecheng-11687	99	4	(	(	PUNCT
fumecheng-11687	99	5	10	10	NUM
fumecheng-11687	99	6	)	)	PUNCT
fumecheng-11687	99	7	solving	solve	VERB
fumecheng-11687	99	8	both	both	PRON
fumecheng-11687	99	9	eq	eq	ADP
fumecheng-11687	99	10	.	.	PUNCT
fumecheng-11687	100	1	(	(	PUNCT
fumecheng-11687	100	2	9	9	NUM
fumecheng-11687	100	3	)	)	PUNCT
fumecheng-11687	100	4	and	and	CCONJ
fumecheng-11687	100	5	eq	eq	NOUN
fumecheng-11687	100	6	.	.	PUNCT
fumecheng-11687	101	1	(	(	PUNCT
fumecheng-11687	101	2	10	10	NUM
fumecheng-11687	101	3	)	)	PUNCT
fumecheng-11687	101	4	yields	yield	VERB
fumecheng-11687	101	5	2	2	NUM
fumecheng-11687	101	6	2	2	NUM
fumecheng-11687	101	7	0	0	NUM
fumecheng-11687	101	8	2	2	NUM
fumecheng-11687	101	9	0	0	NUM
fumecheng-11687	101	10	(	(	PUNCT
fumecheng-11687	101	11	)	)	PUNCT
fumecheng-11687	101	12	(	(	PUNCT
fumecheng-11687	101	13	,	,	PUNCT
fumecheng-11687	101	14	,	,	PUNCT
fumecheng-11687	101	15	)	)	PUNCT
fumecheng-11687	101	16	(	(	PUNCT
fumecheng-11687	101	17	)	)	PUNCT
fumecheng-11687	101	18	(	(	PUNCT
fumecheng-11687	101	19	)	)	PUNCT
fumecheng-11687	101	20	t	t	NOUN
fumecheng-11687	101	21	t	t	PROPN
fumecheng-11687	101	22	u	u	NOUN
fumecheng-11687	101	23	t	t	PROPN
fumecheng-11687	101	24	f	f	X
fumecheng-11687	101	25	u	u	NOUN
fumecheng-11687	101	26	u	u	X
fumecheng-11687	101	27	u	u	NOUN
fumecheng-11687	101	28	dt	dt	X
fumecheng-11687	101	29	u	u	NOUN
fumecheng-11687	101	30	t	t	X
fumecheng-11687	101	31	dt	dt	X
fumecheng-11687	101	32			PROPN
fumecheng-11687	101	33			PROPN
fumecheng-11687	102	1	=	=	NOUN
fumecheng-11687	102	2			X
fumecheng-11687	102	3			PUNCT
fumecheng-11687	102	4	(	(	PUNCT
fumecheng-11687	102	5	11	11	NUM
fumecheng-11687	102	6	)	)	SYM
fumecheng-11687	103	1	2	2	NUM
fumecheng-11687	103	2	0	0	NUM
fumecheng-11687	103	3	2	2	NUM
fumecheng-11687	103	4	0	0	NUM
fumecheng-11687	103	5	(	(	PUNCT
fumecheng-11687	103	6	)	)	PUNCT
fumecheng-11687	103	7	(	(	PUNCT
fumecheng-11687	103	8	)	)	PUNCT
fumecheng-11687	103	9	(	(	PUNCT
fumecheng-11687	103	10	)	)	PUNCT
fumecheng-11687	103	11	(	(	PUNCT
fumecheng-11687	103	12	)	)	PUNCT
fumecheng-11687	103	13	t	t	NOUN
fumecheng-11687	103	14	t	t	PROPN
fumecheng-11687	103	15	u	u	NOUN
fumecheng-11687	103	16	t	t	PROPN
fumecheng-11687	103	17	g	g	X
fumecheng-11687	103	18	u	u	X
fumecheng-11687	103	19	dt	dt	X
fumecheng-11687	103	20	u	u	NOUN
fumecheng-11687	103	21	t	t	NOUN
fumecheng-11687	103	22	dt	dt	NOUN
fumecheng-11687	103	23			NOUN
fumecheng-11687	103	24			PROPN
fumecheng-11687	104	1	=	=	NOUN
fumecheng-11687	105	1			X
fumecheng-11687	105	2			PUNCT
fumecheng-11687	105	3	(	(	PUNCT
fumecheng-11687	105	4	12	12	X
fumecheng-11687	105	5	)	)	PUNCT
fumecheng-11687	105	6	performing	perform	VERB
fumecheng-11687	105	7	the	the	DET
fumecheng-11687	105	8	aforementioned	aforementione	VERB
fumecheng-11687	105	9	integrals	integral	NOUN
fumecheng-11687	105	10	gives	give	VERB
fumecheng-11687	105	11	the	the	DET
fumecheng-11687	105	12	equivalent	equivalent	ADJ
fumecheng-11687	105	13	damping	damp	VERB
fumecheng-11687	105	14	coefficient	coefficient	NOUN
fumecheng-11687	105	15	and	and	CCONJ
fumecheng-11687	105	16	the	the	DET
fumecheng-11687	105	17	equivalent	equivalent	ADJ
fumecheng-11687	105	18	conservative	conservative	ADJ
fumecheng-11687	105	19	frequency	frequency	NOUN
fumecheng-11687	105	20	.	.	PUNCT
fumecheng-11687	106	1	the	the	DET
fumecheng-11687	106	2	up	up	ADV
fumecheng-11687	106	3	-	-	PUNCT
fumecheng-11687	106	4	grating	grate	VERB
fumecheng-11687	106	5	rank	rank	NOUN
fumecheng-11687	106	6	approach	approach	NOUN
fumecheng-11687	106	7	to	to	PART
fumecheng-11687	106	8	solve	solve	VERB
fumecheng-11687	106	9	a	a	DET
fumecheng-11687	106	10	forced	force	VERB
fumecheng-11687	106	11	fractal	fractal	ADJ
fumecheng-11687	106	12	duffing	duffing	NOUN
fumecheng-11687	106	13	oscillator	oscillator	NOUN
fumecheng-11687	106	14	by	by	ADP
fumecheng-11687	106	15	the	the	DET
fumecheng-11687	106	16	np	np	PROPN
fumecheng-11687	106	17	technique	technique	NOUN
fumecheng-11687	106	18	203	203	NUM
fumecheng-11687	106	19	3	3	NUM
fumecheng-11687	106	20	.	.	PUNCT
fumecheng-11687	107	1	the	the	DET
fumecheng-11687	107	2	fractal	fractal	ADJ
fumecheng-11687	107	3	forced	force	VERB
fumecheng-11687	107	4	duffing	duffing	NOUN
fumecheng-11687	107	5	equation	equation	NOUN
fumecheng-11687	107	6	ineffective	ineffective	ADJ
fumecheng-11687	107	7	modelling	modelling	NOUN
fumecheng-11687	107	8	of	of	ADP
fumecheng-11687	107	9	the	the	DET
fumecheng-11687	107	10	system	system	NOUN
fumecheng-11687	107	11	is	be	AUX
fumecheng-11687	107	12	a	a	DET
fumecheng-11687	107	13	major	major	ADJ
fumecheng-11687	107	14	obstacle	obstacle	NOUN
fumecheng-11687	107	15	for	for	ADP
fumecheng-11687	107	16	a	a	DET
fumecheng-11687	107	17	nonlinear	nonlinear	ADJ
fumecheng-11687	107	18	oscillation	oscillation	NOUN
fumecheng-11687	107	19	system	system	NOUN
fumecheng-11687	107	20	in	in	ADP
fumecheng-11687	107	21	the	the	DET
fumecheng-11687	107	22	fractal	fractal	ADJ
fumecheng-11687	107	23	space	space	NOUN
fumecheng-11687	107	24	.	.	PUNCT
fumecheng-11687	108	1	particularly	particularly	ADV
fumecheng-11687	108	2	,	,	PUNCT
fumecheng-11687	108	3	the	the	DET
fumecheng-11687	108	4	distribution	distribution	NOUN
fumecheng-11687	108	5	of	of	ADP
fumecheng-11687	108	6	the	the	DET
fumecheng-11687	108	7	periodic	periodic	ADJ
fumecheng-11687	108	8	property	property	NOUN
fumecheng-11687	108	9	's	's	PART
fumecheng-11687	108	10	effect	effect	NOUN
fumecheng-11687	108	11	can	can	AUX
fumecheng-11687	108	12	not	not	PART
fumecheng-11687	108	13	be	be	AUX
fumecheng-11687	108	14	explained	explain	VERB
fumecheng-11687	108	15	by	by	ADP
fumecheng-11687	108	16	differential	differential	ADJ
fumecheng-11687	108	17	equation	equation	NOUN
fumecheng-11687	108	18	models	model	NOUN
fumecheng-11687	108	19	.	.	PUNCT
fumecheng-11687	109	1	in	in	ADP
fumecheng-11687	109	2	order	order	NOUN
fumecheng-11687	109	3	to	to	PART
fumecheng-11687	109	4	do	do	AUX
fumecheng-11687	109	5	this	this	PRON
fumecheng-11687	109	6	,	,	PUNCT
fumecheng-11687	109	7	the	the	DET
fumecheng-11687	109	8	current	current	ADJ
fumecheng-11687	109	9	work	work	NOUN
fumecheng-11687	109	10	develops	develop	VERB
fumecheng-11687	109	11	a	a	DET
fumecheng-11687	109	12	fractal	fractal	ADJ
fumecheng-11687	109	13	-	-	PUNCT
fumecheng-11687	109	14	differential	differential	NOUN
fumecheng-11687	109	15	model	model	NOUN
fumecheng-11687	109	16	,	,	PUNCT
fumecheng-11687	109	17	and	and	CCONJ
fumecheng-11687	109	18	a	a	DET
fumecheng-11687	109	19	forced	force	VERB
fumecheng-11687	109	20	fractal	fractal	ADJ
fumecheng-11687	109	21	duffing	duffing	NOUN
fumecheng-11687	109	22	oscillator	oscillator	NOUN
fumecheng-11687	109	23	is	be	AUX
fumecheng-11687	109	24	used	use	VERB
fumecheng-11687	109	25	as	as	ADP
fumecheng-11687	109	26	an	an	DET
fumecheng-11687	109	27	example	example	NOUN
fumecheng-11687	109	28	to	to	PART
fumecheng-11687	109	29	show	show	VERB
fumecheng-11687	109	30	the	the	DET
fumecheng-11687	109	31	fundamental	fundamental	ADJ
fumecheng-11687	109	32	characteristics	characteristic	NOUN
fumecheng-11687	109	33	of	of	ADP
fumecheng-11687	109	34	the	the	DET
fumecheng-11687	109	35	fractal	fractal	ADJ
fumecheng-11687	109	36	oscillator	oscillator	NOUN
fumecheng-11687	109	37	subjected	subject	VERB
fumecheng-11687	109	38	to	to	ADP
fumecheng-11687	109	39	harmonic	harmonic	ADJ
fumecheng-11687	109	40	force	force	NOUN
fumecheng-11687	109	41	.	.	PUNCT
fumecheng-11687	110	1	whereas	whereas	SCONJ
fumecheng-11687	110	2	a	a	DET
fumecheng-11687	110	3	lot	lot	NOUN
fumecheng-11687	110	4	of	of	ADP
fumecheng-11687	110	5	research	research	NOUN
fumecheng-11687	110	6	articles	article	NOUN
fumecheng-11687	110	7	focused	focus	VERB
fumecheng-11687	110	8	on	on	ADP
fumecheng-11687	110	9	a	a	DET
fumecheng-11687	110	10	simple	simple	ADJ
fumecheng-11687	110	11	oscillation	oscillation	NOUN
fumecheng-11687	110	12	in	in	ADP
fumecheng-11687	110	13	fractal	fractal	ADJ
fumecheng-11687	110	14	space	space	NOUN
fumecheng-11687	110	15	[	[	X
fumecheng-11687	110	16	40	40	NUM
fumecheng-11687	110	17	-	-	SYM
fumecheng-11687	110	18	42	42	NUM
fumecheng-11687	110	19	]	]	PUNCT
fumecheng-11687	110	20	,	,	PUNCT
fumecheng-11687	110	21	this	this	DET
fumecheng-11687	110	22	work	work	NOUN
fumecheng-11687	110	23	investigates	investigate	VERB
fumecheng-11687	110	24	a	a	DET
fumecheng-11687	110	25	more	more	ADV
fumecheng-11687	110	26	generalized	generalized	ADJ
fumecheng-11687	110	27	fractal	fractal	ADJ
fumecheng-11687	110	28	vibration	vibration	NOUN
fumecheng-11687	110	29	system	system	NOUN
fumecheng-11687	110	30	that	that	PRON
fumecheng-11687	110	31	is	be	AUX
fumecheng-11687	110	32	modeled	model	VERB
fumecheng-11687	110	33	by	by	ADP
fumecheng-11687	110	34	the	the	DET
fumecheng-11687	110	35	form	form	NOUN
fumecheng-11687	110	36	:	:	PUNCT
fumecheng-11687	110	37	2	2	NUM
fumecheng-11687	110	38	3	3	NUM
fumecheng-11687	110	39	02	02	NUM
fumecheng-11687	110	40	cos	cos	X
fumecheng-11687	110	41	;	;	PUNCT
fumecheng-11687	110	42	0	0	NUM
fumecheng-11687	110	43	1	1	NUM
fumecheng-11687	110	44	du	du	PROPN
fumecheng-11687	110	45	u	u	PROPN
fumecheng-11687	110	46	qu	qu	X
fumecheng-11687	110	47	t	t	PROPN
fumecheng-11687	110	48	dt	dt	NOUN
fumecheng-11687	110	49			X
fumecheng-11687	110	50			PROPN
fumecheng-11687	110	51			NUM
fumecheng-11687	110	52	+	+	NOUN
fumecheng-11687	110	53	+	+	SYM
fumecheng-11687	110	54	=	=	SYM
fumecheng-11687	110	55			PROPN
fumecheng-11687	110	56			PROPN
fumecheng-11687	110	57			PROPN
fumecheng-11687	110	58	(	(	PUNCT
fumecheng-11687	110	59	13	13	NUM
fumecheng-11687	110	60	)	)	PUNCT
fumecheng-11687	110	61	here	here	ADV
fumecheng-11687	110	62	,	,	PUNCT
fumecheng-11687	110	63			NOUN
fumecheng-11687	110	64	,	,	PUNCT
fumecheng-11687	110	65			PROPN
fumecheng-11687	110	66	,	,	PUNCT
fumecheng-11687	110	67	q	q	INTJ
fumecheng-11687	110	68	,	,	PUNCT
fumecheng-11687	110	69			PROPN
fumecheng-11687	110	70	,	,	PUNCT
fumecheng-11687	110	71	and	and	CCONJ
fumecheng-11687	110	72			NUM
fumecheng-11687	110	73	are	be	AUX
fumecheng-11687	110	74	the	the	DET
fumecheng-11687	110	75	non	non	ADJ
fumecheng-11687	110	76	-	-	ADJ
fumecheng-11687	110	77	zero	zero	NUM
fumecheng-11687	110	78	coefficients	coefficient	NOUN
fumecheng-11687	110	79	,	,	PUNCT
fumecheng-11687	110	80	fractal	fractal	ADJ
fumecheng-11687	110	81	factor	factor	NOUN
fumecheng-11687	110	82	,	,	PUNCT
fumecheng-11687	110	83	vibration	vibration	NOUN
fumecheng-11687	110	84	natural	natural	ADJ
fumecheng-11687	110	85	frequency	frequency	NOUN
fumecheng-11687	110	86	,	,	PUNCT
fumecheng-11687	110	87	duffing	duffe	VERB
fumecheng-11687	110	88	coefficient	coefficient	NOUN
fumecheng-11687	110	89	,	,	PUNCT
fumecheng-11687	110	90	parametric	parametric	ADJ
fumecheng-11687	110	91	force	force	NOUN
fumecheng-11687	110	92	,	,	PUNCT
fumecheng-11687	110	93	and	and	CCONJ
fumecheng-11687	110	94	amplitude	amplitude	NOUN
fumecheng-11687	110	95	,	,	PUNCT
fumecheng-11687	110	96	respectively	respectively	ADV
fumecheng-11687	110	97	.	.	PUNCT
fumecheng-11687	111	1	assuming	assume	VERB
fumecheng-11687	111	2	that	that	SCONJ
fumecheng-11687	111	3	the	the	DET
fumecheng-11687	111	4	initial	initial	ADJ
fumecheng-11687	111	5	conditions	condition	NOUN
fumecheng-11687	111	6	are	be	AUX
fumecheng-11687	111	7	described	describe	VERB
fumecheng-11687	111	8	as	as	ADP
fumecheng-11687	111	9	(	(	PUNCT
fumecheng-11687	111	10	0	0	NUM
fumecheng-11687	111	11	)	)	PUNCT
fumecheng-11687	111	12	(	(	PUNCT
fumecheng-11687	111	13	0	0	NUM
fumecheng-11687	111	14	)	)	PUNCT
fumecheng-11687	111	15	,	,	PUNCT
fumecheng-11687	111	16	0	0	NUM
fumecheng-11687	111	17	du	du	PROPN
fumecheng-11687	111	18	u	u	PROPN
fumecheng-11687	111	19	a	a	DET
fumecheng-11687	111	20	dt	dt	NOUN
fumecheng-11687	111	21	=	=	PUNCT
fumecheng-11687	111	22	=	=	SYM
fumecheng-11687	111	23	(	(	PUNCT
fumecheng-11687	111	24	14	14	NUM
fumecheng-11687	111	25	)	)	PUNCT
fumecheng-11687	111	26	the	the	DET
fumecheng-11687	111	27	fractal	fractal	ADJ
fumecheng-11687	111	28	theory	theory	NOUN
fumecheng-11687	111	29	has	have	AUX
fumecheng-11687	111	30	grown	grow	VERB
fumecheng-11687	111	31	in	in	ADP
fumecheng-11687	111	32	importance	importance	NOUN
fumecheng-11687	111	33	in	in	ADP
fumecheng-11687	111	34	both	both	PRON
fumecheng-11687	111	35	mathematics	mathematic	NOUN
fumecheng-11687	111	36	and	and	CCONJ
fumecheng-11687	111	37	mechanical	mechanical	ADJ
fumecheng-11687	111	38	engineering	engineering	NOUN
fumecheng-11687	111	39	because	because	SCONJ
fumecheng-11687	111	40	it	it	PRON
fumecheng-11687	111	41	is	be	AUX
fumecheng-11687	111	42	useful	useful	ADJ
fumecheng-11687	111	43	in	in	ADP
fumecheng-11687	111	44	developing	develop	VERB
fumecheng-11687	111	45	a	a	DET
fumecheng-11687	111	46	governing	govern	VERB
fumecheng-11687	111	47	equation	equation	NOUN
fumecheng-11687	111	48	in	in	ADP
fumecheng-11687	111	49	a	a	DET
fumecheng-11687	111	50	fractal	fractal	ADJ
fumecheng-11687	111	51	environment	environment	NOUN
fumecheng-11687	111	52	.	.	PUNCT
fumecheng-11687	112	1	there	there	PRON
fumecheng-11687	112	2	are	be	VERB
fumecheng-11687	112	3	numerous	numerous	ADJ
fumecheng-11687	112	4	definitions	definition	NOUN
fumecheng-11687	112	5	for	for	ADP
fumecheng-11687	112	6	the	the	DET
fumecheng-11687	112	7	fractional	fractional	ADJ
fumecheng-11687	112	8	derivatives	derivative	NOUN
fumecheng-11687	112	9	.	.	PUNCT
fumecheng-11687	113	1	most	most	ADJ
fumecheng-11687	113	2	definitions	definition	NOUN
fumecheng-11687	113	3	often	often	ADV
fumecheng-11687	113	4	used	use	VERB
fumecheng-11687	113	5	ones	one	NOUN
fumecheng-11687	113	6	include	include	VERB
fumecheng-11687	113	7	riemann	riemann	PROPN
fumecheng-11687	113	8	-	-	PUNCT
fumecheng-11687	113	9	liouville	liouville	PROPN
fumecheng-11687	113	10	,	,	PUNCT
fumecheng-11687	113	11	caputo	caputo	PROPN
fumecheng-11687	113	12	,	,	PUNCT
fumecheng-11687	113	13	xiao	xiao	PROPN
fumecheng-11687	113	14	-	-	PUNCT
fumecheng-11687	113	15	jun	jun	PROPN
fumecheng-11687	113	16	yang	yang	PROPN
fumecheng-11687	113	17	,	,	PUNCT
fumecheng-11687	113	18	and	and	CCONJ
fumecheng-11687	113	19	jumarie	jumarie	NOUN
fumecheng-11687	113	20	for	for	ADP
fumecheng-11687	113	21	further	further	ADJ
fumecheng-11687	113	22	justification	justification	NOUN
fumecheng-11687	113	23	see	see	VERB
fumecheng-11687	113	24	[	[	X
fumecheng-11687	113	25	43	43	NUM
fumecheng-11687	113	26	-	-	SYM
fumecheng-11687	113	27	45	45	NUM
fumecheng-11687	113	28	]	]	PUNCT
fumecheng-11687	113	29	.	.	PUNCT
fumecheng-11687	114	1	the	the	DET
fumecheng-11687	114	2	he	he	PRON
fumecheng-11687	114	3	's	's	PART
fumecheng-11687	114	4	fractal	fractal	ADJ
fumecheng-11687	114	5	derivative	derivative	NOUN
fumecheng-11687	114	6	is	be	AUX
fumecheng-11687	114	7	defined	define	VERB
fumecheng-11687	114	8	as	as	ADP
fumecheng-11687	114	9	[	[	X
fumecheng-11687	114	10	7	7	NUM
fumecheng-11687	114	11	,	,	PUNCT
fumecheng-11687	114	12	46	46	NUM
fumecheng-11687	114	13	,	,	PUNCT
fumecheng-11687	114	14	47	47	NUM
fumecheng-11687	114	15	]	]	PUNCT
fumecheng-11687	114	16	:	:	PUNCT
fumecheng-11687	114	17	0	0	NUM
fumecheng-11687	114	18	0	0	NUM
fumecheng-11687	114	19	00	00	PUNCT
fumecheng-11687	115	1	(	(	PUNCT
fumecheng-11687	115	2	)	)	PUNCT
fumecheng-11687	115	3	(	(	PUNCT
fumecheng-11687	115	4	)	)	PUNCT
fumecheng-11687	115	5	(	(	PUNCT
fumecheng-11687	115	6	1	1	X
fumecheng-11687	115	7	)	)	PUNCT
fumecheng-11687	115	8	(	(	PUNCT
fumecheng-11687	115	9	)	)	PUNCT
fumecheng-11687	115	10	t	t	NOUN
fumecheng-11687	115	11	t	t	PROPN
fumecheng-11687	115	12	t	t	PROPN
fumecheng-11687	115	13	t	t	PROPN
fumecheng-11687	115	14	u	u	NOUN
fumecheng-11687	115	15	t	t	PROPN
fumecheng-11687	115	16	u	u	NOUN
fumecheng-11687	115	17	td	td	PROPN
fumecheng-11687	115	18	u	u	PROPN
fumecheng-11687	115	19	lim	lim	PROPN
fumecheng-11687	115	20	dt	dt	PROPN
fumecheng-11687	115	21	t	t	PROPN
fumecheng-11687	115	22	t	t	PROPN
fumecheng-11687	115	23			X
fumecheng-11687	115	24			X
fumecheng-11687	115	25			X
fumecheng-11687	115	26			X
fumecheng-11687	115	27	−	−	NOUN
fumecheng-11687	115	28	→	→	PUNCT
fumecheng-11687	115	29			PUNCT
fumecheng-11687	115	30			NOUN
fumecheng-11687	115	31	−	−	NOUN
fumecheng-11687	115	32	=	=	SYM
fumecheng-11687	116	1			VERB
fumecheng-11687	116	2	+	+	NUM
fumecheng-11687	116	3	−	−	PROPN
fumecheng-11687	116	4	(	(	PUNCT
fumecheng-11687	116	5	15	15	NUM
fumecheng-11687	116	6	)	)	PUNCT
fumecheng-11687	116	7	in	in	ADP
fumecheng-11687	116	8	this	this	DET
fumecheng-11687	116	9	case	case	NOUN
fumecheng-11687	116	10	,	,	PUNCT
fumecheng-11687	116	11	the	the	DET
fumecheng-11687	116	12	fractal	fractal	ADJ
fumecheng-11687	116	13	factor	factor	NOUN
fumecheng-11687	116	14			PRON
fumecheng-11687	116	15	runs	run	VERB
fumecheng-11687	116	16	along	along	ADP
fumecheng-11687	116	17	the	the	DET
fumecheng-11687	116	18	t	t	PROPN
fumecheng-11687	116	19	dimension	dimension	NOUN
fumecheng-11687	116	20	.	.	PUNCT
fumecheng-11687	117	1	if	if	SCONJ
fumecheng-11687	117	2	we	we	PRON
fumecheng-11687	117	3	see	see	VERB
fumecheng-11687	117	4	a	a	DET
fumecheng-11687	117	5	motion	motion	NOUN
fumecheng-11687	117	6	on	on	ADP
fumecheng-11687	117	7	a	a	DET
fumecheng-11687	117	8	vast	vast	ADJ
fumecheng-11687	117	9	size	size	NOUN
fumecheng-11687	117	10	,	,	PUNCT
fumecheng-11687	117	11	it	it	PRON
fumecheng-11687	117	12	might	might	AUX
fumecheng-11687	117	13	alter	alter	VERB
fumecheng-11687	117	14	continuously	continuously	ADV
fumecheng-11687	117	15	,	,	PUNCT
fumecheng-11687	117	16	but	but	CCONJ
fumecheng-11687	117	17	if	if	SCONJ
fumecheng-11687	117	18	we	we	PRON
fumecheng-11687	117	19	observe	observe	VERB
fumecheng-11687	117	20	it	it	PRON
fumecheng-11687	117	21	on	on	ADP
fumecheng-11687	117	22	a	a	DET
fumecheng-11687	117	23	tiny	tiny	ADJ
fumecheng-11687	117	24	scale	scale	NOUN
fumecheng-11687	117	25	,	,	PUNCT
fumecheng-11687	117	26	it	it	PRON
fumecheng-11687	117	27	might	might	AUX
fumecheng-11687	117	28	discontinue	discontinue	VERB
fumecheng-11687	117	29	.	.	PUNCT
fumecheng-11687	118	1	as	as	ADP
fumecheng-11687	118	2	a	a	DET
fumecheng-11687	118	3	result	result	NOUN
fumecheng-11687	118	4	,	,	PUNCT
fumecheng-11687	118	5	the	the	DET
fumecheng-11687	118	6	fractal	fractal	ADJ
fumecheng-11687	118	7	theory	theory	NOUN
fumecheng-11687	118	8	is	be	AUX
fumecheng-11687	118	9	an	an	DET
fumecheng-11687	118	10	effective	effective	ADJ
fumecheng-11687	118	11	mathematical	mathematical	ADJ
fumecheng-11687	118	12	instrument	instrument	NOUN
fumecheng-11687	118	13	for	for	ADP
fumecheng-11687	118	14	conducting	conduct	VERB
fumecheng-11687	118	15	more	more	ADV
fumecheng-11687	118	16	thorough	thorough	ADJ
fumecheng-11687	118	17	global	global	ADJ
fumecheng-11687	118	18	research	research	NOUN
fumecheng-11687	118	19	.	.	PUNCT
fumecheng-11687	119	1	moreover	moreover	ADV
fumecheng-11687	119	2	,	,	PUNCT
fumecheng-11687	119	3	this	this	DET
fumecheng-11687	119	4	fractal	fractal	ADJ
fumecheng-11687	119	5	derivative	derivative	NOUN
fumecheng-11687	119	6	exhibits	exhibit	VERB
fumecheng-11687	119	7	some	some	PRON
fumecheng-11687	119	8	of	of	ADP
fumecheng-11687	119	9	the	the	DET
fumecheng-11687	119	10	following	following	ADJ
fumecheng-11687	119	11	characteristics	characteristic	NOUN
fumecheng-11687	119	12	[	[	X
fumecheng-11687	119	13	48	48	NUM
fumecheng-11687	119	14	-	-	SYM
fumecheng-11687	119	15	50	50	NUM
fumecheng-11687	119	16	]	]	PUNCT
fumecheng-11687	119	17	:	:	PUNCT
fumecheng-11687	119	18	0	0	NUM
fumecheng-11687	119	19	1	1	NUM
fumecheng-11687	119	20	2	2	NUM
fumecheng-11687	119	21	,	,	PUNCT
fumecheng-11687	119	22	and	and	CCONJ
fumecheng-11687	119	23	→	→	SYM
fumecheng-11687	119	24	→	→	SYM
fumecheng-11687	119	25	→	→	SYM
fumecheng-11687	119	26	=	=	SYM
fumecheng-11687	119	27	=	=	SYM
fumecheng-11687	119	28	=	=	SYM
fumecheng-11687	119	29	du	du	PROPN
fumecheng-11687	119	30	du	du	PROPN
fumecheng-11687	119	31	du	du	PROPN
fumecheng-11687	119	32	lim	lim	PROPN
fumecheng-11687	119	33	u	u	PROPN
fumecheng-11687	119	34	lim	lim	PROPN
fumecheng-11687	119	35	u	u	PROPN
fumecheng-11687	119	36	lim	lim	PROPN
fumecheng-11687	119	37	u	u	X
fumecheng-11687	119	38	dt	dt	X
fumecheng-11687	119	39	dt	dt	AUX
fumecheng-11687	119	40	dt	dt	VERB
fumecheng-11687	119	41			NOUN
fumecheng-11687	119	42			ADP
fumecheng-11687	119	43			NUM
fumecheng-11687	119	44			X
fumecheng-11687	119	45	(	(	PUNCT
fumecheng-11687	119	46	16	16	NUM
fumecheng-11687	119	47	)	)	PUNCT
fumecheng-11687	119	48	here	here	ADV
fumecheng-11687	119	49	the	the	DET
fumecheng-11687	119	50	over	over	NOUN
fumecheng-11687	119	51	-	-	PUNCT
fumecheng-11687	119	52	dot	dot	NOUN
fumecheng-11687	119	53	refers	refer	VERB
fumecheng-11687	119	54	to	to	ADP
fumecheng-11687	119	55	the	the	DET
fumecheng-11687	119	56	time	time	NOUN
fumecheng-11687	119	57	classical	classical	ADJ
fumecheng-11687	119	58	derivative	derivative	NOUN
fumecheng-11687	119	59	.	.	PUNCT
fumecheng-11687	120	1	the	the	DET
fumecheng-11687	120	2	fractal	fractal	ADJ
fumecheng-11687	120	3	derivative	derivative	NOUN
fumecheng-11687	120	4	given	give	VERB
fumecheng-11687	120	5	in	in	ADP
fumecheng-11687	120	6	eq	eq	ADP
fumecheng-11687	120	7	.	.	PUNCT
fumecheng-11687	121	1	(	(	PUNCT
fumecheng-11687	121	2	15	15	NUM
fumecheng-11687	121	3	)	)	PUNCT
fumecheng-11687	121	4	has	have	AUX
fumecheng-11687	121	5	widely	widely	ADV
fumecheng-11687	121	6	been	be	AUX
fumecheng-11687	121	7	used	use	VERB
fumecheng-11687	121	8	to	to	PART
fumecheng-11687	121	9	deal	deal	VERB
fumecheng-11687	121	10	with	with	ADP
fumecheng-11687	121	11	porous	porous	ADJ
fumecheng-11687	121	12	or	or	CCONJ
fumecheng-11687	121	13	hierarchical	hierarchical	ADJ
fumecheng-11687	121	14	structures	structure	NOUN
fumecheng-11687	122	1	[	[	X
fumecheng-11687	122	2	46	46	NUM
fumecheng-11687	122	3	-	-	SYM
fumecheng-11687	122	4	50	50	NUM
fumecheng-11687	122	5	]	]	PUNCT
fumecheng-11687	122	6	with	with	ADP
fumecheng-11687	122	7	great	great	ADJ
fumecheng-11687	122	8	success	success	NOUN
fumecheng-11687	122	9	.	.	PUNCT
fumecheng-11687	123	1	if	if	SCONJ
fumecheng-11687	123	2	we	we	PRON
fumecheng-11687	123	3	see	see	VERB
fumecheng-11687	123	4	a	a	DET
fumecheng-11687	123	5	motion	motion	NOUN
fumecheng-11687	123	6	on	on	ADP
fumecheng-11687	123	7	a	a	DET
fumecheng-11687	123	8	vast	vast	ADJ
fumecheng-11687	123	9	size	size	NOUN
fumecheng-11687	123	10	,	,	PUNCT
fumecheng-11687	123	11	it	it	PRON
fumecheng-11687	123	12	might	might	AUX
fumecheng-11687	123	13	alter	alter	VERB
fumecheng-11687	123	14	continuously	continuously	ADV
fumecheng-11687	123	15	,	,	PUNCT
fumecheng-11687	123	16	but	but	CCONJ
fumecheng-11687	123	17	if	if	SCONJ
fumecheng-11687	123	18	we	we	PRON
fumecheng-11687	123	19	observe	observe	VERB
fumecheng-11687	123	20	it	it	PRON
fumecheng-11687	123	21	on	on	ADP
fumecheng-11687	123	22	a	a	DET
fumecheng-11687	123	23	tiny	tiny	ADJ
fumecheng-11687	123	24	scale	scale	NOUN
fumecheng-11687	123	25	,	,	PUNCT
fumecheng-11687	123	26	it	it	PRON
fumecheng-11687	123	27	might	might	AUX
fumecheng-11687	123	28	discontinue	discontinue	VERB
fumecheng-11687	123	29	.	.	PUNCT
fumecheng-11687	124	1	as	as	ADP
fumecheng-11687	124	2	a	a	DET
fumecheng-11687	124	3	result	result	NOUN
fumecheng-11687	124	4	,	,	PUNCT
fumecheng-11687	124	5	the	the	DET
fumecheng-11687	124	6	fractal	fractal	ADJ
fumecheng-11687	124	7	theory	theory	NOUN
fumecheng-11687	124	8	is	be	AUX
fumecheng-11687	124	9	an	an	DET
fumecheng-11687	124	10	effective	effective	ADJ
fumecheng-11687	124	11	mathematical	mathematical	ADJ
fumecheng-11687	124	12	instrument	instrument	NOUN
fumecheng-11687	124	13	for	for	ADP
fumecheng-11687	124	14	conducting	conduct	VERB
fumecheng-11687	124	15	more	more	ADV
fumecheng-11687	124	16	thorough	thorough	ADJ
fumecheng-11687	124	17	global	global	ADJ
fumecheng-11687	124	18	research	research	NOUN
fumecheng-11687	124	19	.	.	PUNCT
fumecheng-11687	125	1	the	the	DET
fumecheng-11687	125	2	technique	technique	NOUN
fumecheng-11687	125	3	of	of	ADP
fumecheng-11687	125	4	creating	create	VERB
fumecheng-11687	125	5	mathematical	mathematical	ADJ
fumecheng-11687	125	6	models	model	NOUN
fumecheng-11687	125	7	and	and	CCONJ
fumecheng-11687	125	8	the	the	DET
fumecheng-11687	125	9	geometric	geometric	ADJ
fumecheng-11687	125	10	physical	physical	ADJ
fumecheng-11687	125	11	interpretation	interpretation	NOUN
fumecheng-11687	125	12	of	of	ADP
fumecheng-11687	125	13	fractal	fractal	ADJ
fumecheng-11687	125	14	derivatives	derivative	NOUN
fumecheng-11687	125	15	were	be	AUX
fumecheng-11687	125	16	discussed	discuss	VERB
fumecheng-11687	125	17	in	in	ADP
fumecheng-11687	125	18	[	[	X
fumecheng-11687	125	19	51	51	NUM
fumecheng-11687	125	20	]	]	PUNCT
fumecheng-11687	125	21	.	.	PUNCT
fumecheng-11687	126	1	defining	define	VERB
fumecheng-11687	126	2	the	the	DET
fumecheng-11687	126	3	restoring	restore	VERB
fumecheng-11687	126	4	force	force	NOUN
fumecheng-11687	126	5	f	f	X
fumecheng-11687	126	6	(	(	PUNCT
fumecheng-11687	126	7	u	u	NOUN
fumecheng-11687	126	8	)	)	PUNCT
fumecheng-11687	126	9	in	in	ADP
fumecheng-11687	126	10	the	the	DET
fumecheng-11687	126	11	current	current	ADJ
fumecheng-11687	126	12	problem	problem	NOUN
fumecheng-11687	126	13	as	as	ADP
fumecheng-11687	126	14	2	2	NUM
fumecheng-11687	126	15	3	3	NUM
fumecheng-11687	126	16	0	0	NUM
fumecheng-11687	126	17	(	(	PUNCT
fumecheng-11687	126	18	)	)	PUNCT
fumecheng-11687	126	19	f	f	PROPN
fumecheng-11687	126	20	u	u	NOUN
fumecheng-11687	126	21	u	u	NOUN
fumecheng-11687	126	22	qu=	qu=	NOUN
fumecheng-11687	126	23	+	+	CCONJ
fumecheng-11687	126	24	(	(	PUNCT
fumecheng-11687	126	25	17	17	NUM
fumecheng-11687	126	26	)	)	PUNCT
fumecheng-11687	126	27	204	204	NUM
fumecheng-11687	126	28	y.o	y.o	PROPN
fumecheng-11687	126	29	.	.	PROPN
fumecheng-11687	126	30	el	el	PROPN
fumecheng-11687	126	31	-	-	PUNCT
fumecheng-11687	126	32	dib	dib	PROPN
fumecheng-11687	126	33	,	,	PUNCT
fumecheng-11687	126	34	n.s	n.s	PROPN
fumecheng-11687	126	35	.	.	PROPN
fumecheng-11687	126	36	elgazery	elgazery	PROPN
fumecheng-11687	126	37	,	,	PUNCT
fumecheng-11687	126	38	h.a	h.a	PROPN
fumecheng-11687	126	39	.	.	PROPN
fumecheng-11687	126	40	alyousef	alyousef	PROPN
fumecheng-11687	126	41	accordingly	accordingly	ADV
fumecheng-11687	126	42	,	,	PUNCT
fumecheng-11687	126	43	eq	eq	ADJ
fumecheng-11687	126	44	.	.	PUNCT
fumecheng-11687	127	1	(	(	PUNCT
fumecheng-11687	127	2	13	13	NUM
fumecheng-11687	127	3	)	)	PUNCT
fumecheng-11687	127	4	can	can	AUX
fumecheng-11687	127	5	be	be	AUX
fumecheng-11687	127	6	written	write	VERB
fumecheng-11687	127	7	as	as	ADP
fumecheng-11687	127	8	2	2	NUM
fumecheng-11687	127	9	(	(	PUNCT
fumecheng-11687	127	10	)	)	PUNCT
fumecheng-11687	127	11	cos	cos	SCONJ
fumecheng-11687	127	12	du	du	PROPN
fumecheng-11687	127	13	f	f	PROPN
fumecheng-11687	127	14	u	u	PROPN
fumecheng-11687	127	15	t	t	NOUN
fumecheng-11687	127	16	dt	dt	NOUN
fumecheng-11687	127	17			PROPN
fumecheng-11687	127	18	+	+	PROPN
fumecheng-11687	127	19	=	=	PUNCT
fumecheng-11687	127	20			PROPN
fumecheng-11687	127	21	(	(	PUNCT
fumecheng-11687	127	22	18	18	NUM
fumecheng-11687	127	23	)	)	PUNCT
fumecheng-11687	127	24	operating	operate	VERB
fumecheng-11687	127	25	𝑑	𝑑	PROPN
fumecheng-11687	127	26	𝑑𝑡𝛼	𝑑𝑡𝛼	NOUN
fumecheng-11687	127	27	on	on	ADP
fumecheng-11687	127	28	eq	eq	PROPN
fumecheng-11687	127	29	.	.	PUNCT
fumecheng-11687	128	1	(	(	PUNCT
fumecheng-11687	128	2	18	18	NUM
fumecheng-11687	128	3	)	)	PUNCT
fumecheng-11687	128	4	one	one	NUM
fumecheng-11687	128	5	time	time	NOUN
fumecheng-11687	129	1	and	and	CCONJ
fumecheng-11687	129	2	𝑑	𝑑	PROPN
fumecheng-11687	129	3	𝑑𝑡2𝛼	𝑑𝑡2𝛼	ADJ
fumecheng-11687	129	4	another	another	DET
fumecheng-11687	129	5	time	time	NOUN
fumecheng-11687	129	6	gives	give	VERB
fumecheng-11687	129	7	3	3	NUM
fumecheng-11687	129	8	(	(	PUNCT
fumecheng-11687	129	9	)	)	PUNCT
fumecheng-11687	129	10	cos	cos	ADP
fumecheng-11687	129	11	du	du	PROPN
fumecheng-11687	129	12	d	d	PROPN
fumecheng-11687	129	13	d	d	X
fumecheng-11687	129	14	f	f	X
fumecheng-11687	129	15	u	u	X
fumecheng-11687	129	16	t	t	X
fumecheng-11687	129	17	dt	dt	X
fumecheng-11687	129	18	dt	dt	AUX
fumecheng-11687	129	19	dt	dt	VERB
fumecheng-11687	129	20			NOUN
fumecheng-11687	129	21			PROPN
fumecheng-11687	129	22	+	+	PROPN
fumecheng-11687	129	23	=	=	PUNCT
fumecheng-11687	129	24			PROPN
fumecheng-11687	129	25	(	(	PUNCT
fumecheng-11687	129	26	19	19	NUM
fumecheng-11687	129	27	)	)	PUNCT
fumecheng-11687	129	28	4	4	NUM
fumecheng-11687	129	29	2	2	NUM
fumecheng-11687	129	30	2	2	NUM
fumecheng-11687	129	31	(	(	PUNCT
fumecheng-11687	129	32	)	)	PUNCT
fumecheng-11687	129	33	cos	cos	ADP
fumecheng-11687	129	34	du	du	PROPN
fumecheng-11687	129	35	df	df	PROPN
fumecheng-11687	129	36	u	u	PROPN
fumecheng-11687	129	37	d	d	PROPN
fumecheng-11687	129	38	t	t	X
fumecheng-11687	129	39	dt	dt	X
fumecheng-11687	129	40	dt	dt	AUX
fumecheng-11687	129	41	dt	dt	VERB
fumecheng-11687	129	42			NOUN
fumecheng-11687	129	43			PROPN
fumecheng-11687	129	44	+	+	PROPN
fumecheng-11687	129	45	=	=	PUNCT
fumecheng-11687	129	46			PROPN
fumecheng-11687	129	47	(	(	PUNCT
fumecheng-11687	129	48	20	20	NUM
fumecheng-11687	129	49	)	)	PUNCT
fumecheng-11687	129	50	to	to	PART
fumecheng-11687	129	51	estimate	estimate	VERB
fumecheng-11687	129	52	𝑑	𝑑	PRON
fumecheng-11687	129	53	𝑑𝑡𝛼	𝑑𝑡𝛼	PROPN
fumecheng-11687	129	54	cos	cos	PROPN
fumecheng-11687	129	55	ω𝑡	ω𝑡	PROPN
fumecheng-11687	129	56	and	and	CCONJ
fumecheng-11687	129	57	𝑑	𝑑	PROPN
fumecheng-11687	129	58	𝑑𝑡2𝛼	𝑑𝑡2𝛼	PROPN
fumecheng-11687	129	59	cos	cos	PROPN
fumecheng-11687	129	60	ω𝑡	ω𝑡	PROPN
fumecheng-11687	129	61	one	one	PRON
fumecheng-11687	129	62	may	may	AUX
fumecheng-11687	129	63	apply	apply	VERB
fumecheng-11687	129	64	the	the	DET
fumecheng-11687	129	65	following	follow	VERB
fumecheng-11687	129	66	fractal	fractal	ADJ
fumecheng-11687	129	67	derivative	derivative	NOUN
fumecheng-11687	129	68	proposed	propose	VERB
fumecheng-11687	129	69	by	by	ADP
fumecheng-11687	129	70	el	el	PROPN
fumecheng-11687	129	71	-	-	PROPN
fumecheng-11687	129	72	dib	dib	PROPN
fumecheng-11687	129	73	and	and	CCONJ
fumecheng-11687	129	74	elgazery	elgazery	NOUN
fumecheng-11687	130	1	[	[	X
fumecheng-11687	130	2	30,31	30,31	PROPN
fumecheng-11687	130	3	]	]	PUNCT
fumecheng-11687	130	4	:	:	PUNCT
fumecheng-11687	130	5	11	11	NUM
fumecheng-11687	130	6	1	1	NUM
fumecheng-11687	130	7	2	2	NUM
fumecheng-11687	130	8	2	2	NUM
fumecheng-11687	130	9	..	..	PUNCT
fumecheng-11687	130	10	(	(	PUNCT
fumecheng-11687	130	11	cos	cos	X
fumecheng-11687	130	12	(	(	PUNCT
fumecheng-11687	130	13	)	)	PUNCT
fumecheng-11687	130	14	sin	sin	NOUN
fumecheng-11687	130	15	(	(	PUNCT
fumecheng-11687	130	16	)	)	PUNCT
fumecheng-11687	130	17	)	)	PUNCT
fumecheng-11687	130	18	..	..	PUNCT
fumecheng-11687	131	1	n	n	CCONJ
fumecheng-11687	132	1	n	n	NOUN
fumecheng-11687	132	2	d	d	NOUN
fumecheng-11687	132	3	s	s	X
fumecheng-11687	132	4	s	s	X
fumecheng-11687	132	5	d	d	X
fumecheng-11687	132	6	dt	dt	X
fumecheng-11687	132	7	−=	−=	X
fumecheng-11687	132	8	+	+	ADP
fumecheng-11687	132	9			NOUN
fumecheng-11687	132	10			X
fumecheng-11687	132	11			NUM
fumecheng-11687	132	12			PROPN
fumecheng-11687	132	13			PROPN
fumecheng-11687	132	14	(	(	PUNCT
fumecheng-11687	132	15	21	21	NUM
fumecheng-11687	132	16	)	)	PUNCT
fumecheng-11687	132	17	therefore	therefore	ADV
fumecheng-11687	132	18	,	,	PUNCT
fumecheng-11687	132	19	one	one	PRON
fumecheng-11687	132	20	gets	get	VERB
fumecheng-11687	132	21	11	11	NUM
fumecheng-11687	132	22	1	1	NUM
fumecheng-11687	132	23	2	2	NUM
fumecheng-11687	132	24	2	2	NUM
fumecheng-11687	132	25	cos	cos	PROPN
fumecheng-11687	132	26	cos	cos	PROPN
fumecheng-11687	132	27	(	(	PUNCT
fumecheng-11687	132	28	)	)	PUNCT
fumecheng-11687	132	29	cos	cos	PROPN
fumecheng-11687	132	30	sin	sin	NOUN
fumecheng-11687	132	31	(	(	PUNCT
fumecheng-11687	132	32	)	)	PUNCT
fumecheng-11687	132	33	sin	sin	NOUN
fumecheng-11687	133	1	d	d	PROPN
fumecheng-11687	133	2	t	t	PROPN
fumecheng-11687	133	3	s	s	PROPN
fumecheng-11687	133	4	t	t	PROPN
fumecheng-11687	133	5	s	s	PROPN
fumecheng-11687	133	6	t	t	NOUN
fumecheng-11687	133	7	dt	dt	X
fumecheng-11687	133	8	−	−	PROPN
fumecheng-11687	133	9	=	=	SYM
fumecheng-11687	133	10			PROPN
fumecheng-11687	134	1	−	−	PROPN
fumecheng-11687	134	2			PROPN
fumecheng-11687	134	3			NOUN
fumecheng-11687	134	4			PUNCT
fumecheng-11687	134	5			NUM
fumecheng-11687	134	6			PROPN
fumecheng-11687	134	7			PROPN
fumecheng-11687	134	8	(	(	PUNCT
fumecheng-11687	134	9	22	22	NUM
fumecheng-11687	134	10	)	)	PUNCT
fumecheng-11687	134	11	2	2	NUM
fumecheng-11687	134	12	2	2	NUM
fumecheng-11687	134	13	2	2	NUM
fumecheng-11687	134	14	2	2	NUM
fumecheng-11687	134	15	2	2	NUM
fumecheng-11687	134	16	cos	cos	PROPN
fumecheng-11687	134	17	(	(	PUNCT
fumecheng-11687	134	18	)	)	PUNCT
fumecheng-11687	134	19	(	(	PUNCT
fumecheng-11687	134	20	(	(	PUNCT
fumecheng-11687	134	21	)	)	PUNCT
fumecheng-11687	134	22	)	)	PUNCT
fumecheng-11687	134	23	cos	cos	ADP
fumecheng-11687	134	24	2	2	NUM
fumecheng-11687	134	25	(	(	PUNCT
fumecheng-11687	134	26	)	)	PUNCT
fumecheng-11687	134	27	(	(	PUNCT
fumecheng-11687	134	28	)	)	PUNCT
fumecheng-11687	134	29	sin	sin	NOUN
fumecheng-11687	135	1	d	d	PROPN
fumecheng-11687	135	2	t	t	PROPN
fumecheng-11687	135	3	b	b	PROPN
fumecheng-11687	135	4	a	a	DET
fumecheng-11687	135	5	t	t	NOUN
fumecheng-11687	135	6	a	a	DET
fumecheng-11687	135	7	b	b	PROPN
fumecheng-11687	135	8	t	t	PROPN
fumecheng-11687	135	9	dt	dt	X
fumecheng-11687	135	10			PROPN
fumecheng-11687	136	1	=	=	SYM
fumecheng-11687	136	2	−	−	PROPN
fumecheng-11687	136	3			PROPN
fumecheng-11687	136	4			PROPN
fumecheng-11687	137	1	−	−	PROPN
fumecheng-11687	137	2			PROPN
fumecheng-11687	137	3			PROPN
fumecheng-11687	137	4			X
fumecheng-11687	137	5			X
fumecheng-11687	137	6			X
fumecheng-11687	137	7			X
fumecheng-11687	137	8			X
fumecheng-11687	137	9	(	(	PUNCT
fumecheng-11687	137	10	23	23	NUM
fumecheng-11687	137	11	)	)	PUNCT
fumecheng-11687	137	12	here	here	ADV
fumecheng-11687	137	13	,	,	PUNCT
fumecheng-11687	137	14	a(	a(	PROPN
fumecheng-11687	137	15	)	)	PUNCT
fumecheng-11687	137	16	and	and	CCONJ
fumecheng-11687	137	17	b(	b(	PROPN
fumecheng-11687	137	18	)	)	PUNCT
fumecheng-11687	137	19	are	be	AUX
fumecheng-11687	137	20	described	describe	VERB
fumecheng-11687	137	21	by	by	ADP
fumecheng-11687	137	22	11	11	NUM
fumecheng-11687	137	23	1	1	NUM
fumecheng-11687	137	24	2	2	NUM
fumecheng-11687	137	25	2	2	NUM
fumecheng-11687	137	26	(	(	PUNCT
fumecheng-11687	137	27	)	)	PUNCT
fumecheng-11687	137	28	cot	cot	NOUN
fumecheng-11687	137	29	(	(	PUNCT
fumecheng-11687	137	30	)	)	PUNCT
fumecheng-11687	137	31	and	and	CCONJ
fumecheng-11687	137	32	(	(	PUNCT
fumecheng-11687	137	33	)	)	PUNCT
fumecheng-11687	137	34	sin	sin	NOUN
fumecheng-11687	137	35	(	(	PUNCT
fumecheng-11687	137	36	)	)	PUNCT
fumecheng-11687	137	37	a	a	DET
fumecheng-11687	137	38	s	s	PROPN
fumecheng-11687	137	39	b	b	X
fumecheng-11687	137	40	s	s	X
fumecheng-11687	137	41	−=	−=	NOUN
fumecheng-11687	137	42	=	=	PUNCT
fumecheng-11687	137	43			PRON
fumecheng-11687	137	44			PROPN
fumecheng-11687	137	45			NUM
fumecheng-11687	137	46			PROPN
fumecheng-11687	137	47	(	(	PUNCT
fumecheng-11687	137	48	24	24	NUM
fumecheng-11687	137	49	)	)	PUNCT
fumecheng-11687	137	50	employing	employ	VERB
fumecheng-11687	137	51	eqs	eqs	PROPN
fumecheng-11687	137	52	.	.	PUNCT
fumecheng-11687	138	1	(	(	PUNCT
fumecheng-11687	138	2	22	22	NUM
fumecheng-11687	138	3	)	)	PUNCT
fumecheng-11687	138	4	and	and	CCONJ
fumecheng-11687	138	5	(	(	PUNCT
fumecheng-11687	138	6	23	23	NUM
fumecheng-11687	138	7	)	)	PUNCT
fumecheng-11687	138	8	into	into	ADP
fumecheng-11687	138	9	eqs	eqs	PROPN
fumecheng-11687	138	10	.	.	PUNCT
fumecheng-11687	139	1	(	(	PUNCT
fumecheng-11687	139	2	19	19	NUM
fumecheng-11687	139	3	)	)	PUNCT
fumecheng-11687	139	4	and	and	CCONJ
fumecheng-11687	139	5	(	(	PUNCT
fumecheng-11687	139	6	20	20	NUM
fumecheng-11687	139	7	)	)	PUNCT
fumecheng-11687	139	8	by	by	ADP
fumecheng-11687	139	9	using	use	VERB
fumecheng-11687	139	10	eq	eq	PROPN
fumecheng-11687	139	11	.	.	PUNCT
fumecheng-11687	140	1	(	(	PUNCT
fumecheng-11687	140	2	18	18	NUM
fumecheng-11687	140	3	)	)	PUNCT
fumecheng-11687	140	4	yields	yield	VERB
fumecheng-11687	140	5	11	11	NUM
fumecheng-11687	140	6	1	1	NUM
fumecheng-11687	140	7	1	1	NUM
fumecheng-11687	140	8	2	2	NUM
fumecheng-11687	140	9	2	2	NUM
fumecheng-11687	140	10	23	23	NUM
fumecheng-11687	140	11	2	2	NUM
fumecheng-11687	140	12	cos	cos	PROPN
fumecheng-11687	140	13	(	(	PUNCT
fumecheng-11687	140	14	)	)	PUNCT
fumecheng-11687	140	15	(	(	PUNCT
fumecheng-11687	140	16	)	)	PUNCT
fumecheng-11687	140	17	cos	cos	PROPN
fumecheng-11687	140	18	(	(	PUNCT
fumecheng-11687	140	19	)	)	PUNCT
fumecheng-11687	140	20	(	(	PUNCT
fumecheng-11687	140	21	)	)	PUNCT
fumecheng-11687	140	22	sin	sin	NOUN
fumecheng-11687	140	23	(	(	PUNCT
fumecheng-11687	140	24	)	)	PUNCT
fumecheng-11687	140	25	sin	sin	PROPN
fumecheng-11687	140	26	du	du	PROPN
fumecheng-11687	140	27	du	du	PROPN
fumecheng-11687	140	28	d	d	PROPN
fumecheng-11687	140	29	s	s	PROPN
fumecheng-11687	140	30	f	f	PROPN
fumecheng-11687	140	31	u	u	PROPN
fumecheng-11687	140	32	s	s	PROPN
fumecheng-11687	140	33	f	f	PROPN
fumecheng-11687	140	34	u	u	PROPN
fumecheng-11687	140	35	s	s	PROPN
fumecheng-11687	140	36	t	t	NOUN
fumecheng-11687	140	37	dt	dt	NOUN
fumecheng-11687	140	38	dt	dt	X
fumecheng-11687	140	39	dt	dt	PROPN
fumecheng-11687	140	40	−−	−−	PROPN
fumecheng-11687	140	41	+	+	CCONJ
fumecheng-11687	140	42	−	−	PROPN
fumecheng-11687	140	43	=	=	SYM
fumecheng-11687	140	44	−	−	PROPN
fumecheng-11687	140	45			PROPN
fumecheng-11687	140	46			NOUN
fumecheng-11687	140	47			NOUN
fumecheng-11687	140	48			X
fumecheng-11687	140	49			X
fumecheng-11687	140	50			X
fumecheng-11687	140	51			NUM
fumecheng-11687	140	52			PROPN
fumecheng-11687	140	53			PROPN
fumecheng-11687	140	54			PROPN
fumecheng-11687	140	55			PROPN
fumecheng-11687	140	56	(	(	PUNCT
fumecheng-11687	140	57	25	25	NUM
fumecheng-11687	140	58	)	)	PUNCT
fumecheng-11687	140	59	(	(	PUNCT
fumecheng-11687	140	60	)	)	SYM
fumecheng-11687	140	61	2	2	NUM
fumecheng-11687	140	62	2	2	NUM
fumecheng-11687	140	63	2	2	NUM
fumecheng-11687	140	64	2	2	NUM
fumecheng-11687	140	65	4	4	NUM
fumecheng-11687	140	66	2	2	NUM
fumecheng-11687	140	67	2	2	NUM
fumecheng-11687	140	68	(	(	PUNCT
fumecheng-11687	140	69	)	)	PUNCT
fumecheng-11687	140	70	(	(	PUNCT
fumecheng-11687	140	71	)	)	PUNCT
fumecheng-11687	140	72	(	(	PUNCT
fumecheng-11687	140	73	)	)	PUNCT
fumecheng-11687	140	74	(	(	PUNCT
fumecheng-11687	140	75	)	)	PUNCT
fumecheng-11687	140	76	2	2	NUM
fumecheng-11687	140	77	(	(	PUNCT
fumecheng-11687	140	78	)	)	PUNCT
fumecheng-11687	140	79	(	(	PUNCT
fumecheng-11687	140	80	)	)	PUNCT
fumecheng-11687	140	81	sin	sin	NOUN
fumecheng-11687	140	82	du	du	PROPN
fumecheng-11687	140	83	df	df	PROPN
fumecheng-11687	140	84	u	u	PROPN
fumecheng-11687	140	85	du	du	PROPN
fumecheng-11687	140	86	b	b	PROPN
fumecheng-11687	140	87	a	a	DET
fumecheng-11687	140	88	f	f	X
fumecheng-11687	140	89	u	u	PROPN
fumecheng-11687	140	90	a	a	DET
fumecheng-11687	140	91	b	b	NOUN
fumecheng-11687	140	92	t	t	NOUN
fumecheng-11687	140	93	dt	dt	X
fumecheng-11687	140	94	dt	dt	X
fumecheng-11687	140	95	dt	dt	VERB
fumecheng-11687	140	96			NOUN
fumecheng-11687	140	97			X
fumecheng-11687	140	98			X
fumecheng-11687	140	99			X
fumecheng-11687	140	100			NUM
fumecheng-11687	140	101			NOUN
fumecheng-11687	140	102			X
fumecheng-11687	140	103			NOUN
fumecheng-11687	140	104			NOUN
fumecheng-11687	141	1	+	+	CCONJ
fumecheng-11687	142	1	−	−	PROPN
fumecheng-11687	142	2	−	−	NUM
fumecheng-11687	142	3			PROPN
fumecheng-11687	143	1	+	+	NUM
fumecheng-11687	143	2	=	=	SYM
fumecheng-11687	143	3	−	−	PROPN
fumecheng-11687	143	4			PROPN
fumecheng-11687	143	5			NUM
fumecheng-11687	143	6			CCONJ
fumecheng-11687	144	1			PROPN
fumecheng-11687	144	2			NOUN
fumecheng-11687	144	3	(	(	PUNCT
fumecheng-11687	144	4	26	26	NUM
fumecheng-11687	144	5	)	)	PUNCT
fumecheng-11687	144	6	removing	remove	VERB
fumecheng-11687	144	7	sin	sin	NOUN
fumecheng-11687	144	8	t	t	NOUN
fumecheng-11687	144	9	between	between	ADP
fumecheng-11687	144	10	eqs	eqs	PROPN
fumecheng-11687	144	11	.	.	PUNCT
fumecheng-11687	145	1	(	(	PUNCT
fumecheng-11687	145	2	25	25	NUM
fumecheng-11687	145	3	)	)	PUNCT
fumecheng-11687	145	4	and	and	CCONJ
fumecheng-11687	145	5	(	(	PUNCT
fumecheng-11687	145	6	26	26	NUM
fumecheng-11687	145	7	)	)	PUNCT
fumecheng-11687	145	8	yields	yield	NOUN
fumecheng-11687	145	9	(	(	PUNCT
fumecheng-11687	145	10	)	)	PUNCT
fumecheng-11687	145	11	(	(	PUNCT
fumecheng-11687	145	12	)	)	SYM
fumecheng-11687	145	13	2	2	NUM
fumecheng-11687	145	14	2	2	NUM
fumecheng-11687	145	15	21	21	NUM
fumecheng-11687	145	16	24	24	NUM
fumecheng-11687	145	17	3	3	NUM
fumecheng-11687	145	18	2	2	NUM
fumecheng-11687	145	19	2	2	NUM
fumecheng-11687	145	20	2	2	NUM
fumecheng-11687	145	21	cos	cos	NOUN
fumecheng-11687	145	22	(	(	PUNCT
fumecheng-11687	145	23	)	)	PUNCT
fumecheng-11687	145	24	(	(	PUNCT
fumecheng-11687	145	25	)	)	PUNCT
fumecheng-11687	145	26	(	(	PUNCT
fumecheng-11687	145	27	)	)	PUNCT
fumecheng-11687	145	28	0	0	PUNCT
fumecheng-11687	145	29	du	du	PROPN
fumecheng-11687	145	30	du	du	PROPN
fumecheng-11687	145	31	df	df	PROPN
fumecheng-11687	145	32	du	du	PROPN
fumecheng-11687	145	33	df	df	PROPN
fumecheng-11687	145	34	s	s	PROPN
fumecheng-11687	145	35	b	b	PROPN
fumecheng-11687	145	36	a	a	DET
fumecheng-11687	145	37	f	f	X
fumecheng-11687	145	38	u	u	NOUN
fumecheng-11687	145	39	dt	dt	NOUN
fumecheng-11687	145	40	dt	dt	X
fumecheng-11687	145	41	dt	dt	X
fumecheng-11687	145	42	dt	dt	X
fumecheng-11687	145	43	dt	dt	X
fumecheng-11687	145	44			X
fumecheng-11687	145	45			X
fumecheng-11687	145	46			X
fumecheng-11687	145	47			X
fumecheng-11687	145	48			X
fumecheng-11687	145	49			NUM
fumecheng-11687	145	50			PROPN
fumecheng-11687	145	51			X
fumecheng-11687	145	52			X
fumecheng-11687	145	53			NOUN
fumecheng-11687	145	54			NOUN
fumecheng-11687	145	55			NOUN
fumecheng-11687	145	56			NOUN
fumecheng-11687	145	57	−	−	PROPN
fumecheng-11687	146	1	+	+	CCONJ
fumecheng-11687	146	2	+	+	PUNCT
fumecheng-11687	146	3	+	+	NUM
fumecheng-11687	146	4			X
fumecheng-11687	147	1	+	+	CCONJ
fumecheng-11687	147	2	+	+	CCONJ
fumecheng-11687	147	3	=	=	PROPN
fumecheng-11687	147	4			PROPN
fumecheng-11687	148	1			PROPN
fumecheng-11687	148	2			PROPN
fumecheng-11687	148	3			PROPN
fumecheng-11687	149	1			ADJ
fumecheng-11687	149	2			PROPN
fumecheng-11687	149	3			PROPN
fumecheng-11687	149	4			NOUN
fumecheng-11687	149	5	(	(	PUNCT
fumecheng-11687	149	6	27	27	NUM
fumecheng-11687	149	7	)	)	PUNCT
fumecheng-11687	149	8	this	this	PRON
fumecheng-11687	149	9	is	be	AUX
fumecheng-11687	149	10	the	the	DET
fumecheng-11687	149	11	alternative	alternative	ADJ
fumecheng-11687	149	12	form	form	NOUN
fumecheng-11687	149	13	of	of	ADP
fumecheng-11687	149	14	the	the	DET
fumecheng-11687	149	15	forced	force	VERB
fumecheng-11687	149	16	fractal	fractal	NOUN
fumecheng-11687	149	17	eq	eq	PROPN
fumecheng-11687	149	18	.	.	PUNCT
fumecheng-11687	150	1	(	(	PUNCT
fumecheng-11687	150	2	18	18	NUM
fumecheng-11687	150	3	)	)	PUNCT
fumecheng-11687	150	4	in	in	ADP
fumecheng-11687	150	5	the	the	DET
fumecheng-11687	150	6	form	form	NOUN
fumecheng-11687	150	7	of	of	ADP
fumecheng-11687	150	8	a	a	DET
fumecheng-11687	150	9	fractal	fractal	ADJ
fumecheng-11687	150	10	fourthorder	fourthorder	NOUN
fumecheng-11687	150	11	equation	equation	NOUN
fumecheng-11687	150	12	.	.	PUNCT
fumecheng-11687	151	1	this	this	DET
fumecheng-11687	151	2	equation	equation	NOUN
fumecheng-11687	151	3	is	be	AUX
fumecheng-11687	151	4	subject	subject	ADJ
fumecheng-11687	151	5	to	to	ADP
fumecheng-11687	151	6	the	the	DET
fumecheng-11687	151	7	following	follow	VERB
fumecheng-11687	151	8	initial	initial	ADJ
fumecheng-11687	151	9	conditions	condition	NOUN
fumecheng-11687	151	10	:	:	PUNCT
fumecheng-11687	151	11	1	1	NUM
fumecheng-11687	151	12	22	22	NUM
fumecheng-11687	151	13	3	3	NUM
fumecheng-11687	151	14	(	(	PUNCT
fumecheng-11687	151	15	0	0	NUM
fumecheng-11687	151	16	)	)	PUNCT
fumecheng-11687	151	17	(	(	PUNCT
fumecheng-11687	151	18	0	0	NUM
fumecheng-11687	151	19	)	)	PUNCT
fumecheng-11687	151	20	(	(	PUNCT
fumecheng-11687	151	21	0	0	NUM
fumecheng-11687	151	22	)	)	PUNCT
fumecheng-11687	151	23	(	(	PUNCT
fumecheng-11687	151	24	0	0	NUM
fumecheng-11687	151	25	)	)	PUNCT
fumecheng-11687	151	26	,	,	PUNCT
fumecheng-11687	151	27	0	0	NUM
fumecheng-11687	151	28	,	,	PUNCT
fumecheng-11687	151	29	(	(	PUNCT
fumecheng-11687	151	30	)	)	PUNCT
fumecheng-11687	151	31	,	,	PUNCT
fumecheng-11687	151	32	cos	cos	PROPN
fumecheng-11687	151	33	(	(	PUNCT
fumecheng-11687	151	34	)	)	PUNCT
fumecheng-11687	151	35	du	du	PROPN
fumecheng-11687	151	36	du	du	PROPN
fumecheng-11687	151	37	du	du	PROPN
fumecheng-11687	151	38	u	u	PROPN
fumecheng-11687	151	39	a	a	PROPN
fumecheng-11687	151	40	f	f	PROPN
fumecheng-11687	151	41	a	a	DET
fumecheng-11687	151	42	s	s	NOUN
fumecheng-11687	151	43	dt	dt	NOUN
fumecheng-11687	151	44	dt	dt	NOUN
fumecheng-11687	151	45	dt	dt	X
fumecheng-11687	152	1	=	=	PUNCT
fumecheng-11687	152	2	=	=	PUNCT
fumecheng-11687	152	3	=	=	PUNCT
fumecheng-11687	152	4	−	−	PROPN
fumecheng-11687	152	5	=	=	SYM
fumecheng-11687	152	6	−	−	NOUN
fumecheng-11687	152	7			X
fumecheng-11687	152	8			X
fumecheng-11687	152	9			X
fumecheng-11687	152	10			X
fumecheng-11687	152	11			X
fumecheng-11687	152	12			X
fumecheng-11687	152	13			X
fumecheng-11687	152	14			X
fumecheng-11687	152	15			X
fumecheng-11687	152	16			PROPN
fumecheng-11687	152	17			PROPN
fumecheng-11687	152	18			PROPN
fumecheng-11687	152	19	(	(	PUNCT
fumecheng-11687	152	20	28	28	NUM
fumecheng-11687	152	21	)	)	PUNCT
fumecheng-11687	152	22	the	the	DET
fumecheng-11687	152	23	up	up	ADV
fumecheng-11687	152	24	-	-	PUNCT
fumecheng-11687	152	25	grating	grate	VERB
fumecheng-11687	152	26	rank	rank	NOUN
fumecheng-11687	152	27	approach	approach	NOUN
fumecheng-11687	152	28	to	to	PART
fumecheng-11687	152	29	solve	solve	VERB
fumecheng-11687	152	30	a	a	DET
fumecheng-11687	152	31	forced	force	VERB
fumecheng-11687	152	32	fractal	fractal	ADJ
fumecheng-11687	152	33	duffing	duffing	NOUN
fumecheng-11687	152	34	oscillator	oscillator	NOUN
fumecheng-11687	152	35	by	by	ADP
fumecheng-11687	152	36	the	the	DET
fumecheng-11687	152	37	np	np	PROPN
fumecheng-11687	152	38	technique	technique	NOUN
fumecheng-11687	152	39	205	205	NUM
fumecheng-11687	152	40	to	to	PART
fumecheng-11687	152	41	convert	convert	VERB
fumecheng-11687	152	42	eq	eq	ADP
fumecheng-11687	152	43	.	.	PUNCT
fumecheng-11687	153	1	(	(	PUNCT
fumecheng-11687	153	2	27	27	NUM
fumecheng-11687	153	3	)	)	PUNCT
fumecheng-11687	153	4	and	and	CCONJ
fumecheng-11687	153	5	its	its	PRON
fumecheng-11687	153	6	corresponding	corresponding	ADJ
fumecheng-11687	153	7	initial	initial	ADJ
fumecheng-11687	153	8	conditions	condition	NOUN
fumecheng-11687	153	9	given	give	VERB
fumecheng-11687	153	10	in	in	ADP
fumecheng-11687	153	11	eq	eq	ADP
fumecheng-11687	153	12	.	.	PUNCT
fumecheng-11687	154	1	(	(	PUNCT
fumecheng-11687	154	2	28	28	NUM
fumecheng-11687	154	3	)	)	PUNCT
fumecheng-11687	154	4	into	into	ADP
fumecheng-11687	154	5	continuous	continuous	ADJ
fumecheng-11687	154	6	space	space	NOUN
fumecheng-11687	154	7	,	,	PUNCT
fumecheng-11687	154	8	the	the	DET
fumecheng-11687	154	9	transformation	transformation	NOUN
fumecheng-11687	154	10	given	give	VERB
fumecheng-11687	154	11	in	in	ADP
fumecheng-11687	154	12	eq	eq	ADP
fumecheng-11687	154	13	.	.	PUNCT
fumecheng-11687	155	1	(	(	PUNCT
fumecheng-11687	155	2	21	21	NUM
fumecheng-11687	155	3	)	)	PUNCT
fumecheng-11687	155	4	may	may	AUX
fumecheng-11687	155	5	be	be	AUX
fumecheng-11687	155	6	used	use	VERB
fumecheng-11687	155	7	.	.	PUNCT
fumecheng-11687	156	1	therefore	therefore	ADV
fumecheng-11687	156	2	,	,	PUNCT
fumecheng-11687	156	3	with	with	ADP
fumecheng-11687	156	4	some	some	DET
fumecheng-11687	156	5	simplifications	simplification	NOUN
fumecheng-11687	156	6	,	,	PUNCT
fumecheng-11687	156	7	one	one	PRON
fumecheng-11687	156	8	gets	get	VERB
fumecheng-11687	156	9	4	4	NUM
fumecheng-11687	156	10	3	3	NUM
fumecheng-11687	156	11	2	2	NUM
fumecheng-11687	156	12	2	2	NUM
fumecheng-11687	156	13	2	2	NUM
fumecheng-11687	156	14	2	2	NUM
fumecheng-11687	156	15	2	2	NUM
fumecheng-11687	156	16	2	2	NUM
fumecheng-11687	156	17	1	1	NUM
fumecheng-11687	156	18	(	(	PUNCT
fumecheng-11687	156	19	)	)	PUNCT
fumecheng-11687	156	20	2	2	NUM
fumecheng-11687	156	21	(	(	PUNCT
fumecheng-11687	156	22	)	)	PUNCT
fumecheng-11687	156	23	(	(	PUNCT
fumecheng-11687	156	24	)	)	PUNCT
fumecheng-11687	156	25	(	(	PUNCT
fumecheng-11687	156	26	)	)	PUNCT
fumecheng-11687	156	27	(	(	PUNCT
fumecheng-11687	156	28	)	)	PUNCT
fumecheng-11687	156	29	(	(	PUNCT
fumecheng-11687	156	30	)	)	PUNCT
fumecheng-11687	156	31	0a	0a	PROPN
fumecheng-11687	156	32	d	d	X
fumecheng-11687	156	33	u	u	PROPN
fumecheng-11687	156	34	a	a	PRON
fumecheng-11687	156	35	a	a	PROPN
fumecheng-11687	156	36	d	d	X
fumecheng-11687	156	37	u	u	PROPN
fumecheng-11687	156	38	b	b	PROPN
fumecheng-11687	156	39	a	a	DET
fumecheng-11687	156	40	a	a	PROPN
fumecheng-11687	156	41	d	d	X
fumecheng-11687	156	42	u	u	X
fumecheng-11687	156	43	d	d	X
fumecheng-11687	156	44	f	f	PROPN
fumecheng-11687	156	45	u	u	X
fumecheng-11687	156	46	b	b	PROPN
fumecheng-11687	156	47	+	+	CCONJ
fumecheng-11687	156	48	−	−	PROPN
fumecheng-11687	157	1	+	+	CCONJ
fumecheng-11687	157	2	+	+	CCONJ
fumecheng-11687	157	3	+	+	NUM
fumecheng-11687	157	4			X
fumecheng-11687	158	1	+	+	CCONJ
fumecheng-11687	158	2	+	+	NUM
fumecheng-11687	158	3			PROPN
fumecheng-11687	159	1	+	+	CCONJ
fumecheng-11687	159	2	=	=	SYM
fumecheng-11687	159	3	(	(	PUNCT
fumecheng-11687	159	4	29	29	NUM
fumecheng-11687	159	5	)	)	PUNCT
fumecheng-11687	159	6	the	the	DET
fumecheng-11687	159	7	operator	operator	NOUN
fumecheng-11687	159	8	d	d	NOUN
fumecheng-11687	159	9	represents	represent	VERB
fumecheng-11687	159	10	the	the	DET
fumecheng-11687	159	11	derivative	derivative	NOUN
fumecheng-11687	159	12	corresponding	corresponding	NOUN
fumecheng-11687	159	13	to	to	ADP
fumecheng-11687	159	14	the	the	DET
fumecheng-11687	159	15	variable	variable	NOUN
fumecheng-11687	159	16	t.	t.	PROPN
fumecheng-11687	159	17	thus	thus	ADV
fumecheng-11687	159	18	,	,	PUNCT
fumecheng-11687	159	19	eq	eq	ADJ
fumecheng-11687	159	20	.	.	PUNCT
fumecheng-11687	160	1	(	(	PUNCT
fumecheng-11687	160	2	29	29	NUM
fumecheng-11687	160	3	)	)	PUNCT
fumecheng-11687	160	4	is	be	AUX
fumecheng-11687	160	5	a	a	DET
fumecheng-11687	160	6	nonlinear	nonlinear	ADJ
fumecheng-11687	160	7	fourth	fourth	ADJ
fumecheng-11687	160	8	-	-	PUNCT
fumecheng-11687	160	9	order	order	NOUN
fumecheng-11687	160	10	equation	equation	NOUN
fumecheng-11687	160	11	free	free	ADJ
fumecheng-11687	160	12	of	of	ADP
fumecheng-11687	160	13	the	the	DET
fumecheng-11687	160	14	variable	variable	ADJ
fumecheng-11687	160	15	coefficients	coefficient	NOUN
fumecheng-11687	160	16	(	(	PUNCT
fumecheng-11687	160	17	4	4	NUM
fumecheng-11687	160	18	)	)	PUNCT
fumecheng-11687	160	19	(	(	PUNCT
fumecheng-11687	160	20	3	3	X
fumecheng-11687	160	21	)	)	SYM
fumecheng-11687	160	22	2	2	NUM
fumecheng-11687	160	23	2	2	NUM
fumecheng-11687	160	24	2	2	NUM
fumecheng-11687	160	25	2	2	NUM
fumecheng-11687	160	26	2	2	NUM
fumecheng-11687	160	27	2	2	NUM
fumecheng-11687	160	28	3	3	NUM
fumecheng-11687	160	29	2	2	NUM
fumecheng-11687	160	30	2	2	NUM
fumecheng-11687	160	31	2	2	NUM
fumecheng-11687	160	32	4	4	NUM
fumecheng-11687	160	33	2	2	NUM
fumecheng-11687	160	34	2	2	NUM
fumecheng-11687	160	35	3	3	NUM
fumecheng-11687	160	36	2	2	NUM
fumecheng-11687	160	37	2	2	NUM
fumecheng-11687	160	38	2	2	NUM
fumecheng-11687	160	39	2	2	NUM
fumecheng-11687	160	40	02	02	NUM
fumecheng-11687	160	41	2	2	NUM
fumecheng-11687	160	42	(	(	PUNCT
fumecheng-11687	160	43	)	)	PUNCT
fumecheng-11687	160	44	2	2	NUM
fumecheng-11687	160	45	(	(	PUNCT
fumecheng-11687	160	46	(	(	PUNCT
fumecheng-11687	160	47	)	)	PUNCT
fumecheng-11687	160	48	)	)	PUNCT
fumecheng-11687	161	1	(	(	PUNCT
fumecheng-11687	161	2	6	6	NUM
fumecheng-11687	161	3	3	3	NUM
fumecheng-11687	161	4	)	)	PUNCT
fumecheng-11687	161	5	1	1	NUM
fumecheng-11687	161	6	(	(	PUNCT
fumecheng-11687	161	7	(	(	PUNCT
fumecheng-11687	161	8	)	)	PUNCT
fumecheng-11687	161	9	)	)	PUNCT
fumecheng-11687	161	10	0	0	NUM
fumecheng-11687	162	1	q	q	PUNCT
fumecheng-11687	162	2	u	u	PROPN
fumecheng-11687	162	3	au	au	PROPN
fumecheng-11687	162	4	b	b	PROPN
fumecheng-11687	162	5	a	a	DET
fumecheng-11687	162	6	u	u	NOUN
fumecheng-11687	162	7	a	a	DET
fumecheng-11687	162	8	b	b	NOUN
fumecheng-11687	162	9	a	a	DET
fumecheng-11687	162	10	a	a	DET
fumecheng-11687	162	11	u	u	NOUN
fumecheng-11687	162	12	u	u	X
fumecheng-11687	162	13	u	u	NOUN
fumecheng-11687	162	14	u	u	NOUN
fumecheng-11687	162	15	u	u	NOUN
fumecheng-11687	162	16	u	u	NOUN
fumecheng-11687	162	17	b	b	PROPN
fumecheng-11687	162	18	a	a	DET
fumecheng-11687	162	19	b	b	NOUN
fumecheng-11687	162	20	a	a	DET
fumecheng-11687	162	21	b	b	NOUN
fumecheng-11687	162	22	a	a	DET
fumecheng-11687	162	23	u	u	NOUN
fumecheng-11687	162	24	b	b	PROPN
fumecheng-11687	162	25	+	+	CCONJ
fumecheng-11687	162	26	+	+	CCONJ
fumecheng-11687	162	27	+	+	NUM
fumecheng-11687	162	28			X
fumecheng-11687	162	29	+	+	CCONJ
fumecheng-11687	162	30	+	+	NUM
fumecheng-11687	162	31			PROPN
fumecheng-11687	162	32	−	−	NOUN
fumecheng-11687	162	33	+	+	NUM
fumecheng-11687	162	34			PROPN
fumecheng-11687	163	1	+	+	X
fumecheng-11687	163	2	+	+	PUNCT
fumecheng-11687	164	1	+	+	CCONJ
fumecheng-11687	164	2	−	−	X
fumecheng-11687	164	3	+	+	CCONJ
fumecheng-11687	165	1	+	+	NUM
fumecheng-11687	165	2			NUM
fumecheng-11687	165	3	+	+	CCONJ
fumecheng-11687	165	4			PROPN
fumecheng-11687	165	5	=	=	PRON
fumecheng-11687	165	6			X
fumecheng-11687	165	7	(	(	PUNCT
fumecheng-11687	165	8	30	30	NUM
fumecheng-11687	165	9	)	)	PUNCT
fumecheng-11687	165	10	this	this	PRON
fumecheng-11687	165	11	is	be	AUX
fumecheng-11687	165	12	the	the	DET
fumecheng-11687	165	13	alternative	alternative	ADJ
fumecheng-11687	165	14	form	form	NOUN
fumecheng-11687	165	15	of	of	ADP
fumecheng-11687	165	16	the	the	DET
fumecheng-11687	165	17	forced	force	VERB
fumecheng-11687	165	18	fractal	fractal	ADJ
fumecheng-11687	165	19	duffing	duffing	NOUN
fumecheng-11687	165	20	eq	eq	ADP
fumecheng-11687	165	21	.	.	PUNCT
fumecheng-11687	166	1	(	(	PUNCT
fumecheng-11687	166	2	13	13	NUM
fumecheng-11687	166	3	)	)	PUNCT
fumecheng-11687	166	4	in	in	ADP
fumecheng-11687	166	5	continuous	continuous	ADJ
fumecheng-11687	166	6	space	space	NOUN
fumecheng-11687	166	7	.	.	PUNCT
fumecheng-11687	167	1	also	also	ADV
fumecheng-11687	167	2	,	,	PUNCT
fumecheng-11687	167	3	the	the	DET
fumecheng-11687	167	4	alternative	alternative	ADJ
fumecheng-11687	167	5	initial	initial	ADJ
fumecheng-11687	167	6	conditions	condition	NOUN
fumecheng-11687	167	7	in	in	ADP
fumecheng-11687	167	8	the	the	DET
fumecheng-11687	167	9	continuous	continuous	ADJ
fumecheng-11687	167	10	space	space	NOUN
fumecheng-11687	167	11	are	be	AUX
fumecheng-11687	167	12	performed	perform	VERB
fumecheng-11687	167	13	in	in	ADP
fumecheng-11687	167	14	the	the	DET
fumecheng-11687	167	15	form	form	NOUN
fumecheng-11687	167	16	(	(	PUNCT
fumecheng-11687	167	17	)	)	PUNCT
fumecheng-11687	167	18	(	(	PUNCT
fumecheng-11687	167	19	)	)	PUNCT
fumecheng-11687	167	20	2	2	NUM
fumecheng-11687	167	21	2	2	NUM
fumecheng-11687	167	22	3	3	NUM
fumecheng-11687	167	23	2	2	NUM
fumecheng-11687	167	24	1	1	NUM
fumecheng-11687	167	25	(	(	PUNCT
fumecheng-11687	167	26	0	0	NUM
fumecheng-11687	167	27	)	)	PUNCT
fumecheng-11687	167	28	,	,	PUNCT
fumecheng-11687	167	29	(	(	PUNCT
fumecheng-11687	167	30	0	0	NUM
fumecheng-11687	167	31	)	)	PUNCT
fumecheng-11687	167	32	(	(	PUNCT
fumecheng-11687	167	33	)	)	PUNCT
fumecheng-11687	167	34	,	,	PUNCT
fumecheng-11687	167	35	(	(	PUNCT
fumecheng-11687	167	36	0	0	NUM
fumecheng-11687	167	37	)	)	PUNCT
fumecheng-11687	167	38	(	(	PUNCT
fumecheng-11687	167	39	(	(	PUNCT
fumecheng-11687	167	40	)	)	PUNCT
fumecheng-11687	167	41	)	)	PUNCT
fumecheng-11687	167	42	(	(	PUNCT
fumecheng-11687	167	43	)	)	PUNCT
fumecheng-11687	167	44	,	,	PUNCT
fumecheng-11687	167	45	(	(	PUNCT
fumecheng-11687	167	46	)	)	PUNCT
fumecheng-11687	167	47	(	(	PUNCT
fumecheng-11687	167	48	)	)	PUNCT
fumecheng-11687	167	49	0	0	NUM
fumecheng-11687	168	1	(	(	PUNCT
fumecheng-11687	168	2	)	)	PUNCT
fumecheng-11687	168	3	4	4	NUM
fumecheng-11687	168	4	3	3	NUM
fumecheng-11687	168	5	(	(	PUNCT
fumecheng-11687	168	6	)	)	PUNCT
fumecheng-11687	168	7	(	(	PUNCT
fumecheng-11687	168	8	)	)	PUNCT
fumecheng-11687	168	9	u	u	NOUN
fumecheng-11687	168	10	a	a	DET
fumecheng-11687	168	11	u	u	X
fumecheng-11687	168	12	aa	aa	NOUN
fumecheng-11687	168	13	u	u	NOUN
fumecheng-11687	168	14	f	f	PROPN
fumecheng-11687	168	15	a	a	PRON
fumecheng-11687	168	16	a	a	DET
fumecheng-11687	168	17	a	a	DET
fumecheng-11687	168	18	b	b	NOUN
fumecheng-11687	168	19	a	a	DET
fumecheng-11687	168	20	u	u	NOUN
fumecheng-11687	168	21	a	a	PRON
fumecheng-11687	168	22	a	a	DET
fumecheng-11687	168	23	f	f	NOUN
fumecheng-11687	168	24	a	a	DET
fumecheng-11687	168	25	b	b	NOUN
fumecheng-11687	168	26			PROPN
fumecheng-11687	168	27	=	=	PUNCT
fumecheng-11687	168	28	=	=	PUNCT
fumecheng-11687	169	1	−	−	PROPN
fumecheng-11687	169	2	=	=	PUNCT
fumecheng-11687	170	1	−	−	PROPN
fumecheng-11687	171	1	+	+	NUM
fumecheng-11687	171	2			NUM
fumecheng-11687	171	3			NUM
fumecheng-11687	171	4			NOUN
fumecheng-11687	171	5	=	=	PROPN
fumecheng-11687	171	6	−	−	PROPN
fumecheng-11687	171	7	−	−	NOUN
fumecheng-11687	171	8	−	−	PROPN
fumecheng-11687	171	9			NUM
fumecheng-11687	171	10			NOUN
fumecheng-11687	171	11			NUM
fumecheng-11687	171	12			NOUN
fumecheng-11687	171	13			X
fumecheng-11687	171	14			X
fumecheng-11687	171	15			X
fumecheng-11687	171	16			NUM
fumecheng-11687	171	17			NOUN
fumecheng-11687	171	18	(	(	PUNCT
fumecheng-11687	171	19	31	31	NUM
fumecheng-11687	171	20	)	)	PUNCT
fumecheng-11687	171	21	it	it	PRON
fumecheng-11687	171	22	is	be	AUX
fumecheng-11687	171	23	noteworthy	noteworthy	ADJ
fumecheng-11687	171	24	,	,	PUNCT
fumecheng-11687	171	25	if	if	SCONJ
fumecheng-11687	171	26	the	the	DET
fumecheng-11687	171	27	initial	initial	ADJ
fumecheng-11687	171	28	velocity	velocity	NOUN
fumecheng-11687	171	29	is	be	AUX
fumecheng-11687	171	30	not	not	PART
fumecheng-11687	171	31	zero	zero	NUM
fumecheng-11687	171	32	such	such	ADJ
fumecheng-11687	171	33	that	that	SCONJ
fumecheng-11687	171	34	u(0	u(0	NOUN
fumecheng-11687	171	35	)	)	PUNCT
fumecheng-11687	172	1	=	=	NOUN
fumecheng-11687	172	2	a	a	PRON
fumecheng-11687	172	3	and	and	CCONJ
fumecheng-11687	172	4	𝑑𝑢(0	𝑑𝑢(0	NOUN
fumecheng-11687	172	5	)	)	PUNCT
fumecheng-11687	172	6	𝑑𝑡𝛼	𝑑𝑡𝛼	NOUN
fumecheng-11687	172	7	=	=	SYM
fumecheng-11687	172	8	𝐵	𝐵	PROPN
fumecheng-11687	172	9	,	,	PUNCT
fumecheng-11687	172	10	the	the	DET
fumecheng-11687	172	11	present	present	ADJ
fumecheng-11687	172	12	approach	approach	NOUN
fumecheng-11687	172	13	has	have	VERB
fumecheng-11687	172	14	a	a	DET
fumecheng-11687	172	15	good	good	ADJ
fumecheng-11687	172	16	applicable	applicable	ADJ
fumecheng-11687	172	17	so	so	SCONJ
fumecheng-11687	172	18	the	the	DET
fumecheng-11687	172	19	application	application	NOUN
fumecheng-11687	172	20	of	of	ADP
fumecheng-11687	172	21	the	the	DET
fumecheng-11687	172	22	formula	formula	NOUN
fumecheng-11687	172	23	given	give	VERB
fumecheng-11687	172	24	in	in	ADP
fumecheng-11687	172	25	eq	eq	ADP
fumecheng-11687	172	26	.	.	PUNCT
fumecheng-11687	173	1	(	(	PUNCT
fumecheng-11687	173	2	9	9	NUM
fumecheng-11687	173	3	)	)	PUNCT
fumecheng-11687	173	4	to	to	ADP
fumecheng-11687	173	5	the	the	DET
fumecheng-11687	173	6	fractal	fractal	ADJ
fumecheng-11687	173	7	initial	initial	ADJ
fumecheng-11687	173	8	condition	condition	NOUN
fumecheng-11687	173	9	has	have	VERB
fumecheng-11687	173	10	the	the	DET
fumecheng-11687	173	11	form	form	NOUN
fumecheng-11687	173	12	11	11	NUM
fumecheng-11687	173	13	1	1	NUM
fumecheng-11687	173	14	2	2	NUM
fumecheng-11687	173	15	2	2	NUM
fumecheng-11687	173	16	(	(	PUNCT
fumecheng-11687	173	17	0	0	NUM
fumecheng-11687	173	18	)	)	PUNCT
fumecheng-11687	173	19	cos	cos	PROPN
fumecheng-11687	173	20	(	(	PUNCT
fumecheng-11687	173	21	)	)	PUNCT
fumecheng-11687	173	22	(	(	PUNCT
fumecheng-11687	173	23	0	0	X
fumecheng-11687	173	24	)	)	PUNCT
fumecheng-11687	173	25	sin	sin	NOUN
fumecheng-11687	173	26	(	(	PUNCT
fumecheng-11687	173	27	)	)	PUNCT
fumecheng-11687	173	28	(	(	PUNCT
fumecheng-11687	173	29	0	0	X
fumecheng-11687	173	30	)	)	PUNCT
fumecheng-11687	173	31	du	du	PROPN
fumecheng-11687	173	32	s	s	PART
fumecheng-11687	173	33	u	u	NOUN
fumecheng-11687	173	34	s	s	NOUN
fumecheng-11687	173	35	u	u	X
fumecheng-11687	173	36	dt	dt	X
fumecheng-11687	173	37	−=	−=	X
fumecheng-11687	173	38	+	+	ADP
fumecheng-11687	173	39			NOUN
fumecheng-11687	173	40			X
fumecheng-11687	173	41			NUM
fumecheng-11687	173	42			PROPN
fumecheng-11687	173	43			PROPN
fumecheng-11687	173	44	(	(	PUNCT
fumecheng-11687	173	45	32	32	NUM
fumecheng-11687	173	46	)	)	PUNCT
fumecheng-11687	173	47	employing	employ	VERB
fumecheng-11687	173	48	the	the	DET
fumecheng-11687	173	49	non	non	ADJ
fumecheng-11687	173	50	-	-	ADJ
fumecheng-11687	173	51	zero	zero	ADJ
fumecheng-11687	173	52	initial	initial	ADJ
fumecheng-11687	173	53	conditions	condition	NOUN
fumecheng-11687	173	54	yields	yield	NOUN
fumecheng-11687	173	55	that	that	PRON
fumecheng-11687	173	56	�	�	VERB
fumecheng-11687	173	57	̇	̇	PROPN
fumecheng-11687	173	58	�	�	AUX
fumecheng-11687	173	59	(0	(0	X
fumecheng-11687	173	60	)	)	PUNCT
fumecheng-11687	174	1	=	=	SYM
fumecheng-11687	174	2	𝐵	𝐵	NOUN
fumecheng-11687	174	3	𝑆𝛼−1𝑠𝑖𝑛	𝑆𝛼−1𝑠𝑖𝑛	PROPN
fumecheng-11687	174	4	(	(	PUNCT
fumecheng-11687	174	5	𝝅𝛂	𝝅𝛂	NOUN
fumecheng-11687	174	6	2	2	NUM
fumecheng-11687	174	7	)	)	PUNCT
fumecheng-11687	174	8	−	−	PROPN
fumecheng-11687	174	9	𝐴	𝐴	PROPN
fumecheng-11687	174	10	𝑆	𝑆	PROPN
fumecheng-11687	174	11	𝑐𝑜𝑡	𝑐𝑜𝑡	INTJ
fumecheng-11687	174	12	(	(	PUNCT
fumecheng-11687	174	13	𝝅𝛂	𝝅𝛂	NOUN
fumecheng-11687	174	14	2	2	NUM
fumecheng-11687	174	15	)	)	PUNCT
fumecheng-11687	174	16	and	and	CCONJ
fumecheng-11687	174	17	u(0)=a	u(0)=a	ADJ
fumecheng-11687	174	18	.	.	PUNCT
fumecheng-11687	175	1	therefore	therefore	ADV
fumecheng-11687	175	2	,	,	PUNCT
fumecheng-11687	175	3	as	as	ADP
fumecheng-11687	175	4	𝐵	𝐵	NOUN
fumecheng-11687	175	5	→	→	SYM
fumecheng-11687	175	6	0	0	NUM
fumecheng-11687	175	7	the	the	DET
fumecheng-11687	175	8	converted	converted	ADJ
fumecheng-11687	175	9	initial	initial	ADJ
fumecheng-11687	175	10	conditions	condition	NOUN
fumecheng-11687	175	11	given	give	VERB
fumecheng-11687	175	12	in	in	ADP
fumecheng-11687	175	13	eq	eq	ADP
fumecheng-11687	175	14	.	.	PUNCT
fumecheng-11687	176	1	(	(	PUNCT
fumecheng-11687	176	2	31	31	NUM
fumecheng-11687	176	3	)	)	PUNCT
fumecheng-11687	176	4	will	will	AUX
fumecheng-11687	176	5	arises	arise	VERB
fumecheng-11687	176	6	.	.	PUNCT
fumecheng-11687	177	1	in	in	ADP
fumecheng-11687	177	2	the	the	DET
fumecheng-11687	177	3	transformation	transformation	NOUN
fumecheng-11687	177	4	given	give	VERB
fumecheng-11687	177	5	in	in	ADP
fumecheng-11687	177	6	eq	eq	ADP
fumecheng-11687	177	7	.	.	PUNCT
fumecheng-11687	178	1	(	(	PUNCT
fumecheng-11687	178	2	21	21	NUM
fumecheng-11687	178	3	)	)	PUNCT
fumecheng-11687	178	4	,	,	PUNCT
fumecheng-11687	178	5	the	the	DET
fumecheng-11687	178	6	fractal	fractal	ADJ
fumecheng-11687	178	7	parameter	parameter	NOUN
fumecheng-11687	178	8	s	s	PART
fumecheng-11687	178	9	could	could	AUX
fumecheng-11687	178	10	be	be	AUX
fumecheng-11687	178	11	estimated	estimate	VERB
fumecheng-11687	178	12	by	by	ADP
fumecheng-11687	178	13	comparing	compare	VERB
fumecheng-11687	178	14	between	between	ADP
fumecheng-11687	178	15	the	the	DET
fumecheng-11687	178	16	linear	linear	ADJ
fumecheng-11687	178	17	frequency	frequency	NOUN
fumecheng-11687	178	18	given	give	VERB
fumecheng-11687	178	19	in	in	ADP
fumecheng-11687	178	20	eq	eq	ADP
fumecheng-11687	178	21	.	.	PUNCT
fumecheng-11687	179	1	(	(	PUNCT
fumecheng-11687	179	2	30	30	NUM
fumecheng-11687	179	3	)	)	PUNCT
fumecheng-11687	179	4	with	with	ADP
fumecheng-11687	179	5	the	the	DET
fumecheng-11687	179	6	linear	linear	ADJ
fumecheng-11687	179	7	one	one	NUM
fumecheng-11687	179	8	of	of	ADP
fumecheng-11687	179	9	the	the	DET
fumecheng-11687	179	10	fractal	fractal	NOUN
fumecheng-11687	179	11	eq	eq	PROPN
fumecheng-11687	179	12	.	.	PUNCT
fumecheng-11687	180	1	(	(	PUNCT
fumecheng-11687	180	2	27	27	NUM
fumecheng-11687	180	3	)	)	PUNCT
fumecheng-11687	180	4	.	.	PUNCT
fumecheng-11687	181	1	this	this	DET
fumecheng-11687	181	2	comparison	comparison	NOUN
fumecheng-11687	181	3	shows	show	VERB
fumecheng-11687	181	4	that	that	SCONJ
fumecheng-11687	181	5	3	3	NUM
fumecheng-11687	181	6	2	2	NUM
fumecheng-11687	181	7	2	2	NUM
fumecheng-11687	181	8	2	2	NUM
fumecheng-11687	181	9	2	2	NUM
fumecheng-11687	181	10	4	4	NUM
fumecheng-11687	181	11	4	4	NUM
fumecheng-11687	181	12	20	20	NUM
fumecheng-11687	181	13	0	0	NUM
fumecheng-11687	181	14	2	2	NUM
fumecheng-11687	181	15	2	2	NUM
fumecheng-11687	181	16	(	(	PUNCT
fumecheng-11687	181	17	)	)	PUNCT
fumecheng-11687	181	18	(	(	PUNCT
fumecheng-11687	181	19	1	1	X
fumecheng-11687	181	20	)	)	PUNCT
fumecheng-11687	181	21	0	0	NUM
fumecheng-11687	181	22	(	(	PUNCT
fumecheng-11687	181	23	1	1	NUM
fumecheng-11687	181	24	)	)	PUNCT
fumecheng-11687	181	25	(	(	PUNCT
fumecheng-11687	181	26	1	1	X
fumecheng-11687	181	27	)	)	PUNCT
fumecheng-11687	181	28	b	b	PROPN
fumecheng-11687	181	29	b	b	X
fumecheng-11687	181	30	b	b	PROPN
fumecheng-11687	181	31	a	a	DET
fumecheng-11687	181	32	a	a	DET
fumecheng-11687	181	33	b	b	PROPN
fumecheng-11687	181	34	b	b	PROPN
fumecheng-11687	181	35	b	b	PROPN
fumecheng-11687	181	36	b	b	PROPN
fumecheng-11687	181	37			PROPN
fumecheng-11687	182	1	−	−	PROPN
fumecheng-11687	182	2			PROPN
fumecheng-11687	182	3	−	−	PROPN
fumecheng-11687	183	1	+	+	CCONJ
fumecheng-11687	183	2	+	+	NUM
fumecheng-11687	183	3	=	=	SYM
fumecheng-11687	183	4	−	−	NOUN
fumecheng-11687	183	5	−	−	NOUN
fumecheng-11687	183	6			X
fumecheng-11687	183	7			X
fumecheng-11687	183	8	(	(	PUNCT
fumecheng-11687	183	9	33	33	NUM
fumecheng-11687	183	10	)	)	PUNCT
fumecheng-11687	183	11	here	here	ADV
fumecheng-11687	183	12	,	,	PUNCT
fumecheng-11687	183	13	b(	b(	PROPN
fumecheng-11687	183	14	)	)	PUNCT
fumecheng-11687	183	15	≠	≠	PROPN
fumecheng-11687	183	16	1	1	NUM
fumecheng-11687	183	17	is	be	AUX
fumecheng-11687	183	18	considered	consider	VERB
fumecheng-11687	183	19	,	,	PUNCT
fumecheng-11687	183	20	unless	unless	SCONJ
fumecheng-11687	183	21			NOUN
fumecheng-11687	183	22	=	=	SYM
fumecheng-11687	183	23	1	1	X
fumecheng-11687	183	24	.	.	X
fumecheng-11687	183	25	employing	employ	VERB
fumecheng-11687	183	26	the	the	DET
fumecheng-11687	183	27	definition	definition	NOUN
fumecheng-11687	183	28	of	of	ADP
fumecheng-11687	183	29	a(	a(	PROPN
fumecheng-11687	183	30	)	)	PUNCT
fumecheng-11687	183	31	given	give	VERB
fumecheng-11687	183	32	in	in	ADP
fumecheng-11687	183	33	eq	eq	ADP
fumecheng-11687	183	34	.	.	PUNCT
fumecheng-11687	184	1	(	(	PUNCT
fumecheng-11687	184	2	24	24	NUM
fumecheng-11687	184	3	)	)	PUNCT
fumecheng-11687	184	4	in	in	ADP
fumecheng-11687	184	5	the	the	DET
fumecheng-11687	184	6	above	above	ADJ
fumecheng-11687	184	7	equation	equation	NOUN
fumecheng-11687	184	8	yields	yield	VERB
fumecheng-11687	184	9	2	2	NUM
fumecheng-11687	184	10	1	1	NUM
fumecheng-11687	184	11	2	2	NUM
fumecheng-11687	184	12	2	2	NUM
fumecheng-11687	184	13	2	2	NUM
fumecheng-11687	184	14	2	2	NUM
fumecheng-11687	184	15	4	4	NUM
fumecheng-11687	184	16	2	2	NUM
fumecheng-11687	184	17	2	2	NUM
fumecheng-11687	184	18	2	2	NUM
fumecheng-11687	184	19	2	2	NUM
fumecheng-11687	184	20	2	2	NUM
fumecheng-11687	184	21	42	42	NUM
fumecheng-11687	184	22	0	0	NUM
fumecheng-11687	184	23	0	0	NUM
fumecheng-11687	184	24	0	0	NUM
fumecheng-11687	184	25	tan	tan	PROPN
fumecheng-11687	184	26	(	(	PUNCT
fumecheng-11687	184	27	)	)	PUNCT
fumecheng-11687	184	28	(	(	PUNCT
fumecheng-11687	184	29	)	)	PUNCT
fumecheng-11687	184	30	(	(	PUNCT
fumecheng-11687	184	31	)	)	PUNCT
fumecheng-11687	184	32	(	(	PUNCT
fumecheng-11687	184	33	)	)	PUNCT
fumecheng-11687	184	34	4(1	4(1	NUM
fumecheng-11687	184	35	)	)	PUNCT
fumecheng-11687	185	1	(	(	PUNCT
fumecheng-11687	185	2	1	1	X
fumecheng-11687	185	3	)	)	SYM
fumecheng-11687	185	4	2	2	NUM
fumecheng-11687	185	5	(	(	PUNCT
fumecheng-11687	185	6	1	1	NUM
fumecheng-11687	185	7	)	)	PUNCT
fumecheng-11687	185	8	s	s	PROPN
fumecheng-11687	185	9	b	b	PROPN
fumecheng-11687	185	10	b	b	PROPN
fumecheng-11687	185	11	b	b	PROPN
fumecheng-11687	185	12	b	b	PROPN
fumecheng-11687	185	13	b	b	PROPN
fumecheng-11687	185	14	b	b	PROPN
fumecheng-11687	185	15	b	b	PROPN
fumecheng-11687	185	16	b	b	PROPN
fumecheng-11687	185	17			PROPN
fumecheng-11687	185	18			PROPN
fumecheng-11687	185	19	=	=	SYM
fumecheng-11687	185	20	−	−	PROPN
fumecheng-11687	185	21			PROPN
fumecheng-11687	186	1	+	+	NUM
fumecheng-11687	186	2			PROPN
fumecheng-11687	187	1	−	−	NOUN
fumecheng-11687	188	1	+	+	CCONJ
fumecheng-11687	188	2	−	−	PROPN
fumecheng-11687	188	3			PROPN
fumecheng-11687	188	4	−	−	PROPN
fumecheng-11687	188	5			NOUN
fumecheng-11687	188	6			PROPN
fumecheng-11687	188	7	−	−	NOUN
fumecheng-11687	188	8			PROPN
fumecheng-11687	188	9			X
fumecheng-11687	189	1			X
fumecheng-11687	189	2			X
fumecheng-11687	189	3	(	(	PUNCT
fumecheng-11687	189	4	34	34	NUM
fumecheng-11687	189	5	)	)	PUNCT
fumecheng-11687	189	6	206	206	NUM
fumecheng-11687	190	1	y.o	y.o	PROPN
fumecheng-11687	190	2	.	.	PROPN
fumecheng-11687	190	3	el	el	PROPN
fumecheng-11687	190	4	-	-	PUNCT
fumecheng-11687	190	5	dib	dib	PROPN
fumecheng-11687	190	6	,	,	PUNCT
fumecheng-11687	190	7	n.s	n.s	PROPN
fumecheng-11687	190	8	.	.	PROPN
fumecheng-11687	190	9	elgazery	elgazery	PROPN
fumecheng-11687	190	10	,	,	PUNCT
fumecheng-11687	190	11	h.a	h.a	PROPN
fumecheng-11687	190	12	.	.	PROPN
fumecheng-11687	190	13	alyousef	alyousef	PROPN
fumecheng-11687	191	1	it	it	PRON
fumecheng-11687	191	2	is	be	AUX
fumecheng-11687	191	3	worthwhile	worthwhile	ADJ
fumecheng-11687	191	4	to	to	PART
fumecheng-11687	191	5	observe	observe	VERB
fumecheng-11687	191	6	that	that	SCONJ
fumecheng-11687	191	7	the	the	DET
fumecheng-11687	191	8	applied	apply	VERB
fumecheng-11687	191	9	frequency	frequency	NOUN
fumecheng-11687	191	10			PROPN
fumecheng-11687	191	11	can	can	AUX
fumecheng-11687	191	12	be	be	AUX
fumecheng-11687	191	13	sought	seek	VERB
fumecheng-11687	191	14	in	in	ADP
fumecheng-11687	191	15	terms	term	NOUN
fumecheng-11687	191	16	of	of	ADP
fumecheng-11687	191	17	the	the	DET
fumecheng-11687	191	18	fractal	fractal	ADJ
fumecheng-11687	191	19	order	order	NOUN
fumecheng-11687	191	20	.	.	NOUN
fumecheng-11687	191	21	this	this	PRON
fumecheng-11687	191	22	can	can	AUX
fumecheng-11687	191	23	be	be	AUX
fumecheng-11687	191	24	read	read	VERB
fumecheng-11687	191	25	from	from	ADP
fumecheng-11687	191	26	eq	eq	PROPN
fumecheng-11687	191	27	.	.	PUNCT
fumecheng-11687	192	1	(	(	PUNCT
fumecheng-11687	192	2	33	33	NUM
fumecheng-11687	192	3	)	)	PUNCT
fumecheng-11687	192	4	to	to	PART
fumecheng-11687	192	5	have	have	VERB
fumecheng-11687	192	6	2	2	NUM
fumecheng-11687	192	7	2	2	NUM
fumecheng-11687	192	8	2	2	NUM
fumecheng-11687	192	9	2	2	NUM
fumecheng-11687	192	10	2	2	NUM
fumecheng-11687	192	11	2	2	NUM
fumecheng-11687	192	12	0	0	NUM
fumecheng-11687	192	13	3	3	NUM
fumecheng-11687	192	14	2	2	NUM
fumecheng-11687	192	15	2	2	NUM
fumecheng-11687	192	16	4	4	NUM
fumecheng-11687	192	17	0	0	NUM
fumecheng-11687	192	18	(	(	PUNCT
fumecheng-11687	192	19	(	(	PUNCT
fumecheng-11687	192	20	1	1	NUM
fumecheng-11687	192	21	)	)	PUNCT
fumecheng-11687	192	22	)	)	PUNCT
fumecheng-11687	193	1	(	(	PUNCT
fumecheng-11687	193	2	)	)	PUNCT
fumecheng-11687	193	3	(	(	PUNCT
fumecheng-11687	193	4	1	1	X
fumecheng-11687	193	5	)	)	PUNCT
fumecheng-11687	193	6	b	b	PROPN
fumecheng-11687	193	7	b	b	NOUN
fumecheng-11687	193	8	a	a	DET
fumecheng-11687	193	9	b	b	NOUN
fumecheng-11687	193	10	a	a	DET
fumecheng-11687	193	11	b	b	NOUN
fumecheng-11687	193	12	a	a	DET
fumecheng-11687	193	13	b	b	NOUN
fumecheng-11687	193	14	−	−	ADP
fumecheng-11687	193	15	−	−	PROPN
fumecheng-11687	193	16			PROPN
fumecheng-11687	193	17	=	=	PUNCT
fumecheng-11687	194	1	+	+	CCONJ
fumecheng-11687	195	1	−	−	PROPN
fumecheng-11687	195	2			X
fumecheng-11687	195	3			X
fumecheng-11687	195	4			X
fumecheng-11687	195	5	(	(	PUNCT
fumecheng-11687	195	6	35	35	NUM
fumecheng-11687	195	7	)	)	PUNCT
fumecheng-11687	195	8	the	the	DET
fumecheng-11687	195	9	trial	trial	NOUN
fumecheng-11687	195	10	solution	solution	NOUN
fumecheng-11687	195	11	for	for	ADP
fumecheng-11687	195	12	the	the	DET
fumecheng-11687	195	13	nonlinear	nonlinear	ADJ
fumecheng-11687	195	14	fourth	fourth	ADJ
fumecheng-11687	195	15	-	-	PUNCT
fumecheng-11687	195	16	order	order	NOUN
fumecheng-11687	195	17	eq	eq	NOUN
fumecheng-11687	195	18	.	.	PUNCT
fumecheng-11687	196	1	(	(	PUNCT
fumecheng-11687	196	2	30	30	NUM
fumecheng-11687	196	3	)	)	PUNCT
fumecheng-11687	196	4	may	may	AUX
fumecheng-11687	196	5	be	be	AUX
fumecheng-11687	196	6	suggested	suggest	VERB
fumecheng-11687	196	7	in	in	ADP
fumecheng-11687	196	8	the	the	DET
fumecheng-11687	196	9	form	form	NOUN
fumecheng-11687	196	10	0	0	NUM
fumecheng-11687	196	11	1	1	NUM
fumecheng-11687	196	12	2	2	NUM
fumecheng-11687	196	13	3	3	NUM
fumecheng-11687	196	14	4	4	NUM
fumecheng-11687	196	15	(	(	PUNCT
fumecheng-11687	196	16	)	)	PUNCT
fumecheng-11687	196	17	cos	cos	ADP
fumecheng-11687	196	18	sin	sin	PROPN
fumecheng-11687	197	1	cos3	cos3	PROPN
fumecheng-11687	197	2	sin3u	sin3u	PROPN
fumecheng-11687	198	1	t	t	PROPN
fumecheng-11687	199	1	k	k	PROPN
fumecheng-11687	199	2	t	t	PROPN
fumecheng-11687	200	1	k	k	PROPN
fumecheng-11687	200	2	t	t	PROPN
fumecheng-11687	201	1	k	k	PROPN
fumecheng-11687	201	2	t	t	PROPN
fumecheng-11687	202	1	k	k	PROPN
fumecheng-11687	202	2	t	t	X
fumecheng-11687	203	1			X
fumecheng-11687	203	2			X
fumecheng-11687	203	3	=	=	PROPN
fumecheng-11687	203	4	+	+	CCONJ
fumecheng-11687	204	1	+	+	CCONJ
fumecheng-11687	204	2	+	+	CCONJ
fumecheng-11687	204	3	(	(	PUNCT
fumecheng-11687	204	4	36	36	NUM
fumecheng-11687	204	5	)	)	PUNCT
fumecheng-11687	204	6	here	here	ADV
fumecheng-11687	204	7	,	,	PUNCT
fumecheng-11687	204	8			PROPN
fumecheng-11687	204	9	represents	represent	VERB
fumecheng-11687	204	10	the	the	DET
fumecheng-11687	204	11	oscillation	oscillation	NOUN
fumecheng-11687	204	12	frequency	frequency	NOUN
fumecheng-11687	204	13	and	and	CCONJ
fumecheng-11687	204	14	the	the	DET
fumecheng-11687	204	15	constant	constant	ADJ
fumecheng-11687	204	16	coefficients	coefficient	NOUN
fumecheng-11687	205	1	k	k	NOUN
fumecheng-11687	205	2	’s	’	VERB
fumecheng-11687	205	3	can	can	AUX
fumecheng-11687	205	4	be	be	AUX
fumecheng-11687	205	5	estimated	estimate	VERB
fumecheng-11687	205	6	by	by	ADP
fumecheng-11687	205	7	using	use	VERB
fumecheng-11687	205	8	the	the	DET
fumecheng-11687	205	9	initial	initial	ADJ
fumecheng-11687	205	10	conditions	condition	NOUN
fumecheng-11687	205	11	given	give	VERB
fumecheng-11687	205	12	in	in	ADP
fumecheng-11687	205	13	eq	eq	ADP
fumecheng-11687	205	14	.	.	PUNCT
fumecheng-11687	206	1	(	(	PUNCT
fumecheng-11687	206	2	31	31	NUM
fumecheng-11687	206	3	)	)	PUNCT
fumecheng-11687	206	4	.	.	PUNCT
fumecheng-11687	207	1	consequently	consequently	ADV
fumecheng-11687	207	2	,	,	PUNCT
fumecheng-11687	207	3	2	2	NUM
fumecheng-11687	207	4	2	2	NUM
fumecheng-11687	207	5	2	2	NUM
fumecheng-11687	207	6	1	1	NUM
fumecheng-11687	207	7	2	2	NUM
fumecheng-11687	207	8	2	2	NUM
fumecheng-11687	207	9	2	2	NUM
fumecheng-11687	207	10	2	2	NUM
fumecheng-11687	207	11	2	2	NUM
fumecheng-11687	207	12	2	2	NUM
fumecheng-11687	207	13	2	2	NUM
fumecheng-11687	207	14	2	2	NUM
fumecheng-11687	207	15	3	3	NUM
fumecheng-11687	207	16	2	2	NUM
fumecheng-11687	207	17	2	2	NUM
fumecheng-11687	207	18	2	2	NUM
fumecheng-11687	207	19	3	3	NUM
fumecheng-11687	207	20	2	2	NUM
fumecheng-11687	207	21	2	2	NUM
fumecheng-11687	207	22	2	2	NUM
fumecheng-11687	207	23	2	2	NUM
fumecheng-11687	207	24	2	2	NUM
fumecheng-11687	207	25	2	2	NUM
fumecheng-11687	207	26	4	4	NUM
fumecheng-11687	207	27	2	2	NUM
fumecheng-11687	207	28	3	3	NUM
fumecheng-11687	207	29	1	1	NUM
fumecheng-11687	207	30	(	(	PUNCT
fumecheng-11687	207	31	(	(	PUNCT
fumecheng-11687	207	32	(	(	PUNCT
fumecheng-11687	207	33	)	)	PUNCT
fumecheng-11687	207	34	9	9	NUM
fumecheng-11687	207	35	)	)	PUNCT
fumecheng-11687	207	36	)	)	PUNCT
fumecheng-11687	207	37	,	,	PUNCT
fumecheng-11687	207	38	8	8	NUM
fumecheng-11687	207	39	(	(	PUNCT
fumecheng-11687	207	40	4	4	NUM
fumecheng-11687	207	41	(	(	PUNCT
fumecheng-11687	207	42	3	3	NUM
fumecheng-11687	207	43	(	(	PUNCT
fumecheng-11687	207	44	)	)	PUNCT
fumecheng-11687	207	45	9	9	NUM
fumecheng-11687	207	46	)	)	PUNCT
fumecheng-11687	207	47	)	)	PUNCT
fumecheng-11687	207	48	,	,	PUNCT
fumecheng-11687	207	49	8	8	NUM
fumecheng-11687	207	50	1	1	NUM
fumecheng-11687	207	51	(	(	PUNCT
fumecheng-11687	207	52	(	(	PUNCT
fumecheng-11687	207	53	(	(	PUNCT
fumecheng-11687	207	54	)	)	PUNCT
fumecheng-11687	207	55	)	)	PUNCT
fumecheng-11687	207	56	)	)	PUNCT
fumecheng-11687	207	57	,	,	PUNCT
fumecheng-11687	207	58	8	8	NUM
fumecheng-11687	207	59	(	(	PUNCT
fumecheng-11687	207	60	4	4	NUM
fumecheng-11687	207	61	(	(	PUNCT
fumecheng-11687	207	62	3	3	NUM
fumecheng-11687	207	63	(	(	PUNCT
fumecheng-11687	207	64	)	)	PUNCT
fumecheng-11687	207	65	)	)	PUNCT
fumecheng-11687	207	66	)	)	PUNCT
fumecheng-11687	208	1	24	24	NUM
fumecheng-11687	208	2	k	k	NOUN
fumecheng-11687	208	3	a	a	DET
fumecheng-11687	208	4	a	a	DET
fumecheng-11687	208	5	f	f	NOUN
fumecheng-11687	208	6	a	a	DET
fumecheng-11687	208	7	b	b	PROPN
fumecheng-11687	208	8	b	b	PROPN
fumecheng-11687	208	9	a	a	X
fumecheng-11687	208	10	k	k	X
fumecheng-11687	208	11	a	a	DET
fumecheng-11687	208	12	a	a	DET
fumecheng-11687	208	13	b	b	NOUN
fumecheng-11687	208	14	f	f	PROPN
fumecheng-11687	208	15	a	a	DET
fumecheng-11687	208	16	b	b	PROPN
fumecheng-11687	208	17	b	b	X
fumecheng-11687	208	18	k	k	PROPN
fumecheng-11687	208	19	a	a	PRON
fumecheng-11687	208	20	a	a	DET
fumecheng-11687	208	21	f	f	NOUN
fumecheng-11687	208	22	a	a	DET
fumecheng-11687	208	23	b	b	PROPN
fumecheng-11687	208	24	b	b	PROPN
fumecheng-11687	208	25	a	a	X
fumecheng-11687	208	26	k	k	X
fumecheng-11687	208	27	a	a	DET
fumecheng-11687	208	28	a	a	DET
fumecheng-11687	208	29	b	b	NOUN
fumecheng-11687	208	30	f	f	PROPN
fumecheng-11687	208	31	a	a	DET
fumecheng-11687	208	32	b	b	X
fumecheng-11687	208	33	b	b	X
fumecheng-11687	208	34			PROPN
fumecheng-11687	208	35	=	=	PUNCT
fumecheng-11687	209	1	+	+	NUM
fumecheng-11687	209	2	−	−	PROPN
fumecheng-11687	210	1	+	+	NUM
fumecheng-11687	210	2			NUM
fumecheng-11687	210	3			NUM
fumecheng-11687	210	4			NUM
fumecheng-11687	210	5	=	=	SYM
fumecheng-11687	210	6	−	−	PROPN
fumecheng-11687	211	1	+	+	CCONJ
fumecheng-11687	211	2	−	−	PROPN
fumecheng-11687	212	1	+	+	NUM
fumecheng-11687	212	2			NUM
fumecheng-11687	212	3			NUM
fumecheng-11687	212	4			NOUN
fumecheng-11687	212	5	=	=	NOUN
fumecheng-11687	212	6	−	−	PROPN
fumecheng-11687	213	1	+	+	CCONJ
fumecheng-11687	213	2	−	−	PROPN
fumecheng-11687	213	3	+	+	NUM
fumecheng-11687	213	4			NUM
fumecheng-11687	213	5			NUM
fumecheng-11687	213	6	=	=	NOUN
fumecheng-11687	213	7	+	+	CCONJ
fumecheng-11687	213	8	−	−	PROPN
fumecheng-11687	214	1	+	+	CCONJ
fumecheng-11687	214	2			NUM
fumecheng-11687	214	3			NUM
fumecheng-11687	214	4			NUM
fumecheng-11687	214	5			X
fumecheng-11687	214	6			PROPN
fumecheng-11687	214	7			NUM
fumecheng-11687	214	8			X
fumecheng-11687	214	9			PROPN
fumecheng-11687	214	10			NUM
fumecheng-11687	214	11			X
fumecheng-11687	214	12			PROPN
fumecheng-11687	214	13			NUM
fumecheng-11687	214	14			X
fumecheng-11687	214	15			X
fumecheng-11687	214	16	(	(	PUNCT
fumecheng-11687	214	17	37	37	NUM
fumecheng-11687	214	18	)	)	PUNCT
fumecheng-11687	214	19	since	since	SCONJ
fumecheng-11687	214	20	the	the	DET
fumecheng-11687	214	21	original	original	ADJ
fumecheng-11687	214	22	system	system	NOUN
fumecheng-11687	214	23	is	be	AUX
fumecheng-11687	214	24	a	a	DET
fumecheng-11687	214	25	second	second	ADJ
fumecheng-11687	214	26	-	-	PUNCT
fumecheng-11687	214	27	order	order	NOUN
fumecheng-11687	214	28	derivative	derivative	NOUN
fumecheng-11687	214	29	,	,	PUNCT
fumecheng-11687	214	30	the	the	DET
fumecheng-11687	214	31	fourth	fourth	ADJ
fumecheng-11687	214	32	-	-	PUNCT
fumecheng-11687	214	33	order	order	NOUN
fumecheng-11687	214	34	derivative	derivative	NOUN
fumecheng-11687	214	35	in	in	ADP
fumecheng-11687	214	36	eq	eq	ADP
fumecheng-11687	214	37	.	.	PUNCT
fumecheng-11687	215	1	(	(	PUNCT
fumecheng-11687	215	2	30	30	NUM
fumecheng-11687	215	3	)	)	PUNCT
fumecheng-11687	215	4	is	be	AUX
fumecheng-11687	215	5	artificial	artificial	ADJ
fumecheng-11687	215	6	and	and	CCONJ
fumecheng-11687	215	7	should	should	AUX
fumecheng-11687	215	8	be	be	AUX
fumecheng-11687	215	9	reduced	reduce	VERB
fumecheng-11687	215	10	to	to	ADP
fumecheng-11687	215	11	the	the	DET
fumecheng-11687	215	12	second	second	ADJ
fumecheng-11687	215	13	-	-	PUNCT
fumecheng-11687	215	14	order	order	NOUN
fumecheng-11687	215	15	one	one	NUM
fumecheng-11687	215	16	.	.	PUNCT
fumecheng-11687	216	1	in	in	ADP
fumecheng-11687	216	2	addition	addition	NOUN
fumecheng-11687	216	3	to	to	ADP
fumecheng-11687	216	4	reducing	reduce	VERB
fumecheng-11687	216	5	rank	rank	NOUN
fumecheng-11687	216	6	of	of	ADP
fumecheng-11687	216	7	eq	eq	PROPN
fumecheng-11687	216	8	.	.	PUNCT
fumecheng-11687	217	1	(	(	PUNCT
fumecheng-11687	217	2	29	29	NUM
fumecheng-11687	217	3	)	)	PUNCT
fumecheng-11687	217	4	to	to	ADP
fumecheng-11687	217	5	the	the	DET
fumecheng-11687	217	6	second	second	ADJ
fumecheng-11687	217	7	-	-	PUNCT
fumecheng-11687	217	8	order	order	NOUN
fumecheng-11687	217	9	form	form	NOUN
fumecheng-11687	217	10	,	,	PUNCT
fumecheng-11687	217	11	our	our	PRON
fumecheng-11687	217	12	goal	goal	NOUN
fumecheng-11687	217	13	is	be	AUX
fumecheng-11687	217	14	to	to	PART
fumecheng-11687	217	15	construct	construct	VERB
fumecheng-11687	217	16	a	a	DET
fumecheng-11687	217	17	linearizing	linearize	VERB
fumecheng-11687	217	18	form	form	NOUN
fumecheng-11687	217	19	for	for	ADP
fumecheng-11687	217	20	it	it	PRON
fumecheng-11687	217	21	.	.	PUNCT
fumecheng-11687	218	1	the	the	DET
fumecheng-11687	218	2	linearizing	linearize	VERB
fumecheng-11687	218	3	method	method	NOUN
fumecheng-11687	218	4	can	can	AUX
fumecheng-11687	218	5	be	be	AUX
fumecheng-11687	218	6	used	use	VERB
fumecheng-11687	218	7	to	to	PART
fumecheng-11687	218	8	achieve	achieve	VERB
fumecheng-11687	218	9	this	this	DET
fumecheng-11687	218	10	goal	goal	NOUN
fumecheng-11687	218	11	.	.	PUNCT
fumecheng-11687	219	1	the	the	DET
fumecheng-11687	219	2	following	follow	VERB
fumecheng-11687	219	3	process	process	NOUN
fumecheng-11687	219	4	may	may	AUX
fumecheng-11687	219	5	be	be	AUX
fumecheng-11687	219	6	suggested	suggest	VERB
fumecheng-11687	219	7	[	[	X
fumecheng-11687	219	8	52	52	NUM
fumecheng-11687	219	9	]	]	PUNCT
fumecheng-11687	219	10	:	:	PUNCT
fumecheng-11687	219	11	rearranged	rearrange	VERB
fumecheng-11687	219	12	eq	eq	ADP
fumecheng-11687	219	13	.	.	PUNCT
fumecheng-11687	220	1	(	(	PUNCT
fumecheng-11687	220	2	30	30	NUM
fumecheng-11687	220	3	)	)	PUNCT
fumecheng-11687	220	4	in	in	ADP
fumecheng-11687	220	5	the	the	DET
fumecheng-11687	220	6	form	form	NOUN
fumecheng-11687	220	7	(	(	PUNCT
fumecheng-11687	220	8	4	4	NUM
fumecheng-11687	220	9	)	)	PUNCT
fumecheng-11687	220	10	(	(	PUNCT
fumecheng-11687	220	11	3	3	X
fumecheng-11687	220	12	)	)	SYM
fumecheng-11687	220	13	2	2	NUM
fumecheng-11687	220	14	2	2	NUM
fumecheng-11687	220	15	2	2	NUM
fumecheng-11687	220	16	(	(	PUNCT
fumecheng-11687	220	17	,	,	PUNCT
fumecheng-11687	220	18	,	,	PUNCT
fumecheng-11687	220	19	)	)	PUNCT
fumecheng-11687	220	20	2	2	NUM
fumecheng-11687	220	21	(	(	PUNCT
fumecheng-11687	220	22	(	(	PUNCT
fumecheng-11687	220	23	)	)	PUNCT
fumecheng-11687	220	24	)	)	PUNCT
fumecheng-11687	221	1	(	(	PUNCT
fumecheng-11687	221	2	,	,	PUNCT
fumecheng-11687	221	3	)	)	PUNCT
fumecheng-11687	221	4	0	0	PUNCT
fumecheng-11687	221	5	g	g	NOUN
fumecheng-11687	221	6	u	u	X
fumecheng-11687	221	7	u	u	X
fumecheng-11687	221	8	u	u	NOUN
fumecheng-11687	221	9	u	u	NOUN
fumecheng-11687	221	10	a	a	DET
fumecheng-11687	221	11	b	b	NOUN
fumecheng-11687	221	12	a	a	PRON
fumecheng-11687	221	13	a	a	DET
fumecheng-11687	221	14	u	u	NOUN
fumecheng-11687	221	15	f	f	PROPN
fumecheng-11687	221	16	u	u	PROPN
fumecheng-11687	221	17	u	u	NOUN
fumecheng-11687	221	18	u+	u+	VERB
fumecheng-11687	221	19	+	+	NUM
fumecheng-11687	221	20			NOUN
fumecheng-11687	221	21	−	−	NOUN
fumecheng-11687	222	1	+	+	CCONJ
fumecheng-11687	222	2	=	=	SYM
fumecheng-11687	222	3	(	(	PUNCT
fumecheng-11687	222	4	38	38	NUM
fumecheng-11687	222	5	)	)	PUNCT
fumecheng-11687	222	6	the	the	DET
fumecheng-11687	222	7	above	above	ADJ
fumecheng-11687	222	8	two	two	NUM
fumecheng-11687	222	9	functions	function	NOUN
fumecheng-11687	222	10	g	g	NOUN
fumecheng-11687	222	11	and	and	CCONJ
fumecheng-11687	222	12	f	f	PROPN
fumecheng-11687	222	13	are	be	AUX
fumecheng-11687	222	14	defined	define	VERB
fumecheng-11687	222	15	as	as	ADP
fumecheng-11687	222	16	(	(	PUNCT
fumecheng-11687	222	17	4	4	NUM
fumecheng-11687	222	18	)	)	PUNCT
fumecheng-11687	222	19	(	(	PUNCT
fumecheng-11687	222	20	3	3	X
fumecheng-11687	222	21	)	)	PUNCT
fumecheng-11687	222	22	(	(	PUNCT
fumecheng-11687	222	23	4	4	NUM
fumecheng-11687	222	24	)	)	PUNCT
fumecheng-11687	222	25	(	(	PUNCT
fumecheng-11687	222	26	3	3	X
fumecheng-11687	222	27	)	)	SYM
fumecheng-11687	222	28	2	2	NUM
fumecheng-11687	222	29	2	2	NUM
fumecheng-11687	222	30	2	2	NUM
fumecheng-11687	222	31	2	2	NUM
fumecheng-11687	222	32	4	4	NUM
fumecheng-11687	222	33	2	2	NUM
fumecheng-11687	222	34	2	2	NUM
fumecheng-11687	222	35	3	3	NUM
fumecheng-11687	222	36	2	2	NUM
fumecheng-11687	222	37	2	2	NUM
fumecheng-11687	222	38	2	2	NUM
fumecheng-11687	222	39	2	2	NUM
fumecheng-11687	222	40	2	2	NUM
fumecheng-11687	222	41	2	2	NUM
fumecheng-11687	222	42	2	2	NUM
fumecheng-11687	222	43	02	02	NUM
fumecheng-11687	222	44	2	2	NUM
fumecheng-11687	222	45	1	1	NUM
fumecheng-11687	222	46	3	3	NUM
fumecheng-11687	222	47	(	(	PUNCT
fumecheng-11687	222	48	,	,	PUNCT
fumecheng-11687	222	49	,	,	PUNCT
fumecheng-11687	222	50	)	)	PUNCT
fumecheng-11687	222	51	2	2	NUM
fumecheng-11687	222	52	(	(	PUNCT
fumecheng-11687	222	53	)	)	PUNCT
fumecheng-11687	222	54	,	,	PUNCT
fumecheng-11687	222	55	1	1	NUM
fumecheng-11687	222	56	(	(	PUNCT
fumecheng-11687	222	57	,	,	PUNCT
fumecheng-11687	222	58	)	)	PUNCT
fumecheng-11687	222	59	(	(	PUNCT
fumecheng-11687	222	60	(	(	PUNCT
fumecheng-11687	222	61	)	)	PUNCT
fumecheng-11687	222	62	)	)	PUNCT
fumecheng-11687	223	1	(	(	PUNCT
fumecheng-11687	223	2	6	6	NUM
fumecheng-11687	223	3	)	)	PUNCT
fumecheng-11687	223	4	q	q	NOUN
fumecheng-11687	223	5	g	g	PROPN
fumecheng-11687	223	6	u	u	X
fumecheng-11687	223	7	u	u	X
fumecheng-11687	223	8	u	u	X
fumecheng-11687	223	9	u	u	NOUN
fumecheng-11687	223	10	au	au	PROPN
fumecheng-11687	223	11	b	b	PROPN
fumecheng-11687	223	12	a	a	DET
fumecheng-11687	223	13	u	u	X
fumecheng-11687	223	14	u	u	X
fumecheng-11687	223	15	u	u	NOUN
fumecheng-11687	223	16	u	u	NOUN
fumecheng-11687	223	17	b	b	PROPN
fumecheng-11687	223	18	q	q	X
fumecheng-11687	223	19	f	f	X
fumecheng-11687	223	20	u	u	X
fumecheng-11687	223	21	u	u	NOUN
fumecheng-11687	223	22	a	a	PRON
fumecheng-11687	223	23	b	b	NOUN
fumecheng-11687	223	24	a	a	DET
fumecheng-11687	223	25	b	b	NOUN
fumecheng-11687	223	26	a	a	DET
fumecheng-11687	223	27	u	u	NOUN
fumecheng-11687	223	28	u	u	PROPN
fumecheng-11687	223	29	b	b	PROPN
fumecheng-11687	223	30	b	b	NOUN
fumecheng-11687	223	31			NOUN
fumecheng-11687	223	32			NOUN
fumecheng-11687	223	33	=	=	PUNCT
fumecheng-11687	224	1	+	+	PUNCT
fumecheng-11687	224	2	+	+	CCONJ
fumecheng-11687	224	3	+	+	NUM
fumecheng-11687	224	4			PRON
fumecheng-11687	225	1	+	+	CCONJ
fumecheng-11687	226	1			NUM
fumecheng-11687	226	2			PRON
fumecheng-11687	226	3			NOUN
fumecheng-11687	226	4			NOUN
fumecheng-11687	226	5			NOUN
fumecheng-11687	226	6	=	=	NOUN
fumecheng-11687	226	7	−	−	PROPN
fumecheng-11687	227	1	+	+	CCONJ
fumecheng-11687	227	2	+	+	NUM
fumecheng-11687	227	3			NUM
fumecheng-11687	228	1	+	+	CCONJ
fumecheng-11687	228	2			PROPN
fumecheng-11687	228	3	+	+	CCONJ
fumecheng-11687	228	4			PROPN
fumecheng-11687	228	5	+	+	CCONJ
fumecheng-11687	228	6			NUM
fumecheng-11687	228	7			X
fumecheng-11687	228	8	(	(	PUNCT
fumecheng-11687	228	9	39	39	NUM
fumecheng-11687	228	10	)	)	PUNCT
fumecheng-11687	228	11	apply	apply	VERB
fumecheng-11687	228	12	caughey	caughey	PROPN
fumecheng-11687	228	13	’s	’s	PART
fumecheng-11687	228	14	linearized	linearize	VERB
fumecheng-11687	228	15	approach	approach	NOUN
fumecheng-11687	228	16	[	[	X
fumecheng-11687	228	17	53	53	NUM
fumecheng-11687	228	18	]	]	PUNCT
fumecheng-11687	228	19	to	to	ADP
fumecheng-11687	228	20	eq	eq	PROPN
fumecheng-11687	228	21	.	.	PUNCT
fumecheng-11687	229	1	(	(	PUNCT
fumecheng-11687	229	2	38	38	NUM
fumecheng-11687	229	3	)	)	PUNCT
fumecheng-11687	229	4	with	with	SCONJ
fumecheng-11687	229	5	considered	consider	VERB
fumecheng-11687	229	6	the	the	DET
fumecheng-11687	229	7	suggested	suggest	VERB
fumecheng-11687	229	8	trial	trial	NOUN
fumecheng-11687	229	9	solution	solution	NOUN
fumecheng-11687	229	10	given	give	VERB
fumecheng-11687	229	11	in	in	ADP
fumecheng-11687	229	12	eq	eq	ADP
fumecheng-11687	229	13	.	.	PUNCT
fumecheng-11687	230	1	(	(	PUNCT
fumecheng-11687	230	2	36	36	NUM
fumecheng-11687	230	3	)	)	PUNCT
fumecheng-11687	230	4	yields	yield	VERB
fumecheng-11687	230	5	2	2	NUM
fumecheng-11687	230	6	2	2	NUM
fumecheng-11687	230	7	2	2	NUM
fumecheng-11687	230	8	0	0	NUM
fumecheng-11687	230	9	1	1	NUM
fumecheng-11687	230	10	(	(	PUNCT
fumecheng-11687	230	11	)	)	PUNCT
fumecheng-11687	230	12	2	2	NUM
fumecheng-11687	230	13	(	(	PUNCT
fumecheng-11687	230	14	(	(	PUNCT
fumecheng-11687	230	15	)	)	PUNCT
fumecheng-11687	230	16	)	)	PUNCT
fumecheng-11687	231	1	(	(	PUNCT
fumecheng-11687	231	2	)	)	PUNCT
fumecheng-11687	231	3	0u	0u	ADJ
fumecheng-11687	231	4	a	a	DET
fumecheng-11687	231	5	b	b	NOUN
fumecheng-11687	231	6	a	a	DET
fumecheng-11687	231	7	a	a	DET
fumecheng-11687	231	8	u	u	NOUN
fumecheng-11687	231	9	u+	u+	NOUN
fumecheng-11687	231	10	+	+	NUM
fumecheng-11687	231	11			PROPN
fumecheng-11687	232	1	−	−	NOUN
fumecheng-11687	233	1	+	+	CCONJ
fumecheng-11687	233	2	=	=	X
fumecheng-11687	233	3			X
fumecheng-11687	233	4			X
fumecheng-11687	233	5			X
fumecheng-11687	233	6			X
fumecheng-11687	233	7	(	(	PUNCT
fumecheng-11687	233	8	40	40	NUM
fumecheng-11687	233	9	)	)	PUNCT
fumecheng-11687	233	10	here	here	ADV
fumecheng-11687	233	11	,	,	PUNCT
fumecheng-11687	233	12	0	0	X
fumecheng-11687	233	13	(	(	PUNCT
fumecheng-11687	233	14			X
fumecheng-11687	233	15	)	)	PUNCT
fumecheng-11687	233	16	and	and	CCONJ
fumecheng-11687	233	17	1	1	PROPN
fumecheng-11687	233	18	(	(	PUNCT
fumecheng-11687	233	19			X
fumecheng-11687	233	20	)	)	PUNCT
fumecheng-11687	233	21	are	be	AUX
fumecheng-11687	233	22	estimated	estimate	VERB
fumecheng-11687	233	23	using	use	VERB
fumecheng-11687	233	24	the	the	DET
fumecheng-11687	233	25	following	follow	VERB
fumecheng-11687	233	26	formula	formula	NOUN
fumecheng-11687	233	27	proposed	propose	VERB
fumecheng-11687	233	28	by	by	ADP
fumecheng-11687	233	29	el	el	PROPN
fumecheng-11687	233	30	-	-	PROPN
fumecheng-11687	233	31	dib	dib	PROPN
fumecheng-11687	234	1	[	[	X
fumecheng-11687	234	2	38	38	NUM
fumecheng-11687	234	3	]	]	PUNCT
fumecheng-11687	234	4	the	the	DET
fumecheng-11687	234	5	up	up	ADV
fumecheng-11687	234	6	-	-	PUNCT
fumecheng-11687	234	7	grating	grate	VERB
fumecheng-11687	234	8	rank	rank	NOUN
fumecheng-11687	234	9	approach	approach	NOUN
fumecheng-11687	234	10	to	to	PART
fumecheng-11687	234	11	solve	solve	VERB
fumecheng-11687	234	12	a	a	DET
fumecheng-11687	234	13	forced	force	VERB
fumecheng-11687	234	14	fractal	fractal	ADJ
fumecheng-11687	234	15	duffing	duffing	NOUN
fumecheng-11687	234	16	oscillator	oscillator	NOUN
fumecheng-11687	234	17	by	by	ADP
fumecheng-11687	234	18	the	the	DET
fumecheng-11687	234	19	np	np	PROPN
fumecheng-11687	234	20	technique	technique	NOUN
fumecheng-11687	234	21	207	207	NUM
fumecheng-11687	234	22	(	(	PUNCT
fumecheng-11687	234	23	4	4	NUM
fumecheng-11687	234	24	)	)	PUNCT
fumecheng-11687	234	25	(	(	PUNCT
fumecheng-11687	234	26	3	3	X
fumecheng-11687	234	27	)	)	PUNCT
fumecheng-11687	235	1	2	2	NUM
fumecheng-11687	235	2	0	0	NUM
fumecheng-11687	235	3	0	0	NUM
fumecheng-11687	235	4	0	0	NUM
fumecheng-11687	235	5	0	0	NUM
fumecheng-11687	235	6	0	0	NUM
fumecheng-11687	235	7	0	0	NUM
fumecheng-11687	235	8	2	2	NUM
fumecheng-11687	235	9	0	0	NUM
fumecheng-11687	235	10	0	0	NUM
fumecheng-11687	235	11	(	(	PUNCT
fumecheng-11687	235	12	,	,	PUNCT
fumecheng-11687	235	13	,	,	PUNCT
fumecheng-11687	235	14	)	)	PUNCT
fumecheng-11687	235	15	(	(	PUNCT
fumecheng-11687	235	16	)	)	PUNCT
fumecheng-11687	235	17	2	2	NUM
fumecheng-11687	235	18	(	(	PUNCT
fumecheng-11687	235	19	)	)	PUNCT
fumecheng-11687	235	20	;	;	PUNCT
fumecheng-11687	235	21	(	(	PUNCT
fumecheng-11687	235	22	)	)	PUNCT
fumecheng-11687	235	23	t	t	NOUN
fumecheng-11687	235	24	t	t	NOUN
fumecheng-11687	235	25	g	g	PROPN
fumecheng-11687	235	26	u	u	X
fumecheng-11687	235	27	u	u	X
fumecheng-11687	235	28	u	u	X
fumecheng-11687	235	29	u	u	NOUN
fumecheng-11687	235	30	t	t	X
fumecheng-11687	235	31	dt	dt	X
fumecheng-11687	235	32	t	t	PROPN
fumecheng-11687	235	33	u	u	NOUN
fumecheng-11687	235	34	t	t	NOUN
fumecheng-11687	235	35	dt	dt	NOUN
fumecheng-11687	236	1	=	=	SYM
fumecheng-11687	236	2	=	=	NOUN
fumecheng-11687	236	3			NOUN
fumecheng-11687	236	4			X
fumecheng-11687	236	5			PROPN
fumecheng-11687	236	6			X
fumecheng-11687	236	7			X
fumecheng-11687	236	8			X
fumecheng-11687	236	9	(	(	PUNCT
fumecheng-11687	236	10	41	41	NUM
fumecheng-11687	236	11	)	)	PUNCT
fumecheng-11687	236	12	2	2	NUM
fumecheng-11687	236	13	0	0	NUM
fumecheng-11687	236	14	0	0	NUM
fumecheng-11687	236	15	0	0	NUM
fumecheng-11687	236	16	0	0	NUM
fumecheng-11687	236	17	1	1	NUM
fumecheng-11687	236	18	2	2	NUM
fumecheng-11687	236	19	0	0	NUM
fumecheng-11687	236	20	0	0	NUM
fumecheng-11687	236	21	(	(	PUNCT
fumecheng-11687	236	22	)	)	PUNCT
fumecheng-11687	236	23	(	(	PUNCT
fumecheng-11687	236	24	,	,	PUNCT
fumecheng-11687	236	25	)	)	PUNCT
fumecheng-11687	236	26	(	(	PUNCT
fumecheng-11687	236	27	)	)	PUNCT
fumecheng-11687	236	28	(	(	PUNCT
fumecheng-11687	236	29	)	)	PUNCT
fumecheng-11687	236	30	t	t	NOUN
fumecheng-11687	236	31	t	t	PROPN
fumecheng-11687	236	32	u	u	NOUN
fumecheng-11687	236	33	t	t	PROPN
fumecheng-11687	236	34	f	f	X
fumecheng-11687	236	35	u	u	X
fumecheng-11687	236	36	u	u	NOUN
fumecheng-11687	236	37	dt	dt	X
fumecheng-11687	236	38	u	u	NOUN
fumecheng-11687	236	39	t	t	NOUN
fumecheng-11687	236	40	dt	dt	NOUN
fumecheng-11687	236	41	=	=	SYM
fumecheng-11687	236	42			PUNCT
fumecheng-11687	236	43			PUNCT
fumecheng-11687	236	44			X
fumecheng-11687	236	45			X
fumecheng-11687	236	46	(	(	PUNCT
fumecheng-11687	236	47	42	42	NUM
fumecheng-11687	236	48	)	)	PUNCT
fumecheng-11687	236	49	the	the	DET
fumecheng-11687	236	50	results	result	NOUN
fumecheng-11687	236	51	of	of	ADP
fumecheng-11687	236	52	the	the	DET
fumecheng-11687	236	53	above	above	ADJ
fumecheng-11687	236	54	integrals	integral	NOUN
fumecheng-11687	236	55	are	be	AUX
fumecheng-11687	236	56	straightforward	straightforward	ADJ
fumecheng-11687	236	57	in	in	ADP
fumecheng-11687	236	58	their	their	PRON
fumecheng-11687	236	59	calculations	calculation	NOUN
fumecheng-11687	236	60	and	and	CCONJ
fumecheng-11687	236	61	are	be	AUX
fumecheng-11687	236	62	available	available	ADJ
fumecheng-11687	236	63	from	from	ADP
fumecheng-11687	236	64	the	the	DET
fumecheng-11687	236	65	corresponding	corresponding	ADJ
fumecheng-11687	236	66	author	author	NOUN
fumecheng-11687	236	67	.	.	PUNCT
fumecheng-11687	237	1	it	it	PRON
fumecheng-11687	237	2	should	should	AUX
fumecheng-11687	237	3	be	be	AUX
fumecheng-11687	237	4	noticed	notice	VERB
fumecheng-11687	237	5	that	that	SCONJ
fumecheng-11687	237	6	eq	eq	ADP
fumecheng-11687	237	7	.	.	PUNCT
fumecheng-11687	238	1	(	(	PUNCT
fumecheng-11687	238	2	40	40	NUM
fumecheng-11687	238	3	)	)	PUNCT
fumecheng-11687	238	4	can	can	AUX
fumecheng-11687	238	5	be	be	AUX
fumecheng-11687	238	6	expressed	express	VERB
fumecheng-11687	238	7	in	in	ADP
fumecheng-11687	238	8	the	the	DET
fumecheng-11687	238	9	following	follow	VERB
fumecheng-11687	238	10	manner	manner	NOUN
fumecheng-11687	238	11	:	:	PUNCT
fumecheng-11687	238	12	22	22	NUM
fumecheng-11687	238	13	(	(	PUNCT
fumecheng-11687	238	14	)	)	PUNCT
fumecheng-11687	238	15	(	(	PUNCT
fumecheng-11687	238	16	)	)	PUNCT
fumecheng-11687	238	17	0u	0u	ADJ
fumecheng-11687	238	18	u	u	PRON
fumecheng-11687	238	19	u	u	PUNCT
fumecheng-11687	239	1			PUNCT
fumecheng-11687	239	2			NOUN
fumecheng-11687	240	1	+	+	NOUN
fumecheng-11687	240	2	+	+	CCONJ
fumecheng-11687	241	1	=	=	SYM
fumecheng-11687	241	2	(	(	PUNCT
fumecheng-11687	241	3	43	43	NUM
fumecheng-11687	241	4	)	)	PUNCT
fumecheng-11687	241	5	here	here	ADV
fumecheng-11687	241	6	,	,	PUNCT
fumecheng-11687	241	7	the	the	DET
fumecheng-11687	241	8	coefficients	coefficient	NOUN
fumecheng-11687	241	9			NOUN
fumecheng-11687	241	10	(	(	PUNCT
fumecheng-11687	241	11			X
fumecheng-11687	241	12	)	)	PUNCT
fumecheng-11687	241	13	and	and	CCONJ
fumecheng-11687	241	14	2(	2(	PROPN
fumecheng-11687	241	15	)	)	PUNCT
fumecheng-11687	241	16	are	be	AUX
fumecheng-11687	241	17	constants	constant	NOUN
fumecheng-11687	241	18	functions	function	NOUN
fumecheng-11687	241	19	of	of	ADP
fumecheng-11687	241	20	the	the	DET
fumecheng-11687	241	21	frequency	frequency	NOUN
fumecheng-11687	241	22			X
fumecheng-11687	241	23	given	give	VERB
fumecheng-11687	241	24	by	by	ADP
fumecheng-11687	241	25	2	2	NUM
fumecheng-11687	241	26	2	2	NUM
fumecheng-11687	241	27	2	2	NUM
fumecheng-11687	241	28	0	0	NUM
fumecheng-11687	241	29	(	(	PUNCT
fumecheng-11687	241	30	(	(	PUNCT
fumecheng-11687	241	31	)	)	PUNCT
fumecheng-11687	241	32	)	)	PUNCT
fumecheng-11687	242	1	(	(	PUNCT
fumecheng-11687	242	2	)	)	PUNCT
fumecheng-11687	242	3	(	(	PUNCT
fumecheng-11687	242	4	)	)	PUNCT
fumecheng-11687	242	5	a	a	DET
fumecheng-11687	242	6	b	b	NOUN
fumecheng-11687	242	7	a	a	PRON
fumecheng-11687	242	8	a+	a+	PRON
fumecheng-11687	242	9			PROPN
fumecheng-11687	242	10	−	−	NOUN
fumecheng-11687	242	11	=	=	NOUN
fumecheng-11687	242	12			NOUN
fumecheng-11687	242	13			X
fumecheng-11687	242	14			X
fumecheng-11687	242	15			X
fumecheng-11687	242	16	(	(	PUNCT
fumecheng-11687	242	17	44	44	NUM
fumecheng-11687	242	18	)	)	SYM
fumecheng-11687	242	19	2	2	NUM
fumecheng-11687	242	20	1	1	NUM
fumecheng-11687	242	21	0	0	NUM
fumecheng-11687	242	22	(	(	PUNCT
fumecheng-11687	242	23	)	)	PUNCT
fumecheng-11687	242	24	(	(	PUNCT
fumecheng-11687	242	25	)	)	PUNCT
fumecheng-11687	242	26	(	(	PUNCT
fumecheng-11687	242	27	)	)	PUNCT
fumecheng-11687	242	28			PROPN
fumecheng-11687	242	29			PROPN
fumecheng-11687	242	30			NOUN
fumecheng-11687	242	31			X
fumecheng-11687	242	32			X
fumecheng-11687	242	33			X
fumecheng-11687	242	34	=	=	SYM
fumecheng-11687	242	35	(	(	PUNCT
fumecheng-11687	242	36	45	45	NUM
fumecheng-11687	242	37	)	)	PUNCT
fumecheng-11687	242	38	eq	eq	NOUN
fumecheng-11687	242	39	.	.	PUNCT
fumecheng-11687	243	1	(	(	PUNCT
fumecheng-11687	243	2	43	43	NUM
fumecheng-11687	243	3	)	)	PUNCT
fumecheng-11687	243	4	is	be	AUX
fumecheng-11687	243	5	a	a	DET
fumecheng-11687	243	6	linear	linear	ADJ
fumecheng-11687	243	7	second	second	ADJ
fumecheng-11687	243	8	-	-	PUNCT
fumecheng-11687	243	9	order	order	NOUN
fumecheng-11687	243	10	equation	equation	NOUN
fumecheng-11687	243	11	having	have	VERB
fumecheng-11687	243	12	a	a	DET
fumecheng-11687	243	13	damping	damp	VERB
fumecheng-11687	243	14	force	force	NOUN
fumecheng-11687	243	15	.	.	PUNCT
fumecheng-11687	244	1	the	the	DET
fumecheng-11687	244	2	damping	damp	VERB
fumecheng-11687	244	3	force	force	NOUN
fumecheng-11687	244	4	is	be	AUX
fumecheng-11687	244	5	characterized	characterize	VERB
fumecheng-11687	244	6	by	by	ADP
fumecheng-11687	244	7	the	the	DET
fumecheng-11687	244	8	coefficient	coefficient	NOUN
fumecheng-11687	244	9			NOUN
fumecheng-11687	244	10	(	(	PUNCT
fumecheng-11687	244	11			X
fumecheng-11687	244	12	)	)	PUNCT
fumecheng-11687	244	13	.	.	PUNCT
fumecheng-11687	245	1	the	the	DET
fumecheng-11687	245	2	solution	solution	NOUN
fumecheng-11687	245	3	of	of	ADP
fumecheng-11687	245	4	eq	eq	PROPN
fumecheng-11687	245	5	.	.	PUNCT
fumecheng-11687	246	1	(	(	PUNCT
fumecheng-11687	246	2	43	43	NUM
fumecheng-11687	246	3	)	)	PUNCT
fumecheng-11687	246	4	has	have	VERB
fumecheng-11687	246	5	a	a	DET
fumecheng-11687	246	6	damping	damp	VERB
fumecheng-11687	246	7	behavior	behavior	NOUN
fumecheng-11687	246	8	unless	unless	SCONJ
fumecheng-11687	246	9			NOUN
fumecheng-11687	246	10	is	be	AUX
fumecheng-11687	246	11	equal	equal	ADJ
fumecheng-11687	246	12	unity	unity	NOUN
fumecheng-11687	246	13	.	.	PUNCT
fumecheng-11687	247	1	more	more	ADV
fumecheng-11687	247	2	damping	damp	VERB
fumecheng-11687	247	3	behavior	behavior	NOUN
fumecheng-11687	247	4	is	be	AUX
fumecheng-11687	247	5	found	find	VERB
fumecheng-11687	247	6	as	as	ADP
fumecheng-11687	247	7			X
fumecheng-11687	247	8	having	have	VERB
fumecheng-11687	247	9	a	a	DET
fumecheng-11687	247	10	greater	great	ADJ
fumecheng-11687	247	11	decrease	decrease	NOUN
fumecheng-11687	247	12	than	than	ADP
fumecheng-11687	247	13	unity	unity	NOUN
fumecheng-11687	247	14	[	[	X
fumecheng-11687	247	15	30,31,54	30,31,54	NUM
fumecheng-11687	247	16	]	]	X
fumecheng-11687	247	17	.	.	PUNCT
fumecheng-11687	248	1	the	the	DET
fumecheng-11687	248	2	solution	solution	NOUN
fumecheng-11687	248	3	that	that	PRON
fumecheng-11687	248	4	covers	cover	VERB
fumecheng-11687	248	5	this	this	DET
fumecheng-11687	248	6	behavior	behavior	NOUN
fumecheng-11687	248	7	is	be	AUX
fumecheng-11687	248	8	performed	perform	VERB
fumecheng-11687	248	9	in	in	ADP
fumecheng-11687	248	10	the	the	DET
fumecheng-11687	248	11	following	follow	VERB
fumecheng-11687	248	12	form	form	NOUN
fumecheng-11687	248	13	:	:	PUNCT
fumecheng-11687	248	14	(	(	PUNCT
fumecheng-11687	248	15	)	)	PUNCT
fumecheng-11687	249	1	1	1	NUM
fumecheng-11687	249	2	2	2	NUM
fumecheng-11687	249	3	3	3	NUM
fumecheng-11687	249	4	4	4	NUM
fumecheng-11687	249	5	(	(	PUNCT
fumecheng-11687	249	6	)	)	PUNCT
fumecheng-11687	249	7	(	(	PUNCT
fumecheng-11687	249	8	cos	cos	ADP
fumecheng-11687	249	9	sin	sin	PROPN
fumecheng-11687	249	10	cos3	cos3	PROPN
fumecheng-11687	249	11	sin3	sin3	PROPN
fumecheng-11687	249	12	)	)	PUNCT
fumecheng-11687	250	1	t	t	PROPN
fumecheng-11687	250	2	u	u	NOUN
fumecheng-11687	251	1	t	t	PROPN
fumecheng-11687	251	2	e	e	X
fumecheng-11687	251	3	k	k	PROPN
fumecheng-11687	251	4	t	t	PROPN
fumecheng-11687	252	1	k	k	PROPN
fumecheng-11687	252	2	t	t	PROPN
fumecheng-11687	252	3	k	k	PROPN
fumecheng-11687	252	4	t	t	PROPN
fumecheng-11687	252	5	k	k	PROPN
fumecheng-11687	252	6	t	t	PROPN
fumecheng-11687	252	7	−	−	PROPN
fumecheng-11687	253	1	=	=	PUNCT
fumecheng-11687	254	1	+	+	PUNCT
fumecheng-11687	254	2	+	+	CCONJ
fumecheng-11687	254	3	+	+	NUM
fumecheng-11687	254	4			NOUN
fumecheng-11687	254	5			X
fumecheng-11687	254	6			X
fumecheng-11687	254	7			X
fumecheng-11687	254	8			X
fumecheng-11687	254	9			X
fumecheng-11687	254	10	(	(	PUNCT
fumecheng-11687	254	11	46	46	NUM
fumecheng-11687	254	12	)	)	PUNCT
fumecheng-11687	254	13	the	the	DET
fumecheng-11687	254	14	above	above	ADJ
fumecheng-11687	254	15	solution	solution	NOUN
fumecheng-11687	254	16	is	be	AUX
fumecheng-11687	254	17	obtained	obtain	VERB
fumecheng-11687	254	18	due	due	ADJ
fumecheng-11687	254	19	to	to	ADP
fumecheng-11687	254	20	applying	apply	VERB
fumecheng-11687	254	21	the	the	DET
fumecheng-11687	254	22	normal	normal	ADJ
fumecheng-11687	254	23	form	form	NOUN
fumecheng-11687	254	24	technique	technique	NOUN
fumecheng-11687	254	25	.	.	PUNCT
fumecheng-11687	255	1	in	in	ADP
fumecheng-11687	255	2	this	this	DET
fumecheng-11687	255	3	approach	approach	NOUN
fumecheng-11687	255	4	,	,	PUNCT
fumecheng-11687	255	5	the	the	DET
fumecheng-11687	255	6	frequency	frequency	NOUN
fumecheng-11687	255	7			X
fumecheng-11687	255	8	has	have	VERB
fumecheng-11687	255	9	the	the	DET
fumecheng-11687	255	10	form	form	NOUN
fumecheng-11687	255	11	2	2	NUM
fumecheng-11687	255	12	2	2	NUM
fumecheng-11687	255	13	2	2	NUM
fumecheng-11687	255	14	(	(	PUNCT
fumecheng-11687	255	15	)	)	PUNCT
fumecheng-11687	255	16	(	(	PUNCT
fumecheng-11687	255	17	)	)	PUNCT
fumecheng-11687	255	18			PROPN
fumecheng-11687	255	19			NOUN
fumecheng-11687	255	20			ADJ
fumecheng-11687	255	21			NOUN
fumecheng-11687	255	22	=	=	NOUN
fumecheng-11687	256	1	−	−	PROPN
fumecheng-11687	256	2	(	(	PUNCT
fumecheng-11687	256	3	47	47	NUM
fumecheng-11687	256	4	)	)	PUNCT
fumecheng-11687	256	5	4	4	NUM
fumecheng-11687	256	6	.	.	PUNCT
fumecheng-11687	256	7	numerical	numerical	PROPN
fumecheng-11687	256	8	estimation	estimation	PROPN
fumecheng-11687	256	9	the	the	DET
fumecheng-11687	256	10	numerical	numerical	ADJ
fumecheng-11687	256	11	solution	solution	NOUN
fumecheng-11687	256	12	of	of	ADP
fumecheng-11687	256	13	the	the	DET
fumecheng-11687	256	14	original	original	ADJ
fumecheng-11687	256	15	forced	force	VERB
fumecheng-11687	256	16	fractal	fractal	ADJ
fumecheng-11687	256	17	nonlinear	nonlinear	PROPN
fumecheng-11687	256	18	oscillator	oscillator	NOUN
fumecheng-11687	256	19	given	give	VERB
fumecheng-11687	256	20	in	in	ADP
fumecheng-11687	256	21	eq	eq	ADP
fumecheng-11687	256	22	.	.	PUNCT
fumecheng-11687	257	1	(	(	PUNCT
fumecheng-11687	257	2	13	13	NUM
fumecheng-11687	257	3	)	)	PUNCT
fumecheng-11687	257	4	at	at	ADP
fumecheng-11687	257	5	→	→	NUM
fumecheng-11687	257	6	1	1	NUM
fumecheng-11687	257	7	and	and	CCONJ
fumecheng-11687	257	8	analytical	analytical	ADJ
fumecheng-11687	257	9	solution	solution	NOUN
fumecheng-11687	257	10	given	give	VERB
fumecheng-11687	257	11	in	in	ADP
fumecheng-11687	257	12	eq	eq	ADP
fumecheng-11687	257	13	.	.	PUNCT
fumecheng-11687	258	1	(	(	PUNCT
fumecheng-11687	258	2	46	46	NUM
fumecheng-11687	258	3	)	)	PUNCT
fumecheng-11687	258	4	were	be	AUX
fumecheng-11687	258	5	compared	compare	VERB
fumecheng-11687	258	6	and	and	CCONJ
fumecheng-11687	258	7	shown	show	VERB
fumecheng-11687	258	8	in	in	ADP
fumecheng-11687	258	9	fig	fig	NOUN
fumecheng-11687	258	10	.	.	PUNCT
fumecheng-11687	259	1	1	1	NUM
fumecheng-11687	259	2	for	for	ADP
fumecheng-11687	259	3	the	the	DET
fumecheng-11687	259	4	system	system	NOUN
fumecheng-11687	259	5	having	have	VERB
fumecheng-11687	259	6	a	a	DET
fumecheng-11687	259	7	=	=	X
fumecheng-11687	259	8	0	0	X
fumecheng-11687	259	9	=	=	NOUN
fumecheng-11687	259	10	1	1	NUM
fumecheng-11687	259	11	,	,	PUNCT
fumecheng-11687	259	12	q	q	X
fumecheng-11687	260	1	=	=	SYM
fumecheng-11687	260	2			NUM
fumecheng-11687	260	3	=	=	NOUN
fumecheng-11687	260	4	0.01	0.01	NUM
fumecheng-11687	260	5	,	,	PUNCT
fumecheng-11687	260	6	and	and	CCONJ
fumecheng-11687	260	7	=10	=10	PROPN
fumecheng-11687	260	8	.	.	PUNCT
fumecheng-11687	261	1	the	the	DET
fumecheng-11687	261	2	relative	relative	ADJ
fumecheng-11687	261	3	error	error	NOUN
fumecheng-11687	261	4	is	be	AUX
fumecheng-11687	261	5	estimated	estimate	VERB
fumecheng-11687	261	6	in	in	ADP
fumecheng-11687	261	7	this	this	DET
fumecheng-11687	261	8	calculation	calculation	NOUN
fumecheng-11687	261	9	to	to	PART
fumecheng-11687	261	10	be	be	AUX
fumecheng-11687	261	11	0.1331	0.1331	NUM
fumecheng-11687	261	12	which	which	PRON
fumecheng-11687	261	13	reveals	reveal	VERB
fumecheng-11687	261	14	that	that	SCONJ
fumecheng-11687	261	15	the	the	DET
fumecheng-11687	261	16	two	two	NUM
fumecheng-11687	261	17	solutions	solution	NOUN
fumecheng-11687	261	18	were	be	AUX
fumecheng-11687	261	19	in	in	ADP
fumecheng-11687	261	20	accord	accord	NOUN
fumecheng-11687	261	21	.	.	PUNCT
fumecheng-11687	262	1	further	far	ADV
fumecheng-11687	262	2	,	,	PUNCT
fumecheng-11687	262	3	the	the	DET
fumecheng-11687	262	4	comparison	comparison	NOUN
fumecheng-11687	262	5	of	of	ADP
fumecheng-11687	262	6	the	the	DET
fumecheng-11687	262	7	analytical	analytical	ADJ
fumecheng-11687	262	8	solution	solution	NOUN
fumecheng-11687	262	9	given	give	VERB
fumecheng-11687	262	10	in	in	ADP
fumecheng-11687	262	11	eq	eq	ADP
fumecheng-11687	262	12	.	.	PUNCT
fumecheng-11687	263	1	(	(	PUNCT
fumecheng-11687	263	2	46	46	NUM
fumecheng-11687	263	3	)	)	PUNCT
fumecheng-11687	263	4	of	of	ADP
fumecheng-11687	263	5	the	the	DET
fumecheng-11687	263	6	second	second	ADJ
fumecheng-11687	263	7	-	-	PUNCT
fumecheng-11687	263	8	order	order	NOUN
fumecheng-11687	263	9	eq	eq	NOUN
fumecheng-11687	263	10	.	.	PUNCT
fumecheng-11687	264	1	(	(	PUNCT
fumecheng-11687	264	2	43	43	NUM
fumecheng-11687	264	3	)	)	PUNCT
fumecheng-11687	264	4	with	with	ADP
fumecheng-11687	264	5	the	the	DET
fumecheng-11687	264	6	numerical	numerical	ADJ
fumecheng-11687	264	7	solution	solution	NOUN
fumecheng-11687	264	8	of	of	ADP
fumecheng-11687	264	9	the	the	DET
fumecheng-11687	264	10	fourth	fourth	ADJ
fumecheng-11687	264	11	-	-	PUNCT
fumecheng-11687	264	12	order	order	NOUN
fumecheng-11687	264	13	eq	eq	NOUN
fumecheng-11687	264	14	.	.	PUNCT
fumecheng-11687	265	1	(	(	PUNCT
fumecheng-11687	265	2	30	30	NUM
fumecheng-11687	265	3	)	)	PUNCT
fumecheng-11687	265	4	has	have	AUX
fumecheng-11687	265	5	been	be	AUX
fumecheng-11687	265	6	displayed	display	VERB
fumecheng-11687	265	7	in	in	ADP
fumecheng-11687	265	8	fig	fig	NOUN
fumecheng-11687	265	9	.	.	PUNCT
fumecheng-11687	266	1	2	2	NUM
fumecheng-11687	266	2	for	for	ADP
fumecheng-11687	266	3	the	the	DET
fumecheng-11687	266	4	case	case	NOUN
fumecheng-11687	266	5	of	of	ADP
fumecheng-11687	266	6			NOUN
fumecheng-11687	266	7	is	be	AUX
fumecheng-11687	266	8	close	close	ADJ
fumecheng-11687	266	9	to	to	ADP
fumecheng-11687	266	10	unity	unity	NOUN
fumecheng-11687	266	11	.	.	PUNCT
fumecheng-11687	267	1	the	the	DET
fumecheng-11687	267	2	system	system	NOUN
fumecheng-11687	267	3	that	that	PRON
fumecheng-11687	267	4	is	be	AUX
fumecheng-11687	267	5	used	use	VERB
fumecheng-11687	267	6	in	in	ADP
fumecheng-11687	267	7	these	these	DET
fumecheng-11687	267	8	calculations	calculation	NOUN
fumecheng-11687	267	9	has	have	VERB
fumecheng-11687	267	10	a	a	DET
fumecheng-11687	267	11	=	=	PUNCT
fumecheng-11687	267	12	0	0	X
fumecheng-11687	267	13	=	=	NOUN
fumecheng-11687	267	14	1	1	NUM
fumecheng-11687	267	15	,	,	PUNCT
fumecheng-11687	267	16	q	q	X
fumecheng-11687	268	1	=	=	SYM
fumecheng-11687	268	2			NUM
fumecheng-11687	268	3	=	=	NOUN
fumecheng-11687	268	4	0.01	0.01	NUM
fumecheng-11687	268	5	,	,	PUNCT
fumecheng-11687	268	6	and	and	CCONJ
fumecheng-11687	268	7	=10	=10	PROPN
fumecheng-11687	268	8	.	.	PUNCT
fumecheng-11687	269	1	the	the	DET
fumecheng-11687	269	2	relative	relative	ADJ
fumecheng-11687	269	3	error	error	NOUN
fumecheng-11687	269	4	is	be	AUX
fumecheng-11687	269	5	estimated	estimate	VERB
fumecheng-11687	269	6	in	in	ADP
fumecheng-11687	269	7	this	this	DET
fumecheng-11687	269	8	calculation	calculation	NOUN
fumecheng-11687	269	9	to	to	PART
fumecheng-11687	269	10	be	be	AUX
fumecheng-11687	269	11	0.006445	0.006445	NUM
fumecheng-11687	269	12	which	which	PRON
fumecheng-11687	269	13	208	208	NUM
fumecheng-11687	269	14	y.o	y.o	PROPN
fumecheng-11687	269	15	.	.	PROPN
fumecheng-11687	269	16	el	el	PROPN
fumecheng-11687	269	17	-	-	PUNCT
fumecheng-11687	269	18	dib	dib	PROPN
fumecheng-11687	269	19	,	,	PUNCT
fumecheng-11687	269	20	n.s	n.s	PROPN
fumecheng-11687	269	21	.	.	PROPN
fumecheng-11687	269	22	elgazery	elgazery	PROPN
fumecheng-11687	269	23	,	,	PUNCT
fumecheng-11687	269	24	h.a	h.a	PROPN
fumecheng-11687	269	25	.	.	PROPN
fumecheng-11687	269	26	alyousef	alyousef	PROPN
fumecheng-11687	269	27	demonstrates	demonstrate	VERB
fumecheng-11687	269	28	that	that	SCONJ
fumecheng-11687	269	29	the	the	DET
fumecheng-11687	269	30	analytical	analytical	ADJ
fumecheng-11687	269	31	and	and	CCONJ
fumecheng-11687	269	32	numerical	numerical	ADJ
fumecheng-11687	269	33	solutions	solution	NOUN
fumecheng-11687	269	34	are	be	AUX
fumecheng-11687	269	35	in	in	ADP
fumecheng-11687	269	36	good	good	ADJ
fumecheng-11687	269	37	accord	accord	NOUN
fumecheng-11687	269	38	with	with	ADP
fumecheng-11687	269	39	one	one	NUM
fumecheng-11687	269	40	another	another	DET
fumecheng-11687	269	41	.	.	PUNCT
fumecheng-11687	270	1	it	it	PRON
fumecheng-11687	270	2	is	be	AUX
fumecheng-11687	270	3	noted	note	VERB
fumecheng-11687	270	4	that	that	SCONJ
fumecheng-11687	270	5	the	the	DET
fumecheng-11687	270	6	periodic	periodic	ADJ
fumecheng-11687	270	7	solution	solution	NOUN
fumecheng-11687	270	8	is	be	AUX
fumecheng-11687	270	9	revealed	reveal	VERB
fumecheng-11687	270	10	in	in	ADP
fumecheng-11687	270	11	this	this	DET
fumecheng-11687	270	12	calculation	calculation	NOUN
fumecheng-11687	270	13	.	.	PUNCT
fumecheng-11687	271	1	this	this	DET
fumecheng-11687	271	2	behavior	behavior	NOUN
fumecheng-11687	271	3	is	be	AUX
fumecheng-11687	271	4	expected	expect	VERB
fumecheng-11687	271	5	because	because	SCONJ
fumecheng-11687	271	6	→	→	X
fumecheng-11687	271	7	1	1	NUM
fumecheng-11687	271	8	the	the	DET
fumecheng-11687	271	9	fractal	fractal	ADJ
fumecheng-11687	271	10	parameter	parameter	NOUN
fumecheng-11687	271	11	a(	a(	PROPN
fumecheng-11687	271	12	)	)	PUNCT
fumecheng-11687	271	13	should	should	AUX
fumecheng-11687	271	14	tend	tend	VERB
fumecheng-11687	271	15	to	to	ADP
fumecheng-11687	271	16	zero	zero	NUM
fumecheng-11687	271	17	.	.	PUNCT
fumecheng-11687	272	1	consequently	consequently	ADV
fumecheng-11687	272	2	,	,	PUNCT
fumecheng-11687	272	3	the	the	DET
fumecheng-11687	272	4	damping	damp	VERB
fumecheng-11687	272	5	forces	force	NOUN
fumecheng-11687	272	6	in	in	ADP
fumecheng-11687	272	7	both	both	PRON
fumecheng-11687	272	8	eq	eq	ADJ
fumecheng-11687	272	9	.	.	PUNCT
fumecheng-11687	273	1	(	(	PUNCT
fumecheng-11687	273	2	30	30	NUM
fumecheng-11687	273	3	)	)	PUNCT
fumecheng-11687	273	4	and	and	CCONJ
fumecheng-11687	273	5	eq	eq	NOUN
fumecheng-11687	273	6	.	.	PUNCT
fumecheng-11687	274	1	(	(	PUNCT
fumecheng-11687	274	2	43	43	NUM
fumecheng-11687	274	3	)	)	PUNCT
fumecheng-11687	274	4	will	will	AUX
fumecheng-11687	274	5	disappear	disappear	VERB
fumecheng-11687	274	6	.	.	PUNCT
fumecheng-11687	275	1	the	the	DET
fumecheng-11687	275	2	damping	damp	VERB
fumecheng-11687	275	3	behavior	behavior	NOUN
fumecheng-11687	275	4	will	will	AUX
fumecheng-11687	275	5	appear	appear	VERB
fumecheng-11687	275	6	due	due	ADJ
fumecheng-11687	275	7	to	to	ADP
fumecheng-11687	275	8	the	the	DET
fumecheng-11687	275	9	fractional	fractional	ADJ
fumecheng-11687	275	10	order	order	NOUN
fumecheng-11687	275	11			NOUN
fumecheng-11687	275	12	decreasing	decrease	VERB
fumecheng-11687	275	13	away	away	ADV
fumecheng-11687	275	14	the	the	DET
fumecheng-11687	275	15	unity	unity	NOUN
fumecheng-11687	275	16	as	as	SCONJ
fumecheng-11687	275	17	shown	show	VERB
fumecheng-11687	275	18	in	in	ADP
fumecheng-11687	275	19	fig	fig	NOUN
fumecheng-11687	275	20	.	.	PUNCT
fumecheng-11687	276	1	3	3	X
fumecheng-11687	276	2	.	.	X
fumecheng-11687	276	3	in	in	ADP
fumecheng-11687	276	4	the	the	DET
fumecheng-11687	276	5	graph	graph	NOUN
fumecheng-11687	276	6	of	of	ADP
fumecheng-11687	276	7	fig	fig	NOUN
fumecheng-11687	276	8	.	.	PUNCT
fumecheng-11687	277	1	3	3	NUM
fumecheng-11687	277	2	consequent	consequent	ADJ
fumecheng-11687	277	3	values	value	NOUN
fumecheng-11687	277	4			PRON
fumecheng-11687	277	5	are	be	AUX
fumecheng-11687	277	6	considered	consider	VERB
fumecheng-11687	277	7	and	and	CCONJ
fumecheng-11687	277	8	collected	collect	VERB
fumecheng-11687	277	9	together	together	ADV
fumecheng-11687	277	10	with	with	ADP
fumecheng-11687	277	11	the	the	DET
fumecheng-11687	277	12	case	case	NOUN
fumecheng-11687	277	13	of	of	ADP
fumecheng-11687	277	14			NOUN
fumecheng-11687	277	15			PROPN
fumecheng-11687	277	16	1	1	NUM
fumecheng-11687	277	17	.	.	PUNCT
fumecheng-11687	278	1	the	the	DET
fumecheng-11687	278	2	agreement	agreement	NOUN
fumecheng-11687	278	3	between	between	ADP
fumecheng-11687	278	4	the	the	DET
fumecheng-11687	278	5	numerical	numerical	ADJ
fumecheng-11687	278	6	solution	solution	NOUN
fumecheng-11687	278	7	and	and	CCONJ
fumecheng-11687	278	8	the	the	DET
fumecheng-11687	278	9	analytical	analytical	ADJ
fumecheng-11687	278	10	solution	solution	NOUN
fumecheng-11687	278	11	is	be	AUX
fumecheng-11687	278	12	still	still	ADV
fumecheng-11687	278	13	observed	observe	VERB
fumecheng-11687	278	14	even	even	ADV
fumecheng-11687	278	15	when	when	SCONJ
fumecheng-11687	278	16	the	the	DET
fumecheng-11687	278	17	value	value	NOUN
fumecheng-11687	278	18	of	of	ADP
fumecheng-11687	278	19			NOUN
fumecheng-11687	278	20	decreases	decrease	VERB
fumecheng-11687	278	21	from	from	ADP
fumecheng-11687	278	22	one	one	NUM
fumecheng-11687	278	23	to	to	ADP
fumecheng-11687	278	24	zero	zero	NUM
fumecheng-11687	278	25	.	.	PUNCT
fumecheng-11687	279	1	the	the	DET
fumecheng-11687	279	2	comparison	comparison	NOUN
fumecheng-11687	279	3	shows	show	VERB
fumecheng-11687	279	4	that	that	SCONJ
fumecheng-11687	279	5	the	the	DET
fumecheng-11687	279	6	damping	damp	VERB
fumecheng-11687	279	7	behavior	behavior	NOUN
fumecheng-11687	279	8	increases	increase	VERB
fumecheng-11687	279	9	with	with	ADP
fumecheng-11687	279	10	decreasing	decrease	VERB
fumecheng-11687	279	11	in	in	ADP
fumecheng-11687	279	12	.	.	NOUN
fumecheng-11687	279	13	in	in	ADP
fumecheng-11687	279	14	a	a	DET
fumecheng-11687	279	15	word	word	NOUN
fumecheng-11687	279	16	,	,	PUNCT
fumecheng-11687	279	17	the	the	DET
fumecheng-11687	279	18	computations	computation	NOUN
fumecheng-11687	279	19	revealed	reveal	VERB
fumecheng-11687	279	20	that	that	SCONJ
fumecheng-11687	279	21	for	for	ADP
fumecheng-11687	279	22	every	every	DET
fumecheng-11687	279	23	value	value	NOUN
fumecheng-11687	279	24	of	of	ADP
fumecheng-11687	279	25	the	the	DET
fumecheng-11687	279	26	fraction	fraction	NOUN
fumecheng-11687	279	27	parameter	parameter	NOUN
fumecheng-11687	279	28	,	,	PUNCT
fumecheng-11687	279	29	the	the	DET
fumecheng-11687	279	30	approximation	approximation	NOUN
fumecheng-11687	279	31	and	and	CCONJ
fumecheng-11687	279	32	numerical	numerical	ADJ
fumecheng-11687	279	33	solutions	solution	NOUN
fumecheng-11687	279	34	are	be	AUX
fumecheng-11687	279	35	identical	identical	ADJ
fumecheng-11687	279	36	.	.	PUNCT
fumecheng-11687	280	1	from	from	ADP
fumecheng-11687	280	2	the	the	DET
fumecheng-11687	280	3	above	above	ADJ
fumecheng-11687	280	4	figures	figure	NOUN
fumecheng-11687	280	5	,	,	PUNCT
fumecheng-11687	280	6	the	the	DET
fumecheng-11687	280	7	present	present	ADJ
fumecheng-11687	280	8	study	study	NOUN
fumecheng-11687	280	9	gives	give	VERB
fumecheng-11687	280	10	reliability	reliability	NOUN
fumecheng-11687	280	11	to	to	ADP
fumecheng-11687	280	12	the	the	DET
fumecheng-11687	280	13	technique	technique	NOUN
fumecheng-11687	280	14	of	of	ADP
fumecheng-11687	280	15	reducing	reduce	VERB
fumecheng-11687	280	16	the	the	DET
fumecheng-11687	280	17	order	order	NOUN
fumecheng-11687	280	18	of	of	ADP
fumecheng-11687	280	19	differential	differential	ADJ
fumecheng-11687	280	20	equations	equation	NOUN
fumecheng-11687	280	21	.	.	PUNCT
fumecheng-11687	281	1	this	this	PRON
fumecheng-11687	281	2	makes	make	VERB
fumecheng-11687	281	3	us	we	PRON
fumecheng-11687	281	4	think	think	VERB
fumecheng-11687	281	5	that	that	SCONJ
fumecheng-11687	281	6	the	the	DET
fumecheng-11687	281	7	alternative	alternative	ADJ
fumecheng-11687	281	8	equation	equation	NOUN
fumecheng-11687	281	9	can	can	AUX
fumecheng-11687	281	10	be	be	AUX
fumecheng-11687	281	11	handled	handle	VERB
fumecheng-11687	281	12	,	,	PUNCT
fumecheng-11687	281	13	discussed	discuss	VERB
fumecheng-11687	281	14	,	,	PUNCT
fumecheng-11687	281	15	and	and	CCONJ
fumecheng-11687	281	16	then	then	ADV
fumecheng-11687	281	17	the	the	DET
fumecheng-11687	281	18	solutions	solution	NOUN
fumecheng-11687	281	19	can	can	AUX
fumecheng-11687	281	20	be	be	AUX
fumecheng-11687	281	21	used	use	VERB
fumecheng-11687	281	22	as	as	ADP
fumecheng-11687	281	23	a	a	DET
fumecheng-11687	281	24	reliable	reliable	ADJ
fumecheng-11687	281	25	indicator	indicator	NOUN
fumecheng-11687	281	26	.	.	PUNCT
fumecheng-11687	282	1	fig	fig	NOUN
fumecheng-11687	282	2	.	.	PUNCT
fumecheng-11687	283	1	1	1	NUM
fumecheng-11687	283	2	comparison	comparison	NOUN
fumecheng-11687	283	3	of	of	ADP
fumecheng-11687	283	4	the	the	DET
fumecheng-11687	283	5	numerical	numerical	ADJ
fumecheng-11687	283	6	solution	solution	NOUN
fumecheng-11687	283	7	of	of	ADP
fumecheng-11687	283	8	the	the	DET
fumecheng-11687	283	9	original	original	ADJ
fumecheng-11687	283	10	forced	force	VERB
fumecheng-11687	283	11	fractal	fractal	ADJ
fumecheng-11687	283	12	nonlinear	nonlinear	PROPN
fumecheng-11687	283	13	oscillator	oscillator	NOUN
fumecheng-11687	283	14	given	give	VERB
fumecheng-11687	283	15	in	in	ADP
fumecheng-11687	283	16	eq	eq	ADP
fumecheng-11687	283	17	.	.	PUNCT
fumecheng-11687	284	1	(	(	PUNCT
fumecheng-11687	284	2	13	13	NUM
fumecheng-11687	284	3	)	)	PUNCT
fumecheng-11687	284	4	with	with	ADP
fumecheng-11687	284	5	the	the	DET
fumecheng-11687	284	6	analytical	analytical	ADJ
fumecheng-11687	284	7	solution	solution	NOUN
fumecheng-11687	284	8	given	give	VERB
fumecheng-11687	284	9	in	in	ADP
fumecheng-11687	284	10	eq	eq	ADP
fumecheng-11687	284	11	.	.	PUNCT
fumecheng-11687	285	1	(	(	PUNCT
fumecheng-11687	285	2	46	46	NUM
fumecheng-11687	285	3	)	)	PUNCT
fumecheng-11687	285	4	at	at	ADP
fumecheng-11687	285	5			NOUN
fumecheng-11687	285	6	is	be	AUX
fumecheng-11687	285	7	very	very	ADV
fumecheng-11687	285	8	close	close	ADJ
fumecheng-11687	285	9	to	to	ADP
fumecheng-11687	285	10	unity	unity	NOUN
fumecheng-11687	285	11	for	for	ADP
fumecheng-11687	285	12	the	the	DET
fumecheng-11687	285	13	system	system	NOUN
fumecheng-11687	285	14	having	have	VERB
fumecheng-11687	285	15	a	a	DET
fumecheng-11687	285	16	=	=	X
fumecheng-11687	285	17	0	0	X
fumecheng-11687	285	18	=	=	NOUN
fumecheng-11687	285	19	1	1	NUM
fumecheng-11687	285	20	,	,	PUNCT
fumecheng-11687	285	21	q	q	X
fumecheng-11687	286	1	=	=	SYM
fumecheng-11687	286	2			NUM
fumecheng-11687	286	3	=	=	NOUN
fumecheng-11687	286	4	0.01	0.01	NUM
fumecheng-11687	286	5	,	,	PUNCT
fumecheng-11687	286	6	and	and	CCONJ
fumecheng-11687	286	7	=10	=10	DET
fumecheng-11687	286	8	fig	fig	NOUN
fumecheng-11687	286	9	.	.	PUNCT
fumecheng-11687	287	1	2	2	NUM
fumecheng-11687	287	2	comparison	comparison	NOUN
fumecheng-11687	287	3	of	of	ADP
fumecheng-11687	287	4	the	the	DET
fumecheng-11687	287	5	analytical	analytical	ADJ
fumecheng-11687	287	6	solution	solution	NOUN
fumecheng-11687	287	7	given	give	VERB
fumecheng-11687	287	8	in	in	ADP
fumecheng-11687	287	9	eq	eq	ADP
fumecheng-11687	287	10	.	.	PUNCT
fumecheng-11687	288	1	(	(	PUNCT
fumecheng-11687	288	2	46	46	NUM
fumecheng-11687	288	3	)	)	PUNCT
fumecheng-11687	288	4	with	with	ADP
fumecheng-11687	288	5	the	the	DET
fumecheng-11687	288	6	numerical	numerical	ADJ
fumecheng-11687	288	7	one	one	NUM
fumecheng-11687	288	8	of	of	ADP
fumecheng-11687	288	9	eq	eq	PROPN
fumecheng-11687	288	10	.	.	PUNCT
fumecheng-11687	289	1	(	(	PUNCT
fumecheng-11687	289	2	30	30	NUM
fumecheng-11687	289	3	)	)	PUNCT
fumecheng-11687	289	4	in	in	ADP
fumecheng-11687	289	5	the	the	DET
fumecheng-11687	289	6	case	case	NOUN
fumecheng-11687	289	7	of	of	ADP
fumecheng-11687	289	8	at	at	ADP
fumecheng-11687	289	9	→	→	X
fumecheng-11687	289	10	1	1	NUM
fumecheng-11687	289	11	for	for	ADP
fumecheng-11687	289	12	the	the	DET
fumecheng-11687	289	13	system	system	NOUN
fumecheng-11687	289	14	having	have	VERB
fumecheng-11687	289	15	a	a	DET
fumecheng-11687	289	16	=	=	X
fumecheng-11687	289	17	0	0	X
fumecheng-11687	289	18	=	=	NOUN
fumecheng-11687	289	19	1	1	NUM
fumecheng-11687	289	20	,	,	PUNCT
fumecheng-11687	289	21	q	q	X
fumecheng-11687	290	1	=	=	SYM
fumecheng-11687	290	2			NUM
fumecheng-11687	290	3	=	=	NOUN
fumecheng-11687	290	4	0.01	0.01	NUM
fumecheng-11687	290	5	,	,	PUNCT
fumecheng-11687	290	6	and	and	CCONJ
fumecheng-11687	290	7	=10	=10	ADP
fumecheng-11687	290	8	the	the	DET
fumecheng-11687	290	9	up	up	ADV
fumecheng-11687	290	10	-	-	PUNCT
fumecheng-11687	290	11	grating	grate	VERB
fumecheng-11687	290	12	rank	rank	NOUN
fumecheng-11687	290	13	approach	approach	NOUN
fumecheng-11687	290	14	to	to	PART
fumecheng-11687	290	15	solve	solve	VERB
fumecheng-11687	290	16	a	a	DET
fumecheng-11687	290	17	forced	force	VERB
fumecheng-11687	290	18	fractal	fractal	ADJ
fumecheng-11687	290	19	duffing	duffing	NOUN
fumecheng-11687	290	20	oscillator	oscillator	NOUN
fumecheng-11687	290	21	by	by	ADP
fumecheng-11687	290	22	the	the	DET
fumecheng-11687	290	23	np	np	PROPN
fumecheng-11687	290	24	technique	technique	NOUN
fumecheng-11687	290	25	209	209	NUM
fumecheng-11687	290	26	fig	fig	NOUN
fumecheng-11687	290	27	.	.	PUNCT
fumecheng-11687	291	1	3	3	NUM
fumecheng-11687	291	2	represents	represent	VERB
fumecheng-11687	291	3	to	to	ADP
fumecheng-11687	291	4	the	the	DET
fumecheng-11687	291	5	influence	influence	NOUN
fumecheng-11687	291	6	of	of	ADP
fumecheng-11687	291	7	the	the	DET
fumecheng-11687	291	8	variation	variation	NOUN
fumecheng-11687	291	9	in	in	ADP
fumecheng-11687	291	10			NOUN
fumecheng-11687	291	11	on	on	ADP
fumecheng-11687	291	12	the	the	DET
fumecheng-11687	291	13	comparison	comparison	NOUN
fumecheng-11687	291	14	of	of	ADP
fumecheng-11687	291	15	the	the	DET
fumecheng-11687	291	16	analytical	analytical	ADJ
fumecheng-11687	291	17	solution	solution	NOUN
fumecheng-11687	291	18	given	give	VERB
fumecheng-11687	291	19	in	in	ADP
fumecheng-11687	291	20	eq	eq	ADP
fumecheng-11687	291	21	.	.	PUNCT
fumecheng-11687	292	1	(	(	PUNCT
fumecheng-11687	292	2	46	46	NUM
fumecheng-11687	292	3	)	)	PUNCT
fumecheng-11687	292	4	with	with	ADP
fumecheng-11687	292	5	the	the	DET
fumecheng-11687	292	6	numerical	numerical	ADJ
fumecheng-11687	292	7	one	one	NUM
fumecheng-11687	292	8	of	of	ADP
fumecheng-11687	292	9	eq	eq	PROPN
fumecheng-11687	292	10	.	.	PUNCT
fumecheng-11687	293	1	(	(	PUNCT
fumecheng-11687	293	2	30	30	NUM
fumecheng-11687	293	3	)	)	PUNCT
fumecheng-11687	293	4	for	for	ADP
fumecheng-11687	293	5	a	a	DET
fumecheng-11687	293	6	=	=	X
fumecheng-11687	293	7	0	0	X
fumecheng-11687	293	8	=	=	NOUN
fumecheng-11687	293	9	1	1	NUM
fumecheng-11687	293	10	,	,	PUNCT
fumecheng-11687	293	11	q	q	NOUN
fumecheng-11687	294	1	=	=	SYM
fumecheng-11687	294	2			NUM
fumecheng-11687	294	3	=	=	SYM
fumecheng-11687	294	4	0.01	0.01	NUM
fumecheng-11687	294	5	,	,	PUNCT
fumecheng-11687	294	6	and	and	CCONJ
fumecheng-11687	294	7			NUM
fumecheng-11687	295	1	=	=	NOUN
fumecheng-11687	295	2	10	10	NUM
fumecheng-11687	295	3	in	in	ADP
fumecheng-11687	295	4	figs	fig	NOUN
fumecheng-11687	295	5	.	.	PUNCT
fumecheng-11687	296	1	4	4	NUM
fumecheng-11687	296	2	-	-	SYM
fumecheng-11687	296	3	6	6	NUM
fumecheng-11687	296	4	the	the	DET
fumecheng-11687	296	5	examinations	examination	NOUN
fumecheng-11687	296	6	are	be	AUX
fumecheng-11687	296	7	done	do	VERB
fumecheng-11687	296	8	for	for	ADP
fumecheng-11687	296	9	the	the	DET
fumecheng-11687	296	10	amplitude	amplitude	NOUN
fumecheng-11687	296	11	and	and	CCONJ
fumecheng-11687	296	12	the	the	DET
fumecheng-11687	296	13	frequency	frequency	NOUN
fumecheng-11687	296	14	of	of	ADP
fumecheng-11687	296	15	the	the	DET
fumecheng-11687	296	16	applied	apply	VERB
fumecheng-11687	296	17	periodic	periodic	ADJ
fumecheng-11687	296	18	force	force	NOUN
fumecheng-11687	296	19	.	.	PUNCT
fumecheng-11687	297	1	for	for	ADP
fumecheng-11687	297	2	this	this	DET
fumecheng-11687	297	3	purpose	purpose	NOUN
fumecheng-11687	297	4	,	,	PUNCT
fumecheng-11687	297	5	the	the	DET
fumecheng-11687	297	6	fractional	fractional	ADJ
fumecheng-11687	297	7	order	order	NOUN
fumecheng-11687	297	8	is	be	AUX
fumecheng-11687	297	9	held	hold	VERB
fumecheng-11687	297	10	at	at	ADP
fumecheng-11687	297	11			NOUN
fumecheng-11687	297	12	=	=	SYM
fumecheng-11687	297	13	.	.	PROPN
fumecheng-11687	297	14	the	the	DET
fumecheng-11687	297	15	calculations	calculation	NOUN
fumecheng-11687	297	16	are	be	AUX
fumecheng-11687	297	17	used	use	VERB
fumecheng-11687	297	18	in	in	ADP
fumecheng-11687	297	19	the	the	DET
fumecheng-11687	297	20	same	same	ADJ
fumecheng-11687	297	21	system	system	NOUN
fumecheng-11687	297	22	as	as	SCONJ
fumecheng-11687	297	23	given	give	VERB
fumecheng-11687	297	24	in	in	ADP
fumecheng-11687	297	25	fig	fig	NOUN
fumecheng-11687	297	26	.	.	PUNCT
fumecheng-11687	298	1	2	2	NUM
fumecheng-11687	298	2	,	,	PUNCT
fumecheng-11687	298	3	with	with	ADP
fumecheng-11687	298	4	alternative	alternative	ADJ
fumecheng-11687	298	5	values	value	NOUN
fumecheng-11687	298	6	of	of	ADP
fumecheng-11687	298	7	the	the	DET
fumecheng-11687	298	8	parameters	parameter	NOUN
fumecheng-11687	298	9			NUM
fumecheng-11687	298	10	and	and	CCONJ
fumecheng-11687	298	11	.	.	NUM
fumecheng-11687	298	12	it	it	PRON
fumecheng-11687	298	13	is	be	AUX
fumecheng-11687	298	14	noted	note	VERB
fumecheng-11687	298	15	that	that	SCONJ
fumecheng-11687	298	16	the	the	DET
fumecheng-11687	298	17	relative	relative	ADJ
fumecheng-11687	298	18	error	error	NOUN
fumecheng-11687	298	19	is	be	AUX
fumecheng-11687	298	20	0.1189	0.1189	NUM
fumecheng-11687	298	21	when	when	SCONJ
fumecheng-11687	298	22			ADJ
fumecheng-11687	298	23	=	=	NOUN
fumecheng-11687	298	24	0.1	0.1	NUM
fumecheng-11687	298	25	,	,	PUNCT
fumecheng-11687	298	26	see	see	VERB
fumecheng-11687	298	27	fig	fig	NOUN
fumecheng-11687	298	28	.	.	PUNCT
fumecheng-11687	299	1	4	4	NUM
fumecheng-11687	299	2	,	,	PUNCT
fumecheng-11687	299	3	but	but	CCONJ
fumecheng-11687	299	4	this	this	DET
fumecheng-11687	299	5	error	error	NOUN
fumecheng-11687	299	6	becomes	become	VERB
fumecheng-11687	299	7	0.3281	0.3281	NUM
fumecheng-11687	299	8	as	as	ADP
fumecheng-11687	299	9			NUM
fumecheng-11687	299	10	=	=	SYM
fumecheng-11687	299	11	0.2	0.2	NUM
fumecheng-11687	299	12	shown	show	VERB
fumecheng-11687	299	13	in	in	ADP
fumecheng-11687	299	14	fig	fig	NOUN
fumecheng-11687	299	15	.	.	PUNCT
fumecheng-11687	300	1	5	5	X
fumecheng-11687	300	2	.	.	X
fumecheng-11687	300	3	therefore	therefore	ADV
fumecheng-11687	300	4	,	,	PUNCT
fumecheng-11687	300	5	when	when	SCONJ
fumecheng-11687	300	6	comparing	compare	VERB
fumecheng-11687	300	7	fig	fig	NOUN
fumecheng-11687	300	8	.	.	PUNCT
fumecheng-11687	300	9	4	4	NUM
fumecheng-11687	300	10	with	with	ADP
fumecheng-11687	300	11	fig	fig	NOUN
fumecheng-11687	300	12	.	.	PUNCT
fumecheng-11687	301	1	5	5	NUM
fumecheng-11687	301	2	,	,	PUNCT
fumecheng-11687	301	3	it	it	PRON
fumecheng-11687	301	4	becomes	become	VERB
fumecheng-11687	301	5	clear	clear	ADJ
fumecheng-11687	301	6	that	that	SCONJ
fumecheng-11687	301	7	small	small	ADJ
fumecheng-11687	301	8	delta	delta	NOUN
fumecheng-11687	301	9	values	value	NOUN
fumecheng-11687	301	10	make	make	VERB
fumecheng-11687	301	11	the	the	DET
fumecheng-11687	301	12	solution	solution	NOUN
fumecheng-11687	301	13	more	more	ADV
fumecheng-11687	301	14	accurate	accurate	ADJ
fumecheng-11687	301	15	than	than	ADP
fumecheng-11687	301	16	larger	large	ADJ
fumecheng-11687	301	17	values	value	NOUN
fumecheng-11687	301	18	.	.	PUNCT
fumecheng-11687	302	1	when	when	SCONJ
fumecheng-11687	302	2			PROPN
fumecheng-11687	302	3	is	be	AUX
fumecheng-11687	302	4	held	hold	VERB
fumecheng-11687	302	5	at	at	ADP
fumecheng-11687	302	6			NUM
fumecheng-11687	302	7	=	=	NOUN
fumecheng-11687	302	8	0.1	0.1	NUM
fumecheng-11687	302	9	with	with	ADP
fumecheng-11687	302	10	changes	change	NOUN
fumecheng-11687	302	11	in	in	ADP
fumecheng-11687	302	12			PROPN
fumecheng-11687	302	13	from	from	ADP
fumecheng-11687	302	14	7	7	NUM
fumecheng-11687	302	15	to	to	PART
fumecheng-11687	302	16	10	10	NUM
fumecheng-11687	302	17	as	as	ADV
fumecheng-11687	302	18	observed	observe	VERB
fumecheng-11687	302	19	in	in	ADP
fumecheng-11687	302	20	fig	fig	NOUN
fumecheng-11687	302	21	.	.	PUNCT
fumecheng-11687	303	1	6	6	NUM
fumecheng-11687	303	2	,	,	PUNCT
fumecheng-11687	303	3	the	the	DET
fumecheng-11687	303	4	relative	relative	ADJ
fumecheng-11687	303	5	error	error	NOUN
fumecheng-11687	303	6	has	have	AUX
fumecheng-11687	303	7	increased	increase	VERB
fumecheng-11687	303	8	for	for	ADP
fumecheng-11687	303	9	the	the	DET
fumecheng-11687	303	10	case	case	NOUN
fumecheng-11687	303	11	of	of	ADP
fumecheng-11687	303	12	large	large	ADJ
fumecheng-11687	303	13	values	value	NOUN
fumecheng-11687	303	14	of	of	ADP
fumecheng-11687	303	15	.	.	X
fumecheng-11687	303	16	hence	hence	ADV
fumecheng-11687	303	17	,	,	PUNCT
fumecheng-11687	303	18	the	the	DET
fumecheng-11687	303	19	comparison	comparison	NOUN
fumecheng-11687	303	20	between	between	ADP
fumecheng-11687	303	21	figs	fig	NOUN
fumecheng-11687	303	22	.	.	PUNCT
fumecheng-11687	304	1	4	4	NUM
fumecheng-11687	304	2	and	and	CCONJ
fumecheng-11687	304	3	6	6	NUM
fumecheng-11687	304	4	means	mean	VERB
fumecheng-11687	304	5	that	that	SCONJ
fumecheng-11687	304	6	the	the	DET
fumecheng-11687	304	7	increase	increase	NOUN
fumecheng-11687	304	8	in	in	ADP
fumecheng-11687	304	9			PROPN
fumecheng-11687	304	10	leads	lead	VERB
fumecheng-11687	304	11	to	to	ADP
fumecheng-11687	304	12	improving	improve	VERB
fumecheng-11687	304	13	the	the	DET
fumecheng-11687	304	14	accuracy	accuracy	NOUN
fumecheng-11687	304	15	of	of	ADP
fumecheng-11687	304	16	the	the	DET
fumecheng-11687	304	17	solution	solution	NOUN
fumecheng-11687	304	18	.	.	PUNCT
fumecheng-11687	305	1	it	it	PRON
fumecheng-11687	305	2	should	should	AUX
fumecheng-11687	305	3	be	be	AUX
fumecheng-11687	305	4	noted	note	VERB
fumecheng-11687	305	5	that	that	SCONJ
fumecheng-11687	305	6	one	one	NUM
fumecheng-11687	305	7	of	of	ADP
fumecheng-11687	305	8	the	the	DET
fumecheng-11687	305	9	most	most	ADV
fumecheng-11687	305	10	important	important	ADJ
fumecheng-11687	305	11	features	feature	NOUN
fumecheng-11687	305	12	of	of	ADP
fumecheng-11687	305	13	these	these	DET
fumecheng-11687	305	14	calculations	calculation	NOUN
fumecheng-11687	305	15	is	be	AUX
fumecheng-11687	305	16	that	that	SCONJ
fumecheng-11687	305	17	the	the	DET
fumecheng-11687	305	18	fourth	fourth	ADJ
fumecheng-11687	305	19	-	-	PUNCT
fumecheng-11687	305	20	order	order	NOUN
fumecheng-11687	305	21	equation	equation	NOUN
fumecheng-11687	305	22	can	can	AUX
fumecheng-11687	305	23	be	be	AUX
fumecheng-11687	305	24	reduced	reduce	VERB
fumecheng-11687	305	25	to	to	ADP
fumecheng-11687	305	26	a	a	DET
fumecheng-11687	305	27	second	second	ADJ
fumecheng-11687	305	28	-	-	PUNCT
fumecheng-11687	305	29	order	order	NOUN
fumecheng-11687	305	30	one	one	NOUN
fumecheng-11687	305	31	via	via	ADP
fumecheng-11687	305	32	the	the	DET
fumecheng-11687	305	33	non	non	ADJ
fumecheng-11687	305	34	-	-	ADJ
fumecheng-11687	305	35	perturbative	perturbative	ADJ
fumecheng-11687	305	36	approach	approach	NOUN
fumecheng-11687	305	37	.	.	PUNCT
fumecheng-11687	306	1	fig	fig	NOUN
fumecheng-11687	306	2	.	.	PUNCT
fumecheng-11687	307	1	4	4	NUM
fumecheng-11687	307	2	the	the	DET
fumecheng-11687	307	3	relative	relative	ADJ
fumecheng-11687	307	4	error	error	NOUN
fumecheng-11687	307	5	due	due	ADP
fumecheng-11687	307	6	to	to	ADP
fumecheng-11687	307	7	the	the	DET
fumecheng-11687	307	8	comparison	comparison	NOUN
fumecheng-11687	307	9	of	of	ADP
fumecheng-11687	307	10	the	the	DET
fumecheng-11687	307	11	analytical	analytical	ADJ
fumecheng-11687	307	12	solution	solution	NOUN
fumecheng-11687	307	13	given	give	VERB
fumecheng-11687	307	14	in	in	ADP
fumecheng-11687	307	15	eq	eq	ADP
fumecheng-11687	307	16	.	.	PUNCT
fumecheng-11687	308	1	(	(	PUNCT
fumecheng-11687	308	2	46	46	NUM
fumecheng-11687	308	3	)	)	PUNCT
fumecheng-11687	308	4	with	with	ADP
fumecheng-11687	308	5	the	the	DET
fumecheng-11687	308	6	numerical	numerical	ADJ
fumecheng-11687	308	7	one	one	NUM
fumecheng-11687	308	8	of	of	ADP
fumecheng-11687	308	9	eq	eq	PROPN
fumecheng-11687	308	10	.	.	PUNCT
fumecheng-11687	309	1	(	(	PUNCT
fumecheng-11687	309	2	30	30	NUM
fumecheng-11687	309	3	)	)	PUNCT
fumecheng-11687	309	4	for	for	ADP
fumecheng-11687	309	5	a	a	DET
fumecheng-11687	309	6	=	=	X
fumecheng-11687	309	7	0	0	X
fumecheng-11687	309	8	=	=	NOUN
fumecheng-11687	309	9	1	1	NUM
fumecheng-11687	309	10	,	,	PUNCT
fumecheng-11687	309	11	q	q	NOUN
fumecheng-11687	310	1	=	=	NOUN
fumecheng-11687	310	2	0.01	0.01	NUM
fumecheng-11687	310	3	,	,	PUNCT
fumecheng-11687	310	4			NUM
fumecheng-11687	310	5	=	=	SYM
fumecheng-11687	310	6	0.1	0.1	NUM
fumecheng-11687	310	7	,	,	PUNCT
fumecheng-11687	310	8			X
fumecheng-11687	310	9	=	=	SYM
fumecheng-11687	310	10	0.9	0.9	NUM
fumecheng-11687	310	11	,	,	PUNCT
fumecheng-11687	310	12	and	and	CCONJ
fumecheng-11687	310	13			NUM
fumecheng-11687	310	14	=	=	NOUN
fumecheng-11687	310	15	7	7	NUM
fumecheng-11687	310	16	210	210	NUM
fumecheng-11687	310	17	y.o	y.o	PROPN
fumecheng-11687	310	18	.	.	PROPN
fumecheng-11687	310	19	el	el	PROPN
fumecheng-11687	310	20	-	-	PUNCT
fumecheng-11687	310	21	dib	dib	PROPN
fumecheng-11687	310	22	,	,	PUNCT
fumecheng-11687	310	23	n.s	n.s	PROPN
fumecheng-11687	310	24	.	.	PROPN
fumecheng-11687	310	25	elgazery	elgazery	PROPN
fumecheng-11687	310	26	,	,	PUNCT
fumecheng-11687	310	27	h.a	h.a	PROPN
fumecheng-11687	310	28	.	.	PROPN
fumecheng-11687	310	29	alyousef	alyousef	PROPN
fumecheng-11687	310	30	fig	fig	PROPN
fumecheng-11687	310	31	.	.	PUNCT
fumecheng-11687	310	32	5	5	NUM
fumecheng-11687	311	1	the	the	DET
fumecheng-11687	311	2	relative	relative	ADJ
fumecheng-11687	311	3	error	error	NOUN
fumecheng-11687	311	4	due	due	ADP
fumecheng-11687	311	5	to	to	ADP
fumecheng-11687	311	6	the	the	DET
fumecheng-11687	311	7	comparison	comparison	NOUN
fumecheng-11687	311	8	of	of	ADP
fumecheng-11687	311	9	the	the	DET
fumecheng-11687	311	10	analytical	analytical	ADJ
fumecheng-11687	311	11	solution	solution	NOUN
fumecheng-11687	311	12	given	give	VERB
fumecheng-11687	311	13	in	in	ADP
fumecheng-11687	311	14	eq	eq	ADP
fumecheng-11687	311	15	.	.	PUNCT
fumecheng-11687	312	1	(	(	PUNCT
fumecheng-11687	312	2	46	46	NUM
fumecheng-11687	312	3	)	)	PUNCT
fumecheng-11687	312	4	with	with	ADP
fumecheng-11687	312	5	the	the	DET
fumecheng-11687	312	6	numerical	numerical	ADJ
fumecheng-11687	312	7	one	one	NUM
fumecheng-11687	312	8	of	of	ADP
fumecheng-11687	312	9	eq	eq	PROPN
fumecheng-11687	312	10	.	.	PUNCT
fumecheng-11687	313	1	(	(	PUNCT
fumecheng-11687	313	2	30	30	NUM
fumecheng-11687	313	3	)	)	PUNCT
fumecheng-11687	313	4	for	for	ADP
fumecheng-11687	313	5	a	a	DET
fumecheng-11687	313	6	=	=	X
fumecheng-11687	313	7	0	0	X
fumecheng-11687	313	8	=	=	NOUN
fumecheng-11687	313	9	1	1	NUM
fumecheng-11687	313	10	,	,	PUNCT
fumecheng-11687	313	11	q	q	NOUN
fumecheng-11687	314	1	=	=	NOUN
fumecheng-11687	314	2	0.01	0.01	NUM
fumecheng-11687	314	3	,	,	PUNCT
fumecheng-11687	314	4			NUM
fumecheng-11687	314	5	=	=	SYM
fumecheng-11687	314	6	0.2	0.2	NUM
fumecheng-11687	314	7	,	,	PUNCT
fumecheng-11687	314	8			X
fumecheng-11687	314	9	=	=	SYM
fumecheng-11687	314	10	0.9	0.9	NUM
fumecheng-11687	314	11	,	,	PUNCT
fumecheng-11687	314	12	and	and	CCONJ
fumecheng-11687	314	13			NUM
fumecheng-11687	314	14	=	=	SYM
fumecheng-11687	314	15	7	7	NUM
fumecheng-11687	314	16	fig	fig	NOUN
fumecheng-11687	314	17	.	.	PUNCT
fumecheng-11687	315	1	6	6	NUM
fumecheng-11687	315	2	the	the	DET
fumecheng-11687	315	3	relative	relative	ADJ
fumecheng-11687	315	4	error	error	NOUN
fumecheng-11687	315	5	due	due	ADP
fumecheng-11687	315	6	to	to	ADP
fumecheng-11687	315	7	the	the	DET
fumecheng-11687	315	8	comparison	comparison	NOUN
fumecheng-11687	315	9	of	of	ADP
fumecheng-11687	315	10	the	the	DET
fumecheng-11687	315	11	analytical	analytical	ADJ
fumecheng-11687	315	12	solution	solution	NOUN
fumecheng-11687	315	13	given	give	VERB
fumecheng-11687	315	14	in	in	ADP
fumecheng-11687	315	15	eq	eq	ADP
fumecheng-11687	315	16	.	.	PUNCT
fumecheng-11687	316	1	(	(	PUNCT
fumecheng-11687	316	2	46	46	NUM
fumecheng-11687	316	3	)	)	PUNCT
fumecheng-11687	316	4	with	with	ADP
fumecheng-11687	316	5	the	the	DET
fumecheng-11687	316	6	numerical	numerical	ADJ
fumecheng-11687	316	7	one	one	NUM
fumecheng-11687	316	8	of	of	ADP
fumecheng-11687	316	9	eq	eq	PROPN
fumecheng-11687	316	10	.	.	PUNCT
fumecheng-11687	317	1	(	(	PUNCT
fumecheng-11687	317	2	30	30	NUM
fumecheng-11687	317	3	)	)	PUNCT
fumecheng-11687	317	4	for	for	ADP
fumecheng-11687	317	5	a	a	DET
fumecheng-11687	317	6	=	=	X
fumecheng-11687	317	7	0	0	X
fumecheng-11687	317	8	=	=	NOUN
fumecheng-11687	317	9	1	1	NUM
fumecheng-11687	317	10	,	,	PUNCT
fumecheng-11687	317	11	q	q	NOUN
fumecheng-11687	318	1	=	=	NOUN
fumecheng-11687	318	2	0.01	0.01	NUM
fumecheng-11687	318	3	,	,	PUNCT
fumecheng-11687	318	4			NUM
fumecheng-11687	318	5	=	=	SYM
fumecheng-11687	318	6	0.1	0.1	NUM
fumecheng-11687	318	7	,	,	PUNCT
fumecheng-11687	318	8			X
fumecheng-11687	318	9	=	=	SYM
fumecheng-11687	318	10	0.9	0.9	NUM
fumecheng-11687	318	11	,	,	PUNCT
fumecheng-11687	318	12	and	and	CCONJ
fumecheng-11687	318	13			NUM
fumecheng-11687	318	14	=	=	NOUN
fumecheng-11687	318	15	10	10	NUM
fumecheng-11687	318	16	5	5	NUM
fumecheng-11687	318	17	.	.	PUNCT
fumecheng-11687	318	18	periodic	periodic	ADJ
fumecheng-11687	318	19	solution	solution	NOUN
fumecheng-11687	318	20	on	on	ADP
fumecheng-11687	318	21	the	the	DET
fumecheng-11687	318	22	other	other	ADJ
fumecheng-11687	318	23	side	side	NOUN
fumecheng-11687	318	24	,	,	PUNCT
fumecheng-11687	318	25	the	the	DET
fumecheng-11687	318	26	periodic	periodic	ADJ
fumecheng-11687	318	27	solution	solution	NOUN
fumecheng-11687	318	28	of	of	ADP
fumecheng-11687	318	29	eq	eq	PROPN
fumecheng-11687	318	30	.	.	PUNCT
fumecheng-11687	319	1	(	(	PUNCT
fumecheng-11687	319	2	43	43	NUM
fumecheng-11687	319	3	)	)	PUNCT
fumecheng-11687	319	4	can	can	AUX
fumecheng-11687	319	5	be	be	AUX
fumecheng-11687	319	6	established	establish	VERB
fumecheng-11687	319	7	,	,	PUNCT
fumecheng-11687	319	8	for	for	ADP
fumecheng-11687	319	9	a	a	DET
fumecheng-11687	319	10	non	non	ADJ
fumecheng-11687	319	11	-	-	ADJ
fumecheng-11687	319	12	zero	zero	ADJ
fumecheng-11687	319	13	coefficient	coefficient	NOUN
fumecheng-11687	319	14	(	(	NOUN
fumecheng-11687	319	15	)	)	PUNCT
fumecheng-11687	319	16	.	.	PUNCT
fumecheng-11687	320	1	in	in	ADP
fumecheng-11687	320	2	this	this	DET
fumecheng-11687	320	3	case	case	NOUN
fumecheng-11687	320	4	,	,	PUNCT
fumecheng-11687	320	5	the	the	DET
fumecheng-11687	320	6	frequency	frequency	NOUN
fumecheng-11687	320	7			X
fumecheng-11687	320	8	will	will	AUX
fumecheng-11687	320	9	recall	recall	VERB
fumecheng-11687	320	10	�	�	PROPN
fumecheng-11687	320	11	̂	̂	PROPN
fumecheng-11687	320	12	�	�	PROPN
fumecheng-11687	320	13	which	which	PRON
fumecheng-11687	320	14	is	be	AUX
fumecheng-11687	320	15	assumed	assume	VERB
fumecheng-11687	320	16	to	to	PART
fumecheng-11687	320	17	cover	cover	VERB
fumecheng-11687	320	18	the	the	DET
fumecheng-11687	320	19	periodic	periodic	ADJ
fumecheng-11687	320	20	solution	solution	NOUN
fumecheng-11687	320	21	.	.	PUNCT
fumecheng-11687	321	1	to	to	PART
fumecheng-11687	321	2	accomplish	accomplish	VERB
fumecheng-11687	321	3	this	this	DET
fumecheng-11687	321	4	periodic	periodic	ADJ
fumecheng-11687	321	5	solution	solution	NOUN
fumecheng-11687	321	6	,	,	PUNCT
fumecheng-11687	321	7	galerkin	galerkin	PROPN
fumecheng-11687	321	8	’s	’s	PART
fumecheng-11687	321	9	technique	technique	NOUN
fumecheng-11687	321	10	may	may	AUX
fumecheng-11687	321	11	be	be	AUX
fumecheng-11687	321	12	applied	apply	VERB
fumecheng-11687	321	13	to	to	PART
fumecheng-11687	321	14	establish	establish	VERB
fumecheng-11687	321	15	the	the	DET
fumecheng-11687	321	16	frequency	frequency	NOUN
fumecheng-11687	321	17	�	�	PROPN
fumecheng-11687	321	18	̂	̂	NOUN
fumecheng-11687	321	19	�	�	NOUN
fumecheng-11687	321	20	.	.	PUNCT
fumecheng-11687	322	1	to	to	PART
fumecheng-11687	322	2	construct	construct	VERB
fumecheng-11687	322	3	the	the	DET
fumecheng-11687	322	4	residual	residual	ADJ
fumecheng-11687	322	5	function	function	NOUN
fumecheng-11687	322	6	r(	r(	PROPN
fumecheng-11687	322	7	�	�	PROPN
fumecheng-11687	322	8	̂	̂	NOUN
fumecheng-11687	322	9	�	�	NOUN
fumecheng-11687	322	10	;t	;t	NOUN
fumecheng-11687	322	11	)	)	PUNCT
fumecheng-11687	322	12	,	,	PUNCT
fumecheng-11687	322	13	one	one	PRON
fumecheng-11687	322	14	can	can	AUX
fumecheng-11687	322	15	insert	insert	VERB
fumecheng-11687	322	16	the	the	DET
fumecheng-11687	322	17	suggested	suggest	VERB
fumecheng-11687	322	18	solution	solution	NOUN
fumecheng-11687	322	19	given	give	VERB
fumecheng-11687	322	20	in	in	ADP
fumecheng-11687	322	21	eq	eq	ADP
fumecheng-11687	322	22	.	.	PUNCT
fumecheng-11687	323	1	(	(	PUNCT
fumecheng-11687	323	2	36	36	NUM
fumecheng-11687	323	3	)	)	PUNCT
fumecheng-11687	323	4	into	into	ADP
fumecheng-11687	323	5	eq	eq	NOUN
fumecheng-11687	323	6	.	.	PUNCT
fumecheng-11687	324	1	(	(	PUNCT
fumecheng-11687	324	2	43	43	NUM
fumecheng-11687	324	3	)	)	PUNCT
fumecheng-11687	324	4	,	,	PUNCT
fumecheng-11687	324	5	which	which	PRON
fumecheng-11687	324	6	gives	give	VERB
fumecheng-11687	324	7	2	2	NUM
fumecheng-11687	324	8	2	2	NUM
fumecheng-11687	324	9	2	2	NUM
fumecheng-11687	324	10	2	2	NUM
fumecheng-11687	324	11	1	1	NUM
fumecheng-11687	324	12	2	2	NUM
fumecheng-11687	324	13	2	2	NUM
fumecheng-11687	324	14	1	1	NUM
fumecheng-11687	324	15	2	2	NUM
fumecheng-11687	324	16	2	2	NUM
fumecheng-11687	324	17	2	2	NUM
fumecheng-11687	324	18	2	2	NUM
fumecheng-11687	324	19	3	3	NUM
fumecheng-11687	324	20	4	4	NUM
fumecheng-11687	324	21	4	4	NUM
fumecheng-11687	324	22	3	3	NUM
fumecheng-11687	324	23	ˆ	ˆ	NOUN
fumecheng-11687	324	24	ˆ	ˆ	NOUN
fumecheng-11687	324	25	ˆ	ˆ	NOUN
fumecheng-11687	324	26	ˆ	ˆ	NOUN
fumecheng-11687	324	27	ˆ	ˆ	NOUN
fumecheng-11687	324	28	ˆ	ˆ	NOUN
fumecheng-11687	324	29	ˆ	ˆ	ADJ
fumecheng-11687	324	30	(	(	PUNCT
fumecheng-11687	324	31	;	;	PUNCT
fumecheng-11687	324	32	)	)	PUNCT
fumecheng-11687	324	33	(	(	PUNCT
fumecheng-11687	324	34	(	(	PUNCT
fumecheng-11687	324	35	)	)	PUNCT
fumecheng-11687	324	36	2	2	X
fumecheng-11687	324	37	)	)	PUNCT
fumecheng-11687	324	38	cos	cos	X
fumecheng-11687	324	39	(	(	PUNCT
fumecheng-11687	324	40	(	(	PUNCT
fumecheng-11687	324	41	)	)	PUNCT
fumecheng-11687	324	42	2	2	X
fumecheng-11687	324	43	)	)	PUNCT
fumecheng-11687	324	44	sin	sin	NOUN
fumecheng-11687	324	45	ˆ	ˆ	ADV
fumecheng-11687	324	46	ˆ	ˆ	ADV
fumecheng-11687	324	47	ˆ	ˆ	NOUN
fumecheng-11687	324	48	ˆ	ˆ	NOUN
fumecheng-11687	324	49	ˆ	ˆ	NOUN
fumecheng-11687	324	50	ˆ	ˆ	ADJ
fumecheng-11687	324	51	(	(	PUNCT
fumecheng-11687	324	52	(	(	PUNCT
fumecheng-11687	324	53	9	9	NUM
fumecheng-11687	324	54	)	)	PUNCT
fumecheng-11687	324	55	6	6	NUM
fumecheng-11687	324	56	)	)	PUNCT
fumecheng-11687	324	57	cos3	cos3	PROPN
fumecheng-11687	324	58	(	(	PUNCT
fumecheng-11687	324	59	(	(	PUNCT
fumecheng-11687	324	60	9	9	NUM
fumecheng-11687	324	61	)	)	PUNCT
fumecheng-11687	324	62	6	6	NUM
fumecheng-11687	324	63	)	)	PUNCT
fumecheng-11687	325	1	sin3	sin3	NOUN
fumecheng-11687	325	2	r	r	NOUN
fumecheng-11687	325	3	t	t	PROPN
fumecheng-11687	326	1	k	k	PROPN
fumecheng-11687	326	2	k	k	PROPN
fumecheng-11687	327	1	t	t	PROPN
fumecheng-11687	328	1	k	k	PROPN
fumecheng-11687	328	2	k	k	PROPN
fumecheng-11687	329	1	t	t	PROPN
fumecheng-11687	330	1	k	k	PROPN
fumecheng-11687	330	2	k	k	PROPN
fumecheng-11687	331	1	t	t	PROPN
fumecheng-11687	331	2	k	k	PROPN
fumecheng-11687	331	3	k	k	PROPN
fumecheng-11687	331	4	t	t	PROPN
fumecheng-11687	331	5	=	=	PUNCT
fumecheng-11687	332	1	−	−	PROPN
fumecheng-11687	333	1	+	+	CCONJ
fumecheng-11687	333	2	+	+	NUM
fumecheng-11687	333	3	−	−	ADP
fumecheng-11687	333	4	−	−	PROPN
fumecheng-11687	334	1	+	+	CCONJ
fumecheng-11687	334	2	−	−	PROPN
fumecheng-11687	335	1	+	+	CCONJ
fumecheng-11687	335	2	+	+	NUM
fumecheng-11687	335	3	−	−	PROPN
fumecheng-11687	335	4	−	−	PROPN
fumecheng-11687	336	1			PUNCT
fumecheng-11687	336	2			NOUN
fumecheng-11687	336	3			PROPN
fumecheng-11687	336	4			PROPN
fumecheng-11687	337	1			PROPN
fumecheng-11687	337	2			NOUN
fumecheng-11687	337	3			PROPN
fumecheng-11687	337	4			PROPN
fumecheng-11687	338	1			PROPN
fumecheng-11687	338	2			NOUN
fumecheng-11687	338	3			ADJ
fumecheng-11687	338	4			NOUN
fumecheng-11687	338	5			X
fumecheng-11687	339	1			PUNCT
fumecheng-11687	339	2			NOUN
fumecheng-11687	339	3			PROPN
fumecheng-11687	339	4			PROPN
fumecheng-11687	340	1			X
fumecheng-11687	340	2	(	(	PUNCT
fumecheng-11687	340	3	48	48	NUM
fumecheng-11687	340	4	)	)	PUNCT
fumecheng-11687	340	5	to	to	PART
fumecheng-11687	340	6	estimate	estimate	VERB
fumecheng-11687	340	7	the	the	DET
fumecheng-11687	340	8	total	total	ADJ
fumecheng-11687	340	9	frequency	frequency	NOUN
fumecheng-11687	340	10	�	�	PROPN
fumecheng-11687	340	11	̂	̂	VERB
fumecheng-11687	340	12	�	�	PROPN
fumecheng-11687	340	13	,	,	PUNCT
fumecheng-11687	340	14	one	one	PRON
fumecheng-11687	340	15	may	may	AUX
fumecheng-11687	340	16	apply	apply	VERB
fumecheng-11687	340	17	the	the	DET
fumecheng-11687	340	18	following	follow	VERB
fumecheng-11687	340	19	galerkin	galerkin	PROPN
fumecheng-11687	340	20	’s	’s	PART
fumecheng-11687	340	21	formula	formula	NOUN
fumecheng-11687	340	22	:	:	PUNCT
fumecheng-11687	340	23	(	(	PUNCT
fumecheng-11687	340	24	)	)	PUNCT
fumecheng-11687	340	25	0	0	NUM
fumecheng-11687	341	1	ˆ	ˆ	NOUN
fumecheng-11687	341	2	ˆ	ˆ	NOUN
fumecheng-11687	341	3	ˆ	ˆ	NOUN
fumecheng-11687	341	4	ˆ	ˆ	NOUN
fumecheng-11687	341	5	ˆ	ˆ	ADJ
fumecheng-11687	341	6	(	(	PUNCT
fumecheng-11687	341	7	;	;	PUNCT
fumecheng-11687	341	8	)	)	PUNCT
fumecheng-11687	341	9	cos	cos	SCONJ
fumecheng-11687	341	10	sin	sin	PROPN
fumecheng-11687	341	11	cos3	cos3	PROPN
fumecheng-11687	341	12	sin	sin	VERB
fumecheng-11687	341	13	3	3	NUM
fumecheng-11687	341	14	0	0	SYM
fumecheng-11687	341	15	t	t	NOUN
fumecheng-11687	341	16	r	r	NOUN
fumecheng-11687	341	17	t	t	PROPN
fumecheng-11687	341	18	t	t	PROPN
fumecheng-11687	341	19	t	t	PROPN
fumecheng-11687	341	20	t	t	PROPN
fumecheng-11687	341	21	t	t	PROPN
fumecheng-11687	341	22	dt	dt	PROPN
fumecheng-11687	341	23			X
fumecheng-11687	341	24			X
fumecheng-11687	342	1			PUNCT
fumecheng-11687	343	1	+	+	NOUN
fumecheng-11687	343	2	+	+	CCONJ
fumecheng-11687	344	1	+	+	CCONJ
fumecheng-11687	344	2	=	=	NOUN
fumecheng-11687	344	3			X
fumecheng-11687	344	4	(	(	PUNCT
fumecheng-11687	344	5	49	49	NUM
fumecheng-11687	344	6	)	)	PUNCT
fumecheng-11687	344	7	the	the	DET
fumecheng-11687	344	8	up	up	ADV
fumecheng-11687	344	9	-	-	PUNCT
fumecheng-11687	344	10	grating	grate	VERB
fumecheng-11687	344	11	rank	rank	NOUN
fumecheng-11687	344	12	approach	approach	NOUN
fumecheng-11687	344	13	to	to	PART
fumecheng-11687	344	14	solve	solve	VERB
fumecheng-11687	344	15	a	a	DET
fumecheng-11687	344	16	forced	force	VERB
fumecheng-11687	344	17	fractal	fractal	ADJ
fumecheng-11687	344	18	duffing	duffing	NOUN
fumecheng-11687	344	19	oscillator	oscillator	NOUN
fumecheng-11687	344	20	by	by	ADP
fumecheng-11687	344	21	the	the	DET
fumecheng-11687	344	22	np	np	PROPN
fumecheng-11687	344	23	technique	technique	NOUN
fumecheng-11687	344	24	211	211	NUM
fumecheng-11687	344	25	using	use	VERB
fumecheng-11687	344	26	the	the	DET
fumecheng-11687	344	27	definitions	definition	NOUN
fumecheng-11687	344	28	given	give	VERB
fumecheng-11687	344	29	in	in	ADP
fumecheng-11687	344	30	eq	eq	ADP
fumecheng-11687	344	31	.	.	PUNCT
fumecheng-11687	345	1	(	(	PUNCT
fumecheng-11687	345	2	37	37	NUM
fumecheng-11687	345	3	)	)	PUNCT
fumecheng-11687	345	4	and	and	CCONJ
fumecheng-11687	345	5	the	the	DET
fumecheng-11687	345	6	residual	residual	ADJ
fumecheng-11687	345	7	given	give	VERB
fumecheng-11687	345	8	in	in	ADP
fumecheng-11687	345	9	eq	eq	ADP
fumecheng-11687	345	10	.	.	PUNCT
fumecheng-11687	345	11	(	(	PUNCT
fumecheng-11687	345	12	48	48	NUM
fumecheng-11687	345	13	)	)	PUNCT
fumecheng-11687	345	14	,	,	PUNCT
fumecheng-11687	345	15	the	the	DET
fumecheng-11687	345	16	above	above	ADJ
fumecheng-11687	345	17	integral	integral	ADJ
fumecheng-11687	345	18	leads	lead	NOUN
fumecheng-11687	345	19	to	to	ADP
fumecheng-11687	345	20	the	the	DET
fumecheng-11687	345	21	following	follow	VERB
fumecheng-11687	345	22	frequency	frequency	NOUN
fumecheng-11687	345	23	equation	equation	NOUN
fumecheng-11687	345	24	:	:	PUNCT
fumecheng-11687	345	25	4	4	NUM
fumecheng-11687	345	26	3	3	NUM
fumecheng-11687	345	27	2	2	NUM
fumecheng-11687	345	28	4	4	NUM
fumecheng-11687	345	29	3	3	NUM
fumecheng-11687	345	30	2	2	NUM
fumecheng-11687	345	31	0	0	NUM
fumecheng-11687	345	32	ˆ	ˆ	NOUN
fumecheng-11687	345	33	ˆ	ˆ	NOUN
fumecheng-11687	345	34	ˆ	ˆ	ADJ
fumecheng-11687	345	35	0c	0c	NOUN
fumecheng-11687	345	36	c	c	NOUN
fumecheng-11687	346	1	c	c	NOUN
fumecheng-11687	346	2	c	c	VERB
fumecheng-11687	346	3			X
fumecheng-11687	347	1	+	+	NOUN
fumecheng-11687	348	1	+	+	PROPN
fumecheng-11687	348	2	+	+	CCONJ
fumecheng-11687	348	3	=	=	SYM
fumecheng-11687	348	4	(	(	PUNCT
fumecheng-11687	348	5	50	50	NUM
fumecheng-11687	348	6	)	)	PUNCT
fumecheng-11687	348	7	here	here	ADV
fumecheng-11687	348	8	,	,	PUNCT
fumecheng-11687	348	9	the	the	DET
fumecheng-11687	348	10	coefficients	coefficient	NOUN
fumecheng-11687	348	11	c	c	NOUN
fumecheng-11687	348	12	’s	’s	PART
fumecheng-11687	348	13	are	be	AUX
fumecheng-11687	348	14	listed	list	VERB
fumecheng-11687	348	15	below	below	ADP
fumecheng-11687	348	16	:	:	PUNCT
fumecheng-11687	348	17	2	2	NUM
fumecheng-11687	348	18	4	4	NUM
fumecheng-11687	348	19	2	2	NUM
fumecheng-11687	348	20	4	4	NUM
fumecheng-11687	348	21	2	2	NUM
fumecheng-11687	348	22	2	2	NUM
fumecheng-11687	348	23	2	2	NUM
fumecheng-11687	348	24	2	2	NUM
fumecheng-11687	348	25	2	2	NUM
fumecheng-11687	348	26	3	3	NUM
fumecheng-11687	348	27	0	0	NUM
fumecheng-11687	348	28	4	4	NUM
fumecheng-11687	348	29	2	2	NUM
fumecheng-11687	348	30	2	2	NUM
fumecheng-11687	348	31	2	2	NUM
fumecheng-11687	348	32	2	2	NUM
fumecheng-11687	348	33	2	2	NUM
fumecheng-11687	348	34	4	4	NUM
fumecheng-11687	348	35	2	2	NUM
fumecheng-11687	348	36	2	2	NUM
fumecheng-11687	348	37	3	3	NUM
fumecheng-11687	348	38	2	2	NUM
fumecheng-11687	348	39	2	2	NUM
fumecheng-11687	348	40	0	0	NUM
fumecheng-11687	348	41	0	0	NUM
fumecheng-11687	348	42	4	4	NUM
fumecheng-11687	348	43	2	2	NUM
fumecheng-11687	348	44	2	2	NUM
fumecheng-11687	348	45	2	2	NUM
fumecheng-11687	348	46	2	2	NUM
fumecheng-11687	348	47	2	2	NUM
fumecheng-11687	348	48	0	0	NUM
fumecheng-11687	348	49	0	0	NUM
fumecheng-11687	348	50	ˆ9	ˆ9	NOUN
fumecheng-11687	348	51	(	(	PUNCT
fumecheng-11687	348	52	2	2	NUM
fumecheng-11687	348	53	(	(	PUNCT
fumecheng-11687	348	54	)	)	PUNCT
fumecheng-11687	348	55	)	)	PUNCT
fumecheng-11687	349	1	ˆ	ˆ	X
fumecheng-11687	349	2	ˆ12	ˆ12	PROPN
fumecheng-11687	349	3	(	(	PUNCT
fumecheng-11687	349	4	2	2	NUM
fumecheng-11687	349	5	(	(	PUNCT
fumecheng-11687	349	6	)	)	PUNCT
fumecheng-11687	349	7	(	(	PUNCT
fumecheng-11687	349	8	)	)	PUNCT
fumecheng-11687	349	9	)	)	PUNCT
fumecheng-11687	350	1	ˆ	ˆ	X
fumecheng-11687	350	2	ˆ(9	ˆ(9	PROPN
fumecheng-11687	350	3	9	9	NUM
fumecheng-11687	350	4	12	12	NUM
fumecheng-11687	350	5	13	13	NUM
fumecheng-11687	350	6	)	)	PUNCT
fumecheng-11687	350	7	(	(	PUNCT
fumecheng-11687	350	8	)	)	PUNCT
fumecheng-11687	350	9	6	6	NUM
fumecheng-11687	350	10	(	(	PUNCT
fumecheng-11687	350	11	)	)	PUNCT
fumecheng-11687	350	12	(	(	PUNCT
fumecheng-11687	350	13	)	)	PUNCT
fumecheng-11687	350	14	3	3	NUM
fumecheng-11687	350	15	ˆ(3	ˆ(3	NOUN
fumecheng-11687	350	16	3	3	NUM
fumecheng-11687	350	17	4	4	NUM
fumecheng-11687	350	18	)	)	PUNCT
fumecheng-11687	350	19	(	(	PUNCT
fumecheng-11687	350	20	)	)	PUNCT
fumecheng-11687	351	1	c	c	X
fumecheng-11687	351	2	ab	ab	PROPN
fumecheng-11687	352	1	a	a	DET
fumecheng-11687	352	2	c	c	NOUN
fumecheng-11687	352	3	a	a	DET
fumecheng-11687	352	4	a	a	DET
fumecheng-11687	352	5	a	a	DET
fumecheng-11687	352	6	q	q	NOUN
fumecheng-11687	352	7	a	a	DET
fumecheng-11687	352	8	aab	aab	NOUN
fumecheng-11687	352	9	ab	ab	PROPN
fumecheng-11687	352	10	c	c	PROPN
fumecheng-11687	352	11	a	a	DET
fumecheng-11687	352	12	a	a	DET
fumecheng-11687	352	13	q	q	NOUN
fumecheng-11687	352	14	a	a	DET
fumecheng-11687	352	15	ab	ab	NOUN
fumecheng-11687	352	16	a	a	DET
fumecheng-11687	352	17	a	a	DET
fumecheng-11687	352	18	a	a	DET
fumecheng-11687	352	19	q	q	NOUN
fumecheng-11687	352	20	a	a	DET
fumecheng-11687	352	21	aa	aa	NOUN
fumecheng-11687	352	22	b	b	PROPN
fumecheng-11687	352	23	c	c	PROPN
fumecheng-11687	352	24	a	a	DET
fumecheng-11687	352	25	a	a	DET
fumecheng-11687	352	26	q	q	NOUN
fumecheng-11687	352	27	a	a	DET
fumecheng-11687	352	28	aa	aa	PROPN
fumecheng-11687	352	29	b	b	PROPN
fumecheng-11687	352	30	=	=	NOUN
fumecheng-11687	352	31	−	−	PROPN
fumecheng-11687	352	32			NUM
fumecheng-11687	352	33	=	=	SYM
fumecheng-11687	352	34	+	+	NUM
fumecheng-11687	352	35	−	−	PROPN
fumecheng-11687	352	36	−	−	NUM
fumecheng-11687	353	1	−	−	PROPN
fumecheng-11687	354	1	+	+	NUM
fumecheng-11687	354	2			NUM
fumecheng-11687	354	3			NOUN
fumecheng-11687	354	4	=	=	PUNCT
fumecheng-11687	355	1	+	+	NUM
fumecheng-11687	355	2	−	−	PROPN
fumecheng-11687	356	1	−	−	PROPN
fumecheng-11687	357	1	+	+	CCONJ
fumecheng-11687	357	2	+	+	NUM
fumecheng-11687	357	3	−	−	NOUN
fumecheng-11687	357	4	−	−	NUM
fumecheng-11687	358	1	−	−	NOUN
fumecheng-11687	358	2			NUM
fumecheng-11687	358	3			NOUN
fumecheng-11687	358	4	=	=	SYM
fumecheng-11687	358	5	+	+	NUM
fumecheng-11687	358	6	−	−	PROPN
fumecheng-11687	358	7	−	−	PROPN
fumecheng-11687	359	1			PROPN
fumecheng-11687	359	2			NOUN
fumecheng-11687	359	3			PUNCT
fumecheng-11687	359	4			NUM
fumecheng-11687	359	5			ADJ
fumecheng-11687	359	6			NOUN
fumecheng-11687	359	7			PRON
fumecheng-11687	359	8			NOUN
fumecheng-11687	359	9			X
fumecheng-11687	359	10			PROPN
fumecheng-11687	359	11			NUM
fumecheng-11687	359	12			NOUN
fumecheng-11687	359	13			PROPN
fumecheng-11687	359	14			NUM
fumecheng-11687	359	15			ADJ
fumecheng-11687	359	16			NOUN
fumecheng-11687	359	17			X
fumecheng-11687	359	18			PROPN
fumecheng-11687	359	19			NUM
fumecheng-11687	359	20			NOUN
fumecheng-11687	359	21			X
fumecheng-11687	359	22	(	(	PUNCT
fumecheng-11687	359	23	51	51	NUM
fumecheng-11687	359	24	)	)	PUNCT
fumecheng-11687	359	25	given	give	VERB
fumecheng-11687	359	26	the	the	DET
fumecheng-11687	359	27	real	real	ADJ
fumecheng-11687	359	28	roots	root	NOUN
fumecheng-11687	359	29	of	of	ADP
fumecheng-11687	359	30	the	the	DET
fumecheng-11687	359	31	frequency	frequency	NOUN
fumecheng-11687	359	32	in	in	ADP
fumecheng-11687	359	33	eq	eq	PROPN
fumecheng-11687	359	34	.	.	PUNCT
fumecheng-11687	360	1	(	(	PUNCT
fumecheng-11687	360	2	50	50	NUM
fumecheng-11687	360	3	)	)	PUNCT
fumecheng-11687	360	4	,	,	PUNCT
fumecheng-11687	360	5	the	the	DET
fumecheng-11687	360	6	periodic	periodic	ADJ
fumecheng-11687	360	7	solution	solution	NOUN
fumecheng-11687	360	8	of	of	ADP
fumecheng-11687	360	9	eq	eq	PROPN
fumecheng-11687	360	10	.	.	PUNCT
fumecheng-11687	361	1	(	(	PUNCT
fumecheng-11687	361	2	43	43	NUM
fumecheng-11687	361	3	)	)	PUNCT
fumecheng-11687	361	4	can	can	AUX
fumecheng-11687	361	5	be	be	AUX
fumecheng-11687	361	6	obtained	obtain	VERB
fumecheng-11687	361	7	in	in	ADP
fumecheng-11687	361	8	the	the	DET
fumecheng-11687	361	9	form	form	NOUN
fumecheng-11687	361	10	1	1	NUM
fumecheng-11687	361	11	2	2	NUM
fumecheng-11687	361	12	3	3	NUM
fumecheng-11687	361	13	4	4	NUM
fumecheng-11687	361	14	ˆ	ˆ	NOUN
fumecheng-11687	361	15	ˆ	ˆ	NOUN
fumecheng-11687	361	16	ˆ	ˆ	NOUN
fumecheng-11687	361	17	ˆ	ˆ	ADJ
fumecheng-11687	361	18	(	(	PUNCT
fumecheng-11687	361	19	)	)	PUNCT
fumecheng-11687	361	20	cos	cos	ADP
fumecheng-11687	361	21	sin	sin	PROPN
fumecheng-11687	362	1	cos3	cos3	PROPN
fumecheng-11687	362	2	sin3u	sin3u	PROPN
fumecheng-11687	363	1	t	t	PROPN
fumecheng-11687	364	1	k	k	PROPN
fumecheng-11687	364	2	t	t	PROPN
fumecheng-11687	365	1	k	k	PROPN
fumecheng-11687	365	2	t	t	PROPN
fumecheng-11687	366	1	k	k	PROPN
fumecheng-11687	366	2	t	t	PROPN
fumecheng-11687	367	1	k	k	PROPN
fumecheng-11687	367	2	t	t	X
fumecheng-11687	368	1			X
fumecheng-11687	368	2			X
fumecheng-11687	368	3	=	=	PROPN
fumecheng-11687	368	4	+	+	CCONJ
fumecheng-11687	368	5	+	+	CCONJ
fumecheng-11687	369	1	+	+	CCONJ
fumecheng-11687	369	2	(	(	PUNCT
fumecheng-11687	369	3	52	52	NUM
fumecheng-11687	369	4	)	)	PUNCT
fumecheng-11687	369	5	numerical	numerical	ADJ
fumecheng-11687	369	6	illustration	illustration	NOUN
fumecheng-11687	369	7	for	for	ADP
fumecheng-11687	369	8	the	the	DET
fumecheng-11687	369	9	current	current	ADJ
fumecheng-11687	369	10	state	state	NOUN
fumecheng-11687	369	11	is	be	AUX
fumecheng-11687	369	12	shown	show	VERB
fumecheng-11687	369	13	in	in	ADP
fumecheng-11687	369	14	the	the	DET
fumecheng-11687	369	15	figs	fig	NOUN
fumecheng-11687	369	16	.	.	PUNCT
fumecheng-11687	370	1	7	7	NUM
fumecheng-11687	370	2	-	-	SYM
fumecheng-11687	370	3	12	12	NUM
fumecheng-11687	370	4	.	.	PUNCT
fumecheng-11687	371	1	the	the	DET
fumecheng-11687	371	2	calculations	calculation	NOUN
fumecheng-11687	371	3	are	be	AUX
fumecheng-11687	371	4	made	make	VERB
fumecheng-11687	371	5	for	for	ADP
fumecheng-11687	371	6	the	the	DET
fumecheng-11687	371	7	periodic	periodic	ADJ
fumecheng-11687	371	8	solution	solution	NOUN
fumecheng-11687	371	9	given	give	VERB
fumecheng-11687	371	10	in	in	ADP
fumecheng-11687	371	11	eq	eq	ADP
fumecheng-11687	371	12	.	.	PUNCT
fumecheng-11687	372	1	(	(	PUNCT
fumecheng-11687	372	2	52	52	NUM
fumecheng-11687	372	3	)	)	PUNCT
fumecheng-11687	372	4	where	where	SCONJ
fumecheng-11687	372	5	the	the	DET
fumecheng-11687	372	6	frequency	frequency	NOUN
fumecheng-11687	372	7	�	�	PROPN
fumecheng-11687	372	8	̂	̂	VERB
fumecheng-11687	372	9	�	�	NOUN
fumecheng-11687	372	10	is	be	AUX
fumecheng-11687	372	11	estimated	estimate	VERB
fumecheng-11687	372	12	from	from	ADP
fumecheng-11687	372	13	the	the	DET
fumecheng-11687	372	14	frequency	frequency	NOUN
fumecheng-11687	372	15	eq	eq	X
fumecheng-11687	372	16	.	.	PUNCT
fumecheng-11687	373	1	(	(	PUNCT
fumecheng-11687	373	2	50	50	NUM
fumecheng-11687	373	3	)	)	PUNCT
fumecheng-11687	373	4	.	.	PUNCT
fumecheng-11687	374	1	it	it	PRON
fumecheng-11687	374	2	is	be	AUX
fumecheng-11687	374	3	noted	note	VERB
fumecheng-11687	374	4	that	that	SCONJ
fumecheng-11687	374	5	the	the	DET
fumecheng-11687	374	6	coefficients	coefficient	NOUN
fumecheng-11687	374	7	k	k	X
fumecheng-11687	374	8	’s	’s	PART
fumecheng-11687	374	9	are	be	AUX
fumecheng-11687	374	10	depend	depend	VERB
fumecheng-11687	374	11	on	on	ADP
fumecheng-11687	374	12	the	the	DET
fumecheng-11687	374	13	frequency	frequency	NOUN
fumecheng-11687	374	14	�	�	PROPN
fumecheng-11687	374	15	̂	̂	VERB
fumecheng-11687	374	16	�	�	PROPN
fumecheng-11687	374	17	as	as	SCONJ
fumecheng-11687	374	18	defined	define	VERB
fumecheng-11687	374	19	by	by	ADP
fumecheng-11687	374	20	eq	eq	PROPN
fumecheng-11687	374	21	.	.	PUNCT
fumecheng-11687	375	1	(	(	PUNCT
fumecheng-11687	375	2	37	37	NUM
fumecheng-11687	375	3	)	)	PUNCT
fumecheng-11687	375	4	.	.	PUNCT
fumecheng-11687	376	1	the	the	DET
fumecheng-11687	376	2	numerical	numerical	ADJ
fumecheng-11687	376	3	system	system	NOUN
fumecheng-11687	376	4	that	that	PRON
fumecheng-11687	376	5	is	be	AUX
fumecheng-11687	376	6	considered	consider	VERB
fumecheng-11687	376	7	in	in	ADP
fumecheng-11687	376	8	these	these	DET
fumecheng-11687	376	9	calculations	calculation	NOUN
fumecheng-11687	376	10	is	be	AUX
fumecheng-11687	376	11	a	a	DET
fumecheng-11687	376	12	=	=	X
fumecheng-11687	376	13	0	0	X
fumecheng-11687	376	14	=	=	NOUN
fumecheng-11687	376	15	1	1	NUM
fumecheng-11687	376	16	,	,	PUNCT
fumecheng-11687	376	17	q	q	PUNCT
fumecheng-11687	377	1	=	=	SYM
fumecheng-11687	377	2			NUM
fumecheng-11687	377	3	=	=	NOUN
fumecheng-11687	377	4	0.1	0.1	NUM
fumecheng-11687	377	5	,	,	PUNCT
fumecheng-11687	377	6	and	and	CCONJ
fumecheng-11687	377	7	=3	=3	PUNCT
fumecheng-11687	377	8	with	with	ADP
fumecheng-11687	377	9	the	the	DET
fumecheng-11687	377	10	variation	variation	NOUN
fumecheng-11687	377	11	of	of	ADP
fumecheng-11687	377	12	the	the	DET
fumecheng-11687	377	13	fractal	fractal	ADJ
fumecheng-11687	377	14	order	order	NOUN
fumecheng-11687	377	15	.	.	NOUN
fumecheng-11687	377	16	in	in	ADP
fumecheng-11687	377	17	fig	fig	NOUN
fumecheng-11687	377	18	.	.	PUNCT
fumecheng-11687	378	1	7	7	NUM
fumecheng-11687	378	2	,	,	PUNCT
fumecheng-11687	378	3	the	the	DET
fumecheng-11687	378	4	smooth	smooth	ADJ
fumecheng-11687	378	5	periodic	periodic	ADJ
fumecheng-11687	378	6	curve	curve	NOUN
fumecheng-11687	378	7	is	be	AUX
fumecheng-11687	378	8	observed	observe	VERB
fumecheng-11687	378	9	when	when	SCONJ
fumecheng-11687	378	10	the	the	DET
fumecheng-11687	378	11	fractal	fractal	ADJ
fumecheng-11687	378	12	order	order	NOUN
fumecheng-11687	378	13	has	have	VERB
fumecheng-11687	378	14	the	the	DET
fumecheng-11687	378	15	value	value	NOUN
fumecheng-11687	378	16			ADJ
fumecheng-11687	378	17	=	=	SYM
fumecheng-11687	378	18	0.9	0.9	NUM
fumecheng-11687	378	19	.	.	PUNCT
fumecheng-11687	379	1	the	the	DET
fumecheng-11687	379	2	periodic	periodic	ADJ
fumecheng-11687	379	3	curve	curve	NOUN
fumecheng-11687	379	4	due	due	ADP
fumecheng-11687	379	5	to	to	ADP
fumecheng-11687	379	6			NOUN
fumecheng-11687	379	7	=	=	SYM
fumecheng-11687	379	8	0.8	0.8	NUM
fumecheng-11687	379	9	that	that	PRON
fumecheng-11687	379	10	lies	lie	VERB
fumecheng-11687	379	11	in	in	ADP
fumecheng-11687	379	12	fig	fig	NOUN
fumecheng-11687	379	13	.	.	PUNCT
fumecheng-11687	379	14	8	8	NUM
fumecheng-11687	379	15	appears	appear	VERB
fumecheng-11687	379	16	similar	similar	ADJ
fumecheng-11687	379	17	to	to	ADP
fumecheng-11687	379	18	the	the	DET
fumecheng-11687	379	19	case	case	NOUN
fumecheng-11687	379	20	of	of	ADP
fumecheng-11687	379	21	the	the	DET
fumecheng-11687	379	22	first	first	ADJ
fumecheng-11687	379	23	successive	successive	ADJ
fumecheng-11687	379	24	solution	solution	NOUN
fumecheng-11687	379	25	in	in	ADP
fumecheng-11687	379	26	[	[	X
fumecheng-11687	379	27	39	39	NUM
fumecheng-11687	379	28	]	]	PUNCT
fumecheng-11687	379	29	.	.	PUNCT
fumecheng-11687	380	1	this	this	DET
fumecheng-11687	380	2	behavior	behavior	NOUN
fumecheng-11687	380	3	of	of	ADP
fumecheng-11687	380	4	the	the	DET
fumecheng-11687	380	5	periodic	periodic	ADJ
fumecheng-11687	380	6	solution	solution	NOUN
fumecheng-11687	380	7	has	have	AUX
fumecheng-11687	380	8	been	be	AUX
fumecheng-11687	380	9	affected	affect	VERB
fumecheng-11687	380	10	by	by	ADP
fumecheng-11687	380	11	decreasing	decrease	VERB
fumecheng-11687	380	12	in	in	ADP
fumecheng-11687	380	13	the	the	DET
fumecheng-11687	380	14	fractal	fractal	ADJ
fumecheng-11687	380	15	order	order	NOUN
fumecheng-11687	380	16	as	as	SCONJ
fumecheng-11687	380	17	shown	show	VERB
fumecheng-11687	380	18	in	in	ADP
fumecheng-11687	380	19	figs	fig	NOUN
fumecheng-11687	380	20	.	.	PUNCT
fumecheng-11687	381	1	9	9	NUM
fumecheng-11687	381	2	-	-	SYM
fumecheng-11687	381	3	12	12	NUM
fumecheng-11687	381	4	.	.	PUNCT
fumecheng-11687	381	5	fig	fig	NOUN
fumecheng-11687	381	6	.	.	PUNCT
fumecheng-11687	382	1	7	7	NUM
fumecheng-11687	382	2	representation	representation	NOUN
fumecheng-11687	382	3	of	of	ADP
fumecheng-11687	382	4	the	the	DET
fumecheng-11687	382	5	periodic	periodic	ADJ
fumecheng-11687	382	6	solution	solution	NOUN
fumecheng-11687	382	7	given	give	VERB
fumecheng-11687	382	8	in	in	ADP
fumecheng-11687	382	9	eq	eq	ADP
fumecheng-11687	382	10	.	.	PUNCT
fumecheng-11687	383	1	(	(	PUNCT
fumecheng-11687	383	2	52	52	NUM
fumecheng-11687	383	3	)	)	PUNCT
fumecheng-11687	383	4	for	for	ADP
fumecheng-11687	383	5	a	a	DET
fumecheng-11687	383	6	system	system	NOUN
fumecheng-11687	383	7	having	have	VERB
fumecheng-11687	383	8	a	a	DET
fumecheng-11687	383	9	=	=	X
fumecheng-11687	383	10	0	0	X
fumecheng-11687	383	11	=	=	NOUN
fumecheng-11687	383	12	1	1	NUM
fumecheng-11687	383	13	,	,	PUNCT
fumecheng-11687	383	14	q	q	NOUN
fumecheng-11687	384	1	=	=	SYM
fumecheng-11687	384	2			NUM
fumecheng-11687	384	3	=	=	SYM
fumecheng-11687	384	4	0.1	0.1	NUM
fumecheng-11687	384	5	,	,	PUNCT
fumecheng-11687	384	6			X
fumecheng-11687	384	7	=	=	SYM
fumecheng-11687	384	8	0.9	0.9	NUM
fumecheng-11687	384	9	,	,	PUNCT
fumecheng-11687	384	10	and	and	CCONJ
fumecheng-11687	384	11			NUM
fumecheng-11687	384	12	=	=	NOUN
fumecheng-11687	384	13	3	3	NUM
fumecheng-11687	384	14	212	212	NUM
fumecheng-11687	384	15	y.o	y.o	PROPN
fumecheng-11687	384	16	.	.	PROPN
fumecheng-11687	384	17	el	el	PROPN
fumecheng-11687	384	18	-	-	PUNCT
fumecheng-11687	384	19	dib	dib	PROPN
fumecheng-11687	384	20	,	,	PUNCT
fumecheng-11687	384	21	n.s	n.s	PROPN
fumecheng-11687	384	22	.	.	PROPN
fumecheng-11687	384	23	elgazery	elgazery	PROPN
fumecheng-11687	384	24	,	,	PUNCT
fumecheng-11687	384	25	h.a	h.a	PROPN
fumecheng-11687	384	26	.	.	PROPN
fumecheng-11687	384	27	alyousef	alyousef	PROPN
fumecheng-11687	384	28	fig	fig	PROPN
fumecheng-11687	384	29	.	.	PUNCT
fumecheng-11687	385	1	8	8	NUM
fumecheng-11687	385	2	representation	representation	NOUN
fumecheng-11687	385	3	of	of	ADP
fumecheng-11687	385	4	the	the	DET
fumecheng-11687	385	5	periodic	periodic	ADJ
fumecheng-11687	385	6	solution	solution	NOUN
fumecheng-11687	385	7	given	give	VERB
fumecheng-11687	385	8	in	in	ADP
fumecheng-11687	385	9	eq	eq	ADP
fumecheng-11687	385	10	.	.	PUNCT
fumecheng-11687	386	1	(	(	PUNCT
fumecheng-11687	386	2	52	52	NUM
fumecheng-11687	386	3	)	)	PUNCT
fumecheng-11687	386	4	for	for	ADP
fumecheng-11687	386	5	a	a	DET
fumecheng-11687	386	6	=	=	X
fumecheng-11687	386	7	0	0	X
fumecheng-11687	386	8	=	=	NOUN
fumecheng-11687	386	9	1	1	NUM
fumecheng-11687	386	10	,	,	PUNCT
fumecheng-11687	386	11	q	q	NOUN
fumecheng-11687	387	1	=	=	SYM
fumecheng-11687	387	2			NUM
fumecheng-11687	387	3	=	=	SYM
fumecheng-11687	387	4	0.1	0.1	NUM
fumecheng-11687	387	5	,	,	PUNCT
fumecheng-11687	387	6			X
fumecheng-11687	387	7	=	=	SYM
fumecheng-11687	387	8	0.9	0.9	NUM
fumecheng-11687	387	9	,	,	PUNCT
fumecheng-11687	387	10	and	and	CCONJ
fumecheng-11687	387	11			NUM
fumecheng-11687	387	12	=	=	SYM
fumecheng-11687	387	13	3	3	NUM
fumecheng-11687	387	14	fig	fig	NOUN
fumecheng-11687	387	15	.	.	PUNCT
fumecheng-11687	388	1	9	9	NUM
fumecheng-11687	388	2	representation	representation	NOUN
fumecheng-11687	388	3	of	of	ADP
fumecheng-11687	388	4	the	the	DET
fumecheng-11687	388	5	periodic	periodic	ADJ
fumecheng-11687	388	6	solution	solution	NOUN
fumecheng-11687	388	7	given	give	VERB
fumecheng-11687	388	8	in	in	ADP
fumecheng-11687	388	9	eq	eq	ADP
fumecheng-11687	388	10	.	.	PUNCT
fumecheng-11687	389	1	(	(	PUNCT
fumecheng-11687	389	2	52	52	NUM
fumecheng-11687	389	3	)	)	PUNCT
fumecheng-11687	389	4	for	for	ADP
fumecheng-11687	389	5	a	a	DET
fumecheng-11687	389	6	=	=	X
fumecheng-11687	389	7	0	0	X
fumecheng-11687	389	8	=	=	NOUN
fumecheng-11687	389	9	1	1	NUM
fumecheng-11687	389	10	,	,	PUNCT
fumecheng-11687	389	11	q	q	NOUN
fumecheng-11687	390	1	=	=	SYM
fumecheng-11687	390	2			NUM
fumecheng-11687	390	3	=	=	SYM
fumecheng-11687	390	4	0.1	0.1	NUM
fumecheng-11687	390	5	,	,	PUNCT
fumecheng-11687	390	6			X
fumecheng-11687	390	7	=	=	SYM
fumecheng-11687	390	8	0.7	0.7	NUM
fumecheng-11687	390	9	,	,	PUNCT
fumecheng-11687	390	10	and	and	CCONJ
fumecheng-11687	390	11			NUM
fumecheng-11687	390	12	=	=	SYM
fumecheng-11687	390	13	3	3	NUM
fumecheng-11687	390	14	fig	fig	NOUN
fumecheng-11687	390	15	.	.	PUNCT
fumecheng-11687	391	1	10	10	NUM
fumecheng-11687	391	2	representation	representation	NOUN
fumecheng-11687	391	3	of	of	ADP
fumecheng-11687	391	4	the	the	DET
fumecheng-11687	391	5	periodic	periodic	ADJ
fumecheng-11687	391	6	solution	solution	NOUN
fumecheng-11687	391	7	given	give	VERB
fumecheng-11687	391	8	in	in	ADP
fumecheng-11687	391	9	eq	eq	ADP
fumecheng-11687	391	10	.	.	PUNCT
fumecheng-11687	392	1	(	(	PUNCT
fumecheng-11687	392	2	52	52	NUM
fumecheng-11687	392	3	)	)	PUNCT
fumecheng-11687	392	4	for	for	ADP
fumecheng-11687	392	5	a	a	DET
fumecheng-11687	392	6	=	=	X
fumecheng-11687	392	7	0	0	X
fumecheng-11687	392	8	=	=	NOUN
fumecheng-11687	392	9	1	1	NUM
fumecheng-11687	392	10	,	,	PUNCT
fumecheng-11687	392	11	q	q	NOUN
fumecheng-11687	393	1	=	=	SYM
fumecheng-11687	393	2			NUM
fumecheng-11687	393	3	=	=	SYM
fumecheng-11687	393	4	0.1	0.1	NUM
fumecheng-11687	393	5	,	,	PUNCT
fumecheng-11687	393	6			X
fumecheng-11687	393	7	=	=	NOUN
fumecheng-11687	393	8	0.5	0.5	NUM
fumecheng-11687	393	9	,	,	PUNCT
fumecheng-11687	393	10	and	and	CCONJ
fumecheng-11687	393	11			PROPN
fumecheng-11687	394	1	=	=	NOUN
fumecheng-11687	394	2	3	3	NUM
fumecheng-11687	394	3	the	the	DET
fumecheng-11687	394	4	up	up	ADV
fumecheng-11687	394	5	-	-	PUNCT
fumecheng-11687	394	6	grating	grate	VERB
fumecheng-11687	394	7	rank	rank	NOUN
fumecheng-11687	394	8	approach	approach	NOUN
fumecheng-11687	394	9	to	to	PART
fumecheng-11687	394	10	solve	solve	VERB
fumecheng-11687	394	11	a	a	DET
fumecheng-11687	394	12	forced	force	VERB
fumecheng-11687	394	13	fractal	fractal	ADJ
fumecheng-11687	394	14	duffing	duffing	NOUN
fumecheng-11687	394	15	oscillator	oscillator	NOUN
fumecheng-11687	394	16	by	by	ADP
fumecheng-11687	394	17	the	the	DET
fumecheng-11687	394	18	np	np	PROPN
fumecheng-11687	394	19	technique	technique	NOUN
fumecheng-11687	394	20	213	213	NUM
fumecheng-11687	394	21	fig	fig	NOUN
fumecheng-11687	394	22	.	.	PUNCT
fumecheng-11687	395	1	11	11	NUM
fumecheng-11687	395	2	representation	representation	NOUN
fumecheng-11687	395	3	of	of	ADP
fumecheng-11687	395	4	the	the	DET
fumecheng-11687	395	5	periodic	periodic	ADJ
fumecheng-11687	395	6	solution	solution	NOUN
fumecheng-11687	395	7	given	give	VERB
fumecheng-11687	395	8	in	in	ADP
fumecheng-11687	395	9	eq	eq	ADP
fumecheng-11687	395	10	.	.	PUNCT
fumecheng-11687	396	1	(	(	PUNCT
fumecheng-11687	396	2	52	52	NUM
fumecheng-11687	396	3	)	)	PUNCT
fumecheng-11687	396	4	for	for	ADP
fumecheng-11687	396	5	a	a	DET
fumecheng-11687	396	6	=	=	X
fumecheng-11687	396	7	0	0	X
fumecheng-11687	396	8	=	=	NOUN
fumecheng-11687	396	9	1	1	NUM
fumecheng-11687	396	10	,	,	PUNCT
fumecheng-11687	396	11	q	q	NOUN
fumecheng-11687	397	1	=	=	SYM
fumecheng-11687	397	2			NUM
fumecheng-11687	397	3	=	=	SYM
fumecheng-11687	397	4	0.1	0.1	NUM
fumecheng-11687	397	5	,	,	PUNCT
fumecheng-11687	397	6			X
fumecheng-11687	397	7	=	=	SYM
fumecheng-11687	397	8	0.3	0.3	NUM
fumecheng-11687	397	9	,	,	PUNCT
fumecheng-11687	397	10	and	and	CCONJ
fumecheng-11687	397	11			NUM
fumecheng-11687	397	12	=	=	SYM
fumecheng-11687	397	13	3	3	NUM
fumecheng-11687	397	14	fig	fig	NOUN
fumecheng-11687	397	15	.	.	PUNCT
fumecheng-11687	398	1	12	12	NUM
fumecheng-11687	398	2	representation	representation	NOUN
fumecheng-11687	398	3	of	of	ADP
fumecheng-11687	398	4	the	the	DET
fumecheng-11687	398	5	periodic	periodic	ADJ
fumecheng-11687	398	6	solution	solution	NOUN
fumecheng-11687	398	7	given	give	VERB
fumecheng-11687	398	8	in	in	ADP
fumecheng-11687	398	9	eq	eq	ADP
fumecheng-11687	398	10	.	.	PUNCT
fumecheng-11687	399	1	(	(	PUNCT
fumecheng-11687	399	2	52	52	NUM
fumecheng-11687	399	3	)	)	PUNCT
fumecheng-11687	399	4	for	for	ADP
fumecheng-11687	399	5	a	a	DET
fumecheng-11687	399	6	=	=	X
fumecheng-11687	399	7	0	0	X
fumecheng-11687	399	8	=	=	NOUN
fumecheng-11687	399	9	1	1	NUM
fumecheng-11687	399	10	,	,	PUNCT
fumecheng-11687	399	11	q	q	NOUN
fumecheng-11687	400	1	=	=	SYM
fumecheng-11687	400	2			NUM
fumecheng-11687	400	3	=	=	SYM
fumecheng-11687	400	4	0.1	0.1	NUM
fumecheng-11687	400	5	,	,	PUNCT
fumecheng-11687	400	6			X
fumecheng-11687	400	7	=	=	NOUN
fumecheng-11687	400	8	0.1	0.1	NUM
fumecheng-11687	400	9	,	,	PUNCT
fumecheng-11687	400	10	and	and	CCONJ
fumecheng-11687	400	11			NUM
fumecheng-11687	401	1	=	=	NOUN
fumecheng-11687	401	2	3	3	NUM
fumecheng-11687	401	3	6	6	NUM
fumecheng-11687	401	4	.	.	PUNCT
fumecheng-11687	402	1	conclusions	conclusion	NOUN
fumecheng-11687	402	2	a	a	DET
fumecheng-11687	402	3	fractal	fractal	ADJ
fumecheng-11687	402	4	duffing	duffing	NOUN
fumecheng-11687	402	5	oscillator	oscillator	NOUN
fumecheng-11687	402	6	with	with	ADP
fumecheng-11687	402	7	periodic	periodic	ADJ
fumecheng-11687	402	8	force	force	NOUN
fumecheng-11687	402	9	was	be	AUX
fumecheng-11687	402	10	investigated	investigate	VERB
fumecheng-11687	402	11	in	in	ADP
fumecheng-11687	402	12	the	the	DET
fumecheng-11687	402	13	current	current	ADJ
fumecheng-11687	402	14	work	work	NOUN
fumecheng-11687	402	15	.	.	PUNCT
fumecheng-11687	403	1	ultimately	ultimately	ADV
fumecheng-11687	403	2	,	,	PUNCT
fumecheng-11687	403	3	the	the	DET
fumecheng-11687	403	4	present	present	ADJ
fumecheng-11687	403	5	conclusion	conclusion	NOUN
fumecheng-11687	403	6	observations	observation	NOUN
fumecheng-11687	403	7	are	be	AUX
fumecheng-11687	403	8	summarized	summarize	VERB
fumecheng-11687	403	9	as	as	SCONJ
fumecheng-11687	403	10	follows	follow	VERB
fumecheng-11687	403	11	:	:	PUNCT
fumecheng-11687	403	12	▪	▪	NOUN
fumecheng-11687	403	13	by	by	ADP
fumecheng-11687	403	14	using	use	VERB
fumecheng-11687	403	15	the	the	DET
fumecheng-11687	403	16	rank	rank	NOUN
fumecheng-11687	403	17	upgrade	upgrade	NOUN
fumecheng-11687	403	18	technique	technique	NOUN
fumecheng-11687	403	19	,	,	PUNCT
fumecheng-11687	403	20	an	an	DET
fumecheng-11687	403	21	alternative	alternative	ADJ
fumecheng-11687	403	22	unforced	unforced	ADJ
fumecheng-11687	403	23	fractal	fractal	ADJ
fumecheng-11687	403	24	fourth	fourth	ADJ
fumecheng-11687	403	25	-	-	PUNCT
fumecheng-11687	403	26	order	order	NOUN
fumecheng-11687	403	27	equation	equation	NOUN
fumecheng-11687	403	28	was	be	AUX
fumecheng-11687	403	29	obtained	obtain	VERB
fumecheng-11687	403	30	and	and	CCONJ
fumecheng-11687	403	31	converted	convert	VERB
fumecheng-11687	403	32	to	to	ADP
fumecheng-11687	403	33	its	its	PRON
fumecheng-11687	403	34	traditional	traditional	ADJ
fumecheng-11687	403	35	derivative	derivative	ADJ
fumecheng-11687	403	36	form	form	NOUN
fumecheng-11687	403	37	in	in	ADP
fumecheng-11687	403	38	the	the	DET
fumecheng-11687	403	39	continuous	continuous	ADJ
fumecheng-11687	403	40	space	space	NOUN
fumecheng-11687	403	41	.	.	PUNCT
fumecheng-11687	404	1	▪	▪	NOUN
fumecheng-11687	404	2	after	after	ADP
fumecheng-11687	404	3	reducing	reduce	VERB
fumecheng-11687	404	4	its	its	PRON
fumecheng-11687	404	5	rank	rank	NOUN
fumecheng-11687	404	6	,	,	PUNCT
fumecheng-11687	404	7	the	the	DET
fumecheng-11687	404	8	non	non	ADJ
fumecheng-11687	404	9	-	-	ADJ
fumecheng-11687	404	10	perturbative	perturbative	ADJ
fumecheng-11687	404	11	approach	approach	NOUN
fumecheng-11687	404	12	was	be	AUX
fumecheng-11687	404	13	used	use	VERB
fumecheng-11687	404	14	to	to	PART
fumecheng-11687	404	15	calculate	calculate	VERB
fumecheng-11687	404	16	the	the	DET
fumecheng-11687	404	17	analytic	analytic	ADJ
fumecheng-11687	404	18	solution	solution	NOUN
fumecheng-11687	404	19	for	for	ADP
fumecheng-11687	404	20	the	the	DET
fumecheng-11687	404	21	alternate	alternate	ADJ
fumecheng-11687	404	22	equation	equation	NOUN
fumecheng-11687	404	23	in	in	ADP
fumecheng-11687	404	24	the	the	DET
fumecheng-11687	404	25	second	second	ADJ
fumecheng-11687	404	26	-	-	PUNCT
fumecheng-11687	404	27	order	order	NOUN
fumecheng-11687	404	28	form	form	NOUN
fumecheng-11687	404	29	.	.	PUNCT
fumecheng-11687	405	1	▪	▪	NOUN
fumecheng-11687	405	2	it	it	PRON
fumecheng-11687	405	3	is	be	AUX
fumecheng-11687	405	4	seen	see	VERB
fumecheng-11687	405	5	that	that	SCONJ
fumecheng-11687	405	6	the	the	DET
fumecheng-11687	405	7	analytical	analytical	ADJ
fumecheng-11687	405	8	and	and	CCONJ
fumecheng-11687	405	9	numerical	numerical	ADJ
fumecheng-11687	405	10	solutions	solution	NOUN
fumecheng-11687	405	11	agree	agree	VERB
fumecheng-11687	405	12	quite	quite	ADV
fumecheng-11687	405	13	well	well	ADV
fumecheng-11687	405	14	.	.	PUNCT
fumecheng-11687	406	1	▪	▪	NOUN
fumecheng-11687	406	2	the	the	DET
fumecheng-11687	406	3	computations	computation	NOUN
fumecheng-11687	406	4	revealed	reveal	VERB
fumecheng-11687	406	5	that	that	SCONJ
fumecheng-11687	406	6	for	for	ADP
fumecheng-11687	406	7	every	every	DET
fumecheng-11687	406	8	value	value	NOUN
fumecheng-11687	406	9	of	of	ADP
fumecheng-11687	406	10	the	the	DET
fumecheng-11687	406	11	fraction	fraction	NOUN
fumecheng-11687	406	12	parameter	parameter	NOUN
fumecheng-11687	406	13			NOUN
fumecheng-11687	406	14	,	,	PUNCT
fumecheng-11687	406	15	the	the	DET
fumecheng-11687	406	16	approximation	approximation	NOUN
fumecheng-11687	406	17	and	and	CCONJ
fumecheng-11687	406	18	numerical	numerical	ADJ
fumecheng-11687	406	19	solutions	solution	NOUN
fumecheng-11687	406	20	are	be	AUX
fumecheng-11687	406	21	identical	identical	ADJ
fumecheng-11687	406	22	.	.	PUNCT
fumecheng-11687	407	1	▪	▪	NOUN
fumecheng-11687	407	2	𝑑	𝑑	PROPN
fumecheng-11687	407	3	𝑑𝑡𝛼	𝑑𝑡𝛼	PROPN
fumecheng-11687	407	4	cos	cos	PROPN
fumecheng-11687	407	5	ω𝑡	ω𝑡	PROPN
fumecheng-11687	407	6	and	and	CCONJ
fumecheng-11687	407	7	𝑑	𝑑	PROPN
fumecheng-11687	407	8	𝑑𝑡2𝛼	𝑑𝑡2𝛼	PROPN
fumecheng-11687	407	9	cos	cos	PROPN
fumecheng-11687	407	10	ω𝑡	ω𝑡	PROPN
fumecheng-11687	407	11	was	be	AUX
fumecheng-11687	407	12	estimated	estimate	VERB
fumecheng-11687	407	13	,	,	PUNCT
fumecheng-11687	407	14	which	which	PRON
fumecheng-11687	407	15	is	be	AUX
fumecheng-11687	407	16	considered	consider	VERB
fumecheng-11687	407	17	a	a	DET
fumecheng-11687	407	18	new	new	ADJ
fumecheng-11687	407	19	result	result	NOUN
fumecheng-11687	407	20	that	that	PRON
fumecheng-11687	407	21	can	can	AUX
fumecheng-11687	407	22	be	be	AUX
fumecheng-11687	407	23	used	use	VERB
fumecheng-11687	407	24	in	in	ADP
fumecheng-11687	407	25	future	future	ADJ
fumecheng-11687	407	26	works	work	NOUN
fumecheng-11687	407	27	.	.	PUNCT
fumecheng-11687	408	1	214	214	NUM
fumecheng-11687	408	2	y.o	y.o	PROPN
fumecheng-11687	408	3	.	.	PROPN
fumecheng-11687	408	4	el	el	PROPN
fumecheng-11687	408	5	-	-	PUNCT
fumecheng-11687	408	6	dib	dib	PROPN
fumecheng-11687	408	7	,	,	PUNCT
fumecheng-11687	408	8	n.s	n.s	PROPN
fumecheng-11687	408	9	.	.	PROPN
fumecheng-11687	408	10	elgazery	elgazery	PROPN
fumecheng-11687	408	11	,	,	PUNCT
fumecheng-11687	408	12	h.a	h.a	PROPN
fumecheng-11687	408	13	.	.	PROPN
fumecheng-11687	408	14	alyousef	alyousef	PROPN
fumecheng-11687	408	15	▪	▪	ADV
fumecheng-11687	408	16	the	the	DET
fumecheng-11687	408	17	rank	rank	NOUN
fumecheng-11687	408	18	upgrade	upgrade	VERB
fumecheng-11687	408	19	/	/	SYM
fumecheng-11687	408	20	reducing	reduce	VERB
fumecheng-11687	408	21	technique	technique	NOUN
fumecheng-11687	408	22	was	be	AUX
fumecheng-11687	408	23	introduced	introduce	VERB
fumecheng-11687	408	24	as	as	ADP
fumecheng-11687	408	25	a	a	DET
fumecheng-11687	408	26	reliable	reliable	ADJ
fumecheng-11687	408	27	approach	approach	NOUN
fumecheng-11687	408	28	to	to	PART
fumecheng-11687	408	29	overcome	overcome	VERB
fumecheng-11687	408	30	difficulties	difficulty	NOUN
fumecheng-11687	408	31	.	.	PUNCT
fumecheng-11687	409	1	▪	▪	NOUN
fumecheng-11687	409	2	the	the	DET
fumecheng-11687	409	3	present	present	ADJ
fumecheng-11687	409	4	study	study	NOUN
fumecheng-11687	409	5	gives	give	VERB
fumecheng-11687	409	6	reliability	reliability	NOUN
fumecheng-11687	409	7	in	in	ADP
fumecheng-11687	409	8	the	the	DET
fumecheng-11687	409	9	technique	technique	NOUN
fumecheng-11687	409	10	of	of	ADP
fumecheng-11687	409	11	reducing	reduce	VERB
fumecheng-11687	409	12	the	the	DET
fumecheng-11687	409	13	order	order	NOUN
fumecheng-11687	409	14	of	of	ADP
fumecheng-11687	409	15	differential	differential	ADJ
fumecheng-11687	409	16	equations	equation	NOUN
fumecheng-11687	409	17	.	.	PUNCT
fumecheng-11687	410	1	▪	▪	X
fumecheng-11687	410	2	one	one	NUM
fumecheng-11687	410	3	of	of	ADP
fumecheng-11687	410	4	the	the	DET
fumecheng-11687	410	5	most	most	ADV
fumecheng-11687	410	6	important	important	ADJ
fumecheng-11687	410	7	features	feature	NOUN
fumecheng-11687	410	8	of	of	ADP
fumecheng-11687	410	9	these	these	DET
fumecheng-11687	410	10	calculations	calculation	NOUN
fumecheng-11687	410	11	lies	lie	VERB
fumecheng-11687	410	12	in	in	ADP
fumecheng-11687	410	13	the	the	DET
fumecheng-11687	410	14	fact	fact	NOUN
fumecheng-11687	410	15	that	that	SCONJ
fumecheng-11687	410	16	a	a	DET
fumecheng-11687	410	17	fourthorder	fourthorder	NOUN
fumecheng-11687	410	18	equation	equation	NOUN
fumecheng-11687	410	19	can	can	AUX
fumecheng-11687	410	20	be	be	AUX
fumecheng-11687	410	21	reduced	reduce	VERB
fumecheng-11687	410	22	to	to	ADP
fumecheng-11687	410	23	a	a	DET
fumecheng-11687	410	24	second	second	ADJ
fumecheng-11687	410	25	-	-	PUNCT
fumecheng-11687	410	26	order	order	NOUN
fumecheng-11687	410	27	one	one	NOUN
fumecheng-11687	410	28	via	via	ADP
fumecheng-11687	410	29	the	the	DET
fumecheng-11687	410	30	non	non	ADJ
fumecheng-11687	410	31	-	-	ADJ
fumecheng-11687	410	32	perturbative	perturbative	ADJ
fumecheng-11687	410	33	approach	approach	NOUN
fumecheng-11687	410	34	.	.	PUNCT
fumecheng-11687	411	1	▪	▪	NOUN
fumecheng-11687	411	2	galerkin	galerkin	X
fumecheng-11687	411	3	's	's	PART
fumecheng-11687	411	4	method	method	NOUN
fumecheng-11687	411	5	was	be	AUX
fumecheng-11687	411	6	also	also	ADV
fumecheng-11687	411	7	used	use	VERB
fumecheng-11687	411	8	to	to	PART
fumecheng-11687	411	9	find	find	VERB
fumecheng-11687	411	10	the	the	DET
fumecheng-11687	411	11	required	require	VERB
fumecheng-11687	411	12	periodic	periodic	ADJ
fumecheng-11687	411	13	solution	solution	NOUN
fumecheng-11687	411	14	.	.	PUNCT
fumecheng-11687	412	1	▪	▪	NOUN
fumecheng-11687	412	2	decreasing	decrease	VERB
fumecheng-11687	412	3	the	the	DET
fumecheng-11687	412	4	fractal	fractal	ADJ
fumecheng-11687	412	5	order	order	NOUN
fumecheng-11687	412	6	has	have	VERB
fumecheng-11687	412	7	an	an	DET
fumecheng-11687	412	8	impact	impact	NOUN
fumecheng-11687	412	9	on	on	ADP
fumecheng-11687	412	10	the	the	DET
fumecheng-11687	412	11	behaviour	behaviour	NOUN
fumecheng-11687	412	12	of	of	ADP
fumecheng-11687	412	13	periodic	periodic	ADJ
fumecheng-11687	412	14	solution	solution	NOUN
fumecheng-11687	412	15	.	.	PUNCT
fumecheng-11687	413	1	▪	▪	NOUN
fumecheng-11687	413	2	in	in	ADP
fumecheng-11687	413	3	contrast	contrast	NOUN
fumecheng-11687	413	4	to	to	ADP
fumecheng-11687	413	5	the	the	DET
fumecheng-11687	413	6	traditional	traditional	ADJ
fumecheng-11687	413	7	technique	technique	NOUN
fumecheng-11687	413	8	,	,	PUNCT
fumecheng-11687	413	9	which	which	PRON
fumecheng-11687	413	10	worked	work	VERB
fumecheng-11687	413	11	to	to	PART
fumecheng-11687	413	12	transform	transform	VERB
fumecheng-11687	413	13	the	the	DET
fumecheng-11687	413	14	variable	variable	NOUN
fumecheng-11687	413	15	and	and	CCONJ
fumecheng-11687	413	16	was	be	AUX
fumecheng-11687	413	17	valid	valid	ADJ
fumecheng-11687	413	18	only	only	ADV
fumecheng-11687	413	19	in	in	ADP
fumecheng-11687	413	20	the	the	DET
fumecheng-11687	413	21	absence	absence	NOUN
fumecheng-11687	413	22	of	of	ADP
fumecheng-11687	413	23	external	external	ADJ
fumecheng-11687	413	24	forces	force	NOUN
fumecheng-11687	413	25	,	,	PUNCT
fumecheng-11687	413	26	if	if	SCONJ
fumecheng-11687	413	27	there	there	PRON
fumecheng-11687	413	28	was	be	VERB
fumecheng-11687	413	29	an	an	DET
fumecheng-11687	413	30	external	external	ADJ
fumecheng-11687	413	31	force	force	NOUN
fumecheng-11687	413	32	,	,	PUNCT
fumecheng-11687	413	33	it	it	PRON
fumecheng-11687	413	34	leads	lead	VERB
fumecheng-11687	413	35	to	to	ADP
fumecheng-11687	413	36	great	great	ADJ
fumecheng-11687	413	37	mathematical	mathematical	ADJ
fumecheng-11687	413	38	difficulties	difficulty	NOUN
fumecheng-11687	413	39	.	.	PUNCT
fumecheng-11687	414	1	the	the	DET
fumecheng-11687	414	2	current	current	ADJ
fumecheng-11687	414	3	technique	technique	NOUN
fumecheng-11687	414	4	works	work	VERB
fumecheng-11687	414	5	on	on	ADP
fumecheng-11687	414	6	the	the	DET
fumecheng-11687	414	7	operator	operator	NOUN
fumecheng-11687	414	8	,	,	PUNCT
fumecheng-11687	414	9	which	which	PRON
fumecheng-11687	414	10	is	be	AUX
fumecheng-11687	414	11	simple	simple	ADJ
fumecheng-11687	414	12	and	and	CCONJ
fumecheng-11687	414	13	effective	effective	ADJ
fumecheng-11687	414	14	when	when	SCONJ
fumecheng-11687	414	15	fractal	fractal	ADJ
fumecheng-11687	414	16	oscillators	oscillator	NOUN
fumecheng-11687	414	17	with	with	ADP
fumecheng-11687	414	18	external	external	ADJ
fumecheng-11687	414	19	forces	force	NOUN
fumecheng-11687	414	20	are	be	AUX
fumecheng-11687	414	21	investigated	investigate	VERB
fumecheng-11687	414	22	,	,	PUNCT
fumecheng-11687	414	23	it	it	PRON
fumecheng-11687	414	24	is	be	AUX
fumecheng-11687	414	25	easy	easy	ADJ
fumecheng-11687	414	26	to	to	PART
fumecheng-11687	414	27	obtain	obtain	VERB
fumecheng-11687	414	28	analytic	analytic	ADJ
fumecheng-11687	414	29	solutions	solution	NOUN
fumecheng-11687	414	30	,	,	PUNCT
fumecheng-11687	414	31	and	and	CCONJ
fumecheng-11687	414	32	the	the	DET
fumecheng-11687	414	33	technique	technique	NOUN
fumecheng-11687	414	34	does	do	AUX
fumecheng-11687	414	35	n't	not	PART
fumecheng-11687	414	36	lead	lead	VERB
fumecheng-11687	414	37	to	to	ADP
fumecheng-11687	414	38	any	any	DET
fumecheng-11687	414	39	mathematical	mathematical	ADJ
fumecheng-11687	414	40	difficulties	difficulty	NOUN
fumecheng-11687	414	41	.	.	PUNCT
fumecheng-11687	415	1	acknowledgement	acknowledgement	NOUN
fumecheng-11687	415	2	:	:	PUNCT
fumecheng-11687	415	3	the	the	DET
fumecheng-11687	415	4	authors	author	NOUN
fumecheng-11687	415	5	express	express	VERB
fumecheng-11687	415	6	their	their	PRON
fumecheng-11687	415	7	gratitude	gratitude	NOUN
fumecheng-11687	415	8	to	to	PART
fumecheng-11687	415	9	princess	princess	VERB
fumecheng-11687	415	10	nourah	nourah	PROPN
fumecheng-11687	415	11	bint	bint	PROPN
fumecheng-11687	415	12	abdulrahman	abdulrahman	PROPN
fumecheng-11687	415	13	university	university	PROPN
fumecheng-11687	415	14	researchers	researcher	NOUN
fumecheng-11687	415	15	supporting	support	VERB
fumecheng-11687	415	16	project	project	NOUN
fumecheng-11687	415	17	number	number	NOUN
fumecheng-11687	415	18	(	(	PUNCT
fumecheng-11687	415	19	pnursp2023r17	pnursp2023r17	ADJ
fumecheng-11687	415	20	)	)	PUNCT
fumecheng-11687	415	21	,	,	PUNCT
fumecheng-11687	415	22	princess	princess	PROPN
fumecheng-11687	415	23	nourah	nourah	PROPN
fumecheng-11687	415	24	bint	bint	PROPN
fumecheng-11687	415	25	abdulrahman	abdulrahman	PROPN
fumecheng-11687	415	26	university	university	PROPN
fumecheng-11687	415	27	,	,	PUNCT
fumecheng-11687	415	28	riyadh	riyadh	PROPN
fumecheng-11687	415	29	,	,	PUNCT
fumecheng-11687	415	30	saudi	saudi	PROPN
fumecheng-11687	415	31	arabia	arabia	PROPN
fumecheng-11687	415	32	.	.	PUNCT
fumecheng-11687	416	1	references	reference	NOUN
fumecheng-11687	416	2	1	1	NUM
fumecheng-11687	416	3	.	.	PUNCT
fumecheng-11687	417	1	zmeskal	zmeskal	PROPN
fumecheng-11687	417	2	,	,	PUNCT
fumecheng-11687	417	3	o.	o.	PROPN
fumecheng-11687	417	4	,	,	PUNCT
fumecheng-11687	417	5	dzik	dzik	NOUN
fumecheng-11687	417	6	,	,	PUNCT
fumecheng-11687	417	7	p.	p.	NOUN
fumecheng-11687	417	8	,	,	PUNCT
fumecheng-11687	417	9	vesely	vesely	NOUN
fumecheng-11687	417	10	m.	m.	NOUN
fumecheng-11687	417	11	,	,	PUNCT
fumecheng-11687	417	12	2013	2013	NUM
fumecheng-11687	417	13	,	,	PUNCT
fumecheng-11687	417	14	entropy	entropy	NOUN
fumecheng-11687	417	15	of	of	ADP
fumecheng-11687	417	16	fractal	fractal	ADJ
fumecheng-11687	417	17	systems	system	NOUN
fumecheng-11687	417	18	,	,	PUNCT
fumecheng-11687	417	19	computers	computer	NOUN
fumecheng-11687	417	20	&	&	CCONJ
fumecheng-11687	417	21	mathematics	mathematics	PROPN
fumecheng-11687	417	22	with	with	ADP
fumecheng-11687	417	23	applications	application	NOUN
fumecheng-11687	417	24	,	,	PUNCT
fumecheng-11687	417	25	66(2	66(2	NUM
fumecheng-11687	417	26	)	)	PUNCT
fumecheng-11687	417	27	,	,	PUNCT
fumecheng-11687	417	28	pp	pp	PROPN
fumecheng-11687	417	29	.	.	PUNCT
fumecheng-11687	418	1	135	135	NUM
fumecheng-11687	418	2	-	-	SYM
fumecheng-11687	418	3	146	146	NUM
fumecheng-11687	418	4	.	.	NOUN
fumecheng-11687	419	1	2	2	NUM
fumecheng-11687	419	2	.	.	X
fumecheng-11687	419	3	edgar	edgar	PROPN
fumecheng-11687	419	4	,	,	PUNCT
fumecheng-11687	419	5	g.	g.	PROPN
fumecheng-11687	419	6	a.	a.	PROPN
fumecheng-11687	419	7	,	,	PUNCT
fumecheng-11687	419	8	2008	2008	NUM
fumecheng-11687	419	9	,	,	PUNCT
fumecheng-11687	419	10	measure	measure	NOUN
fumecheng-11687	419	11	,	,	PUNCT
fumecheng-11687	419	12	topology	topology	NOUN
fumecheng-11687	419	13	,	,	PUNCT
fumecheng-11687	419	14	and	and	CCONJ
fumecheng-11687	419	15	fractal	fractal	ADJ
fumecheng-11687	419	16	geometry	geometry	NOUN
fumecheng-11687	419	17	,	,	PUNCT
fumecheng-11687	419	18	edition	edition	NOUN
fumecheng-11687	419	19	number	number	NOUN
fumecheng-11687	419	20	2	2	NUM
fumecheng-11687	419	21	,	,	PUNCT
fumecheng-11687	419	22	springer	springer	NOUN
fumecheng-11687	419	23	new	new	PROPN
fumecheng-11687	419	24	york	york	PROPN
fumecheng-11687	419	25	,	,	PUNCT
fumecheng-11687	419	26	ny	ny	PROPN
fumecheng-11687	419	27	.	.	PROPN
fumecheng-11687	420	1	3	3	X
fumecheng-11687	420	2	.	.	X
fumecheng-11687	420	3	chen	chen	PROPN
fumecheng-11687	420	4	,	,	PUNCT
fumecheng-11687	420	5	m.	m.	NOUN
fumecheng-11687	420	6	,	,	PUNCT
fumecheng-11687	420	7	yu	yu	PROPN
fumecheng-11687	420	8	,	,	PUNCT
fumecheng-11687	420	9	b.	b.	PROPN
fumecheng-11687	420	10	,	,	PUNCT
fumecheng-11687	420	11	xu	xu	PROPN
fumecheng-11687	420	12	,	,	PUNCT
fumecheng-11687	420	13	p.	p.	PROPN
fumecheng-11687	420	14	,	,	PUNCT
fumecheng-11687	420	15	chen	chen	PROPN
fumecheng-11687	420	16	,	,	PUNCT
fumecheng-11687	420	17	j.	j.	PROPN
fumecheng-11687	420	18	,	,	PUNCT
fumecheng-11687	420	19	2007	2007	NUM
fumecheng-11687	420	20	,	,	PUNCT
fumecheng-11687	420	21	a	a	DET
fumecheng-11687	420	22	new	new	ADJ
fumecheng-11687	420	23	deterministic	deterministic	ADJ
fumecheng-11687	420	24	complex	complex	ADJ
fumecheng-11687	420	25	network	network	NOUN
fumecheng-11687	420	26	model	model	NOUN
fumecheng-11687	420	27	with	with	ADP
fumecheng-11687	420	28	hierarchical	hierarchical	ADJ
fumecheng-11687	420	29	structure	structure	NOUN
fumecheng-11687	420	30	,	,	PUNCT
fumecheng-11687	420	31	physica	physica	VERB
fumecheng-11687	420	32	a	a	DET
fumecheng-11687	420	33	:	:	PUNCT
fumecheng-11687	420	34	statistical	statistical	ADJ
fumecheng-11687	420	35	mechanics	mechanic	NOUN
fumecheng-11687	420	36	and	and	CCONJ
fumecheng-11687	420	37	its	its	PRON
fumecheng-11687	420	38	applications	application	NOUN
fumecheng-11687	420	39	,	,	PUNCT
fumecheng-11687	420	40	385(2	385(2	NUM
fumecheng-11687	420	41	)	)	PUNCT
fumecheng-11687	420	42	,	,	PUNCT
fumecheng-11687	420	43	pp	pp	ADP
fumecheng-11687	420	44	.	.	PUNCT
fumecheng-11687	421	1	707	707	NUM
fumecheng-11687	421	2	-	-	SYM
fumecheng-11687	421	3	717	717	NUM
fumecheng-11687	421	4	.	.	PUNCT
fumecheng-11687	422	1	4	4	NUM
fumecheng-11687	422	2	.	.	X
fumecheng-11687	422	3	yang	yang	PROPN
fumecheng-11687	422	4	,	,	PUNCT
fumecheng-11687	422	5	s.	s.	PROPN
fumecheng-11687	422	6	,	,	PUNCT
fumecheng-11687	422	7	fu	fu	PROPN
fumecheng-11687	422	8	,	,	PUNCT
fumecheng-11687	422	9	h.	h.	PROPN
fumecheng-11687	422	10	,	,	PUNCT
fumecheng-11687	422	11	yu	yu	PROPN
fumecheng-11687	422	12	,	,	PUNCT
fumecheng-11687	422	13	b.	b.	PROPN
fumecheng-11687	422	14	,	,	PUNCT
fumecheng-11687	422	15	2017	2017	NUM
fumecheng-11687	422	16	,	,	PUNCT
fumecheng-11687	422	17	fractal	fractal	ADJ
fumecheng-11687	422	18	analysis	analysis	NOUN
fumecheng-11687	422	19	of	of	ADP
fumecheng-11687	422	20	flow	flow	NOUN
fumecheng-11687	422	21	resistance	resistance	NOUN
fumecheng-11687	422	22	in	in	ADP
fumecheng-11687	422	23	tree	tree	NOUN
fumecheng-11687	422	24	-	-	PUNCT
fumecheng-11687	422	25	like	like	ADJ
fumecheng-11687	422	26	branching	branch	VERB
fumecheng-11687	422	27	networks	network	NOUN
fumecheng-11687	422	28	with	with	ADP
fumecheng-11687	422	29	roughened	roughen	VERB
fumecheng-11687	422	30	microchannels	microchannel	NOUN
fumecheng-11687	422	31	,	,	PUNCT
fumecheng-11687	422	32	fractals	fractal	NOUN
fumecheng-11687	422	33	,	,	PUNCT
fumecheng-11687	422	34	25(1	25(1	NUM
fumecheng-11687	422	35	)	)	PUNCT
fumecheng-11687	422	36	,	,	PUNCT
fumecheng-11687	422	37	1750008	1750008	NUM
fumecheng-11687	422	38	.	.	PUNCT
fumecheng-11687	423	1	5	5	X
fumecheng-11687	423	2	.	.	X
fumecheng-11687	423	3	miao	miao	NOUN
fumecheng-11687	423	4	,	,	PUNCT
fumecheng-11687	423	5	t.	t.	PROPN
fumecheng-11687	423	6	,	,	PUNCT
fumecheng-11687	423	7	chen	chen	PROPN
fumecheng-11687	423	8	,	,	PUNCT
fumecheng-11687	423	9	a.	a.	PROPN
fumecheng-11687	423	10	,	,	PUNCT
fumecheng-11687	423	11	xu	xu	PROPN
fumecheng-11687	423	12	,	,	PUNCT
fumecheng-11687	423	13	y.	y.	PROPN
fumecheng-11687	423	14	,	,	PUNCT
fumecheng-11687	423	15	yang	yang	PROPN
fumecheng-11687	423	16	,	,	PUNCT
fumecheng-11687	423	17	s.	s.	PROPN
fumecheng-11687	423	18	,	,	PUNCT
fumecheng-11687	423	19	yu	yu	PROPN
fumecheng-11687	423	20	,	,	PUNCT
fumecheng-11687	423	21	b.	b.	PROPN
fumecheng-11687	423	22	,	,	PUNCT
fumecheng-11687	423	23	2016	2016	NUM
fumecheng-11687	423	24	,	,	PUNCT
fumecheng-11687	423	25	optimal	optimal	ADJ
fumecheng-11687	423	26	structure	structure	NOUN
fumecheng-11687	423	27	of	of	ADP
fumecheng-11687	423	28	damaged	damage	VERB
fumecheng-11687	423	29	tree	tree	NOUN
fumecheng-11687	423	30	-	-	PUNCT
fumecheng-11687	423	31	like	like	ADJ
fumecheng-11687	423	32	branching	branch	VERB
fumecheng-11687	423	33	networks	network	NOUN
fumecheng-11687	423	34	for	for	ADP
fumecheng-11687	423	35	the	the	DET
fumecheng-11687	423	36	equivalent	equivalent	ADJ
fumecheng-11687	423	37	thermal	thermal	ADJ
fumecheng-11687	423	38	conductivity	conductivity	NOUN
fumecheng-11687	423	39	,	,	PUNCT
fumecheng-11687	423	40	international	international	ADJ
fumecheng-11687	423	41	journal	journal	NOUN
fumecheng-11687	423	42	of	of	ADP
fumecheng-11687	423	43	thermal	thermal	ADJ
fumecheng-11687	423	44	sciences	science	NOUN
fumecheng-11687	423	45	,	,	PUNCT
fumecheng-11687	423	46	102	102	NUM
fumecheng-11687	423	47	,	,	PUNCT
fumecheng-11687	423	48	pp	pp	ADJ
fumecheng-11687	423	49	.	.	PUNCT
fumecheng-11687	424	1	89–99	89–99	NUM
fumecheng-11687	424	2	.	.	PUNCT
fumecheng-11687	425	1	6	6	NUM
fumecheng-11687	425	2	.	.	X
fumecheng-11687	425	3	liang	liang	PROPN
fumecheng-11687	425	4	,	,	PUNCT
fumecheng-11687	425	5	m.	m.	NOUN
fumecheng-11687	425	6	,	,	PUNCT
fumecheng-11687	425	7	gao	gao	PROPN
fumecheng-11687	425	8	,	,	PUNCT
fumecheng-11687	425	9	y.	y.	PROPN
fumecheng-11687	425	10	,	,	PUNCT
fumecheng-11687	425	11	yang	yang	PROPN
fumecheng-11687	425	12	,	,	PUNCT
fumecheng-11687	425	13	s.	s.	PROPN
fumecheng-11687	425	14	,	,	PUNCT
fumecheng-11687	425	15	xiao	xiao	PROPN
fumecheng-11687	425	16	,	,	PUNCT
fumecheng-11687	425	17	b.	b.	PROPN
fumecheng-11687	425	18	,	,	PUNCT
fumecheng-11687	425	19	wang	wang	PROPN
fumecheng-11687	425	20	,	,	PUNCT
fumecheng-11687	425	21	z.	z.	PROPN
fumecheng-11687	425	22	,	,	PUNCT
fumecheng-11687	425	23	li	li	PROPN
fumecheng-11687	425	24	,	,	PUNCT
fumecheng-11687	425	25	y.	y.	PROPN
fumecheng-11687	425	26	,	,	PUNCT
fumecheng-11687	425	27	2018	2018	NUM
fumecheng-11687	425	28	,	,	PUNCT
fumecheng-11687	425	29	an	an	DET
fumecheng-11687	425	30	analytical	analytical	ADJ
fumecheng-11687	425	31	model	model	NOUN
fumecheng-11687	425	32	for	for	ADP
fumecheng-11687	425	33	two	two	NUM
fumecheng-11687	425	34	-	-	PUNCT
fumecheng-11687	425	35	phase	phase	NOUN
fumecheng-11687	425	36	relative	relative	ADJ
fumecheng-11687	425	37	permeability	permeability	NOUN
fumecheng-11687	425	38	with	with	ADP
fumecheng-11687	425	39	jamin	jamin	PROPN
fumecheng-11687	425	40	effect	effect	NOUN
fumecheng-11687	425	41	in	in	ADP
fumecheng-11687	425	42	porous	porous	ADJ
fumecheng-11687	425	43	media	medium	NOUN
fumecheng-11687	425	44	,	,	PUNCT
fumecheng-11687	425	45	fractals	fractal	NOUN
fumecheng-11687	425	46	,	,	PUNCT
fumecheng-11687	425	47	26(3	26(3	NUM
fumecheng-11687	425	48	)	)	PUNCT
fumecheng-11687	425	49	,	,	PUNCT
fumecheng-11687	425	50	1850037	1850037	NUM
fumecheng-11687	425	51	.	.	PUNCT
fumecheng-11687	426	1	7	7	X
fumecheng-11687	426	2	.	.	X
fumecheng-11687	426	3	he	he	PRON
fumecheng-11687	426	4	,	,	PUNCT
fumecheng-11687	426	5	j.-h	j.-h	PROPN
fumecheng-11687	426	6	.	.	PROPN
fumecheng-11687	426	7	,	,	PUNCT
fumecheng-11687	426	8	kou	kou	PROPN
fumecheng-11687	426	9	,	,	PUNCT
fumecheng-11687	426	10	s.-j	s.-j	PROPN
fumecheng-11687	426	11	.	.	PUNCT
fumecheng-11687	426	12	,	,	PUNCT
fumecheng-11687	426	13	he	he	PRON
fumecheng-11687	426	14	,	,	PUNCT
fumecheng-11687	426	15	c.-h	c.-h	PROPN
fumecheng-11687	426	16	.	.	PUNCT
fumecheng-11687	426	17	,	,	PUNCT
fumecheng-11687	426	18	zhang	zhang	PROPN
fumecheng-11687	426	19	,	,	PUNCT
fumecheng-11687	426	20	z.-w	z.-w	PROPN
fumecheng-11687	426	21	.	.	PUNCT
fumecheng-11687	426	22	,	,	PUNCT
fumecheng-11687	426	23	gepreel	gepreel	PROPN
fumecheng-11687	426	24	,	,	PUNCT
fumecheng-11687	426	25	k.	k.	PROPN
fumecheng-11687	426	26	a.	a.	PROPN
fumecheng-11687	426	27	,	,	PUNCT
fumecheng-11687	426	28	2021	2021	NUM
fumecheng-11687	426	29	,	,	PUNCT
fumecheng-11687	426	30	fractal	fractal	ADJ
fumecheng-11687	426	31	oscillation	oscillation	NOUN
fumecheng-11687	426	32	and	and	CCONJ
fumecheng-11687	426	33	its	its	PRON
fumecheng-11687	426	34	frequencyamplitude	frequencyamplitude	NOUN
fumecheng-11687	426	35	property	property	NOUN
fumecheng-11687	426	36	,	,	PUNCT
fumecheng-11687	426	37	fractals	fractal	NOUN
fumecheng-11687	426	38	,	,	PUNCT
fumecheng-11687	426	39	29(4	29(4	NOUN
fumecheng-11687	426	40	)	)	PUNCT
fumecheng-11687	426	41	,	,	PUNCT
fumecheng-11687	426	42	2150105	2150105	NUM
fumecheng-11687	426	43	.	.	PUNCT
fumecheng-11687	427	1	8	8	X
fumecheng-11687	427	2	.	.	X
fumecheng-11687	428	1	wang	wang	PROPN
fumecheng-11687	428	2	,	,	PUNCT
fumecheng-11687	428	3	k.-l	k.-l	PROPN
fumecheng-11687	428	4	.	.	PUNCT
fumecheng-11687	428	5	,	,	PUNCT
fumecheng-11687	428	6	2022	2022	NUM
fumecheng-11687	428	7	,	,	PUNCT
fumecheng-11687	428	8	exact	exact	ADJ
fumecheng-11687	428	9	solitary	solitary	ADJ
fumecheng-11687	428	10	wave	wave	NOUN
fumecheng-11687	428	11	solution	solution	NOUN
fumecheng-11687	428	12	for	for	ADP
fumecheng-11687	428	13	fractal	fractal	ADJ
fumecheng-11687	428	14	shallow	shallow	ADJ
fumecheng-11687	428	15	water	water	NOUN
fumecheng-11687	428	16	wave	wave	NOUN
fumecheng-11687	428	17	model	model	NOUN
fumecheng-11687	428	18	by	by	ADP
fumecheng-11687	428	19	he	he	PRON
fumecheng-11687	428	20	’s	’	VERB
fumecheng-11687	428	21	variational	variational	ADJ
fumecheng-11687	428	22	method	method	NOUN
fumecheng-11687	428	23	,	,	PUNCT
fumecheng-11687	428	24	modern	modern	ADJ
fumecheng-11687	428	25	physics	physics	NOUN
fumecheng-11687	428	26	letters	letters	PROPN
fumecheng-11687	428	27	b	b	NOUN
fumecheng-11687	428	28	,	,	PUNCT
fumecheng-11687	428	29	36(7	36(7	NUM
fumecheng-11687	428	30	)	)	PUNCT
fumecheng-11687	428	31	,	,	PUNCT
fumecheng-11687	428	32	2150602	2150602	NUM
fumecheng-11687	428	33	.	.	PUNCT
fumecheng-11687	429	1	9	9	X
fumecheng-11687	429	2	.	.	X
fumecheng-11687	429	3	ain	ain	PROPN
fumecheng-11687	429	4	,	,	PUNCT
fumecheng-11687	429	5	q.t	q.t	PROPN
fumecheng-11687	429	6	.	.	PROPN
fumecheng-11687	429	7	,	,	PUNCT
fumecheng-11687	429	8	he	he	PRON
fumecheng-11687	429	9	,	,	PUNCT
fumecheng-11687	429	10	j.-h	j.-h	PROPN
fumecheng-11687	429	11	.	.	PROPN
fumecheng-11687	429	12	,	,	PUNCT
fumecheng-11687	429	13	2019	2019	NUM
fumecheng-11687	429	14	,	,	PUNCT
fumecheng-11687	429	15	on	on	ADP
fumecheng-11687	429	16	two	two	NUM
fumecheng-11687	429	17	-	-	PUNCT
fumecheng-11687	429	18	scale	scale	NOUN
fumecheng-11687	429	19	dimension	dimension	NOUN
fumecheng-11687	429	20	and	and	CCONJ
fumecheng-11687	429	21	its	its	PRON
fumecheng-11687	429	22	applications	application	NOUN
fumecheng-11687	429	23	,	,	PUNCT
fumecheng-11687	429	24	thermal	thermal	ADJ
fumecheng-11687	429	25	science	science	NOUN
fumecheng-11687	429	26	,	,	PUNCT
fumecheng-11687	429	27	23(3	23(3	NUM
fumecheng-11687	429	28	)	)	PUNCT
fumecheng-11687	429	29	part	part	NOUN
fumecheng-11687	429	30	b	b	PROPN
fumecheng-11687	429	31	,	,	PUNCT
fumecheng-11687	429	32	pp	pp	ADJ
fumecheng-11687	429	33	.	.	PUNCT
fumecheng-11687	429	34	1707	1707	NUM
fumecheng-11687	429	35	-	-	SYM
fumecheng-11687	429	36	1712	1712	NUM
fumecheng-11687	429	37	.	.	PUNCT
fumecheng-11687	430	1	10	10	NUM
fumecheng-11687	430	2	.	.	PUNCT
fumecheng-11687	431	1	li	li	PROPN
fumecheng-11687	431	2	,	,	PUNCT
fumecheng-11687	431	3	x.	x.	PROPN
fumecheng-11687	431	4	,	,	PUNCT
fumecheng-11687	431	5	liu	liu	PROPN
fumecheng-11687	431	6	,	,	PUNCT
fumecheng-11687	431	7	z.	z.	PROPN
fumecheng-11687	431	8	,	,	PUNCT
fumecheng-11687	431	9	he	he	PRON
fumecheng-11687	431	10	,	,	PUNCT
fumecheng-11687	431	11	j.-h	j.-h	PROPN
fumecheng-11687	431	12	.	.	PUNCT
fumecheng-11687	431	13	,	,	PUNCT
fumecheng-11687	431	14	2020	2020	NUM
fumecheng-11687	431	15	,	,	PUNCT
fumecheng-11687	431	16	a	a	DET
fumecheng-11687	431	17	fractal	fractal	ADJ
fumecheng-11687	431	18	two	two	NUM
fumecheng-11687	431	19	-	-	PUNCT
fumecheng-11687	431	20	phase	phase	NOUN
fumecheng-11687	431	21	flow	flow	NOUN
fumecheng-11687	431	22	model	model	NOUN
fumecheng-11687	431	23	for	for	ADP
fumecheng-11687	431	24	the	the	DET
fumecheng-11687	431	25	fiber	fiber	NOUN
fumecheng-11687	431	26	motion	motion	NOUN
fumecheng-11687	431	27	in	in	ADP
fumecheng-11687	431	28	a	a	DET
fumecheng-11687	431	29	polymer	polymer	NOUN
fumecheng-11687	431	30	filling	filling	NOUN
fumecheng-11687	431	31	process	process	NOUN
fumecheng-11687	431	32	,	,	PUNCT
fumecheng-11687	431	33	fractals	fractal	NOUN
fumecheng-11687	431	34	,	,	PUNCT
fumecheng-11687	431	35	28(5	28(5	NUM
fumecheng-11687	431	36	)	)	PUNCT
fumecheng-11687	431	37	,	,	PUNCT
fumecheng-11687	431	38	2050093	2050093	NUM
fumecheng-11687	431	39	.	.	PUNCT
fumecheng-11687	432	1	11	11	NUM
fumecheng-11687	432	2	.	.	PUNCT
fumecheng-11687	433	1	zuo	zuo	NOUN
fumecheng-11687	433	2	,	,	PUNCT
fumecheng-11687	433	3	y.	y.	NOUN
fumecheng-11687	433	4	,	,	PUNCT
fumecheng-11687	433	5	2021	2021	NUM
fumecheng-11687	433	6	,	,	PUNCT
fumecheng-11687	433	7	a	a	DET
fumecheng-11687	433	8	gecko	gecko	NOUN
fumecheng-11687	433	9	-	-	PUNCT
fumecheng-11687	433	10	like	like	ADJ
fumecheng-11687	433	11	fractal	fractal	ADJ
fumecheng-11687	433	12	receptor	receptor	NOUN
fumecheng-11687	433	13	of	of	ADP
fumecheng-11687	433	14	a	a	DET
fumecheng-11687	433	15	three	three	NUM
fumecheng-11687	433	16	-	-	PUNCT
fumecheng-11687	433	17	dimensional	dimensional	ADJ
fumecheng-11687	433	18	printing	printing	NOUN
fumecheng-11687	433	19	technology	technology	NOUN
fumecheng-11687	433	20	:	:	PUNCT
fumecheng-11687	433	21	a	a	DET
fumecheng-11687	433	22	fractal	fractal	ADJ
fumecheng-11687	433	23	oscillator	oscillator	NOUN
fumecheng-11687	433	24	,	,	PUNCT
fumecheng-11687	433	25	journal	journal	NOUN
fumecheng-11687	433	26	of	of	ADP
fumecheng-11687	433	27	mathematical	mathematical	ADJ
fumecheng-11687	433	28	chemistry	chemistry	NOUN
fumecheng-11687	433	29	,	,	PUNCT
fumecheng-11687	433	30	59(3	59(3	NUM
fumecheng-11687	433	31	)	)	PUNCT
fumecheng-11687	433	32	,	,	PUNCT
fumecheng-11687	433	33	pp	pp	PROPN
fumecheng-11687	433	34	.	.	PUNCT
fumecheng-11687	434	1	735	735	NUM
fumecheng-11687	434	2	-	-	SYM
fumecheng-11687	434	3	744	744	NUM
fumecheng-11687	434	4	.	.	NOUN
fumecheng-11687	435	1	12	12	NUM
fumecheng-11687	435	2	.	.	PUNCT
fumecheng-11687	436	1	liu	liu	PROPN
fumecheng-11687	436	2	,	,	PUNCT
fumecheng-11687	436	3	c.	c.	PROPN
fumecheng-11687	436	4	,	,	PUNCT
fumecheng-11687	436	5	2021	2021	NUM
fumecheng-11687	436	6	,	,	PUNCT
fumecheng-11687	436	7	periodic	periodic	ADJ
fumecheng-11687	436	8	solution	solution	NOUN
fumecheng-11687	436	9	of	of	ADP
fumecheng-11687	436	10	fractal	fractal	ADJ
fumecheng-11687	436	11	phi-4	phi-4	PRON
fumecheng-11687	436	12	equation	equation	NOUN
fumecheng-11687	436	13	,	,	PUNCT
fumecheng-11687	436	14	thermal	thermal	ADJ
fumecheng-11687	436	15	science	science	NOUN
fumecheng-11687	436	16	,	,	PUNCT
fumecheng-11687	436	17	25(2	25(2	NUM
fumecheng-11687	436	18	)	)	PUNCT
fumecheng-11687	436	19	part	part	NOUN
fumecheng-11687	436	20	b	b	PROPN
fumecheng-11687	436	21	,	,	PUNCT
fumecheng-11687	436	22	pp	pp	ADJ
fumecheng-11687	436	23	.	.	PUNCT
fumecheng-11687	436	24	1345–1350	1345–1350	NUM
fumecheng-11687	436	25	.	.	PUNCT
fumecheng-11687	437	1	13	13	NUM
fumecheng-11687	437	2	.	.	PUNCT
fumecheng-11687	438	1	he	he	PRON
fumecheng-11687	438	2	,	,	PUNCT
fumecheng-11687	438	3	c.-h	c.-h	PROPN
fumecheng-11687	438	4	.	.	PROPN
fumecheng-11687	438	5	,	,	PUNCT
fumecheng-11687	438	6	liu	liu	PROPN
fumecheng-11687	438	7	,	,	PUNCT
fumecheng-11687	438	8	c.	c.	PROPN
fumecheng-11687	438	9	,	,	PUNCT
fumecheng-11687	438	10	he	he	PRON
fumecheng-11687	438	11	,	,	PUNCT
fumecheng-11687	438	12	j.-h	j.-h	PROPN
fumecheng-11687	438	13	.	.	PUNCT
fumecheng-11687	438	14	,	,	PUNCT
fumecheng-11687	438	15	gepreel	gepreel	PROPN
fumecheng-11687	438	16	,	,	PUNCT
fumecheng-11687	438	17	k.a	k.a	PROPN
fumecheng-11687	438	18	.	.	PROPN
fumecheng-11687	438	19	,	,	PUNCT
fumecheng-11687	438	20	2021	2021	NUM
fumecheng-11687	438	21	,	,	PUNCT
fumecheng-11687	438	22	low	low	ADJ
fumecheng-11687	438	23	frequency	frequency	NOUN
fumecheng-11687	438	24	property	property	NOUN
fumecheng-11687	438	25	of	of	ADP
fumecheng-11687	438	26	a	a	DET
fumecheng-11687	438	27	fractal	fractal	ADJ
fumecheng-11687	438	28	vibration	vibration	NOUN
fumecheng-11687	438	29	model	model	NOUN
fumecheng-11687	438	30	for	for	ADP
fumecheng-11687	438	31	a	a	DET
fumecheng-11687	438	32	concrete	concrete	ADJ
fumecheng-11687	438	33	beam	beam	NOUN
fumecheng-11687	438	34	,	,	PUNCT
fumecheng-11687	438	35	fractals	fractal	NOUN
fumecheng-11687	438	36	,	,	PUNCT
fumecheng-11687	438	37	29(5	29(5	NUM
fumecheng-11687	438	38	)	)	PUNCT
fumecheng-11687	438	39	,	,	PUNCT
fumecheng-11687	438	40	2150117	2150117	NUM
fumecheng-11687	438	41	.	.	PUNCT
fumecheng-11687	439	1	14	14	NUM
fumecheng-11687	439	2	.	.	X
fumecheng-11687	440	1	anjum	anjum	PROPN
fumecheng-11687	440	2	,	,	PUNCT
fumecheng-11687	440	3	n.	n.	PROPN
fumecheng-11687	440	4	,	,	PUNCT
fumecheng-11687	440	5	he	he	PRON
fumecheng-11687	440	6	,	,	PUNCT
fumecheng-11687	440	7	c.-h	c.-h	PROPN
fumecheng-11687	440	8	.	.	PUNCT
fumecheng-11687	440	9	,	,	PUNCT
fumecheng-11687	440	10	he	he	PRON
fumecheng-11687	440	11	,	,	PUNCT
fumecheng-11687	440	12	j.-h	j.-h	PROPN
fumecheng-11687	440	13	.	.	PROPN
fumecheng-11687	440	14	,	,	PUNCT
fumecheng-11687	440	15	2021	2021	NUM
fumecheng-11687	440	16	,	,	PUNCT
fumecheng-11687	440	17	two	two	NUM
fumecheng-11687	440	18	-	-	PUNCT
fumecheng-11687	440	19	scale	scale	NOUN
fumecheng-11687	440	20	fractal	fractal	ADJ
fumecheng-11687	440	21	theory	theory	NOUN
fumecheng-11687	440	22	for	for	ADP
fumecheng-11687	440	23	the	the	DET
fumecheng-11687	440	24	population	population	NOUN
fumecheng-11687	440	25	dynamics	dynamic	NOUN
fumecheng-11687	440	26	,	,	PUNCT
fumecheng-11687	440	27	fractals	fractal	NOUN
fumecheng-11687	440	28	,	,	PUNCT
fumecheng-11687	440	29	29(7	29(7	NUM
fumecheng-11687	440	30	)	)	PUNCT
fumecheng-11687	440	31	,	,	PUNCT
fumecheng-11687	440	32	2150182	2150182	NUM
fumecheng-11687	440	33	.	.	PUNCT
fumecheng-11687	441	1	15	15	NUM
fumecheng-11687	441	2	.	.	X
fumecheng-11687	442	1	anjum	anjum	PROPN
fumecheng-11687	442	2	,	,	PUNCT
fumecheng-11687	442	3	n.	n.	PROPN
fumecheng-11687	442	4	,	,	PUNCT
fumecheng-11687	442	5	ain	ain	PROPN
fumecheng-11687	442	6	,	,	PUNCT
fumecheng-11687	442	7	q.t	q.t	PROPN
fumecheng-11687	442	8	.	.	PROPN
fumecheng-11687	442	9	,	,	PUNCT
fumecheng-11687	442	10	li	li	PROPN
fumecheng-11687	442	11	,	,	PUNCT
fumecheng-11687	442	12	x.x	x.x	PROPN
fumecheng-11687	442	13	.	.	PROPN
fumecheng-11687	442	14	,	,	PUNCT
fumecheng-11687	442	15	2021	2021	NUM
fumecheng-11687	442	16	,	,	PUNCT
fumecheng-11687	442	17	two	two	NUM
fumecheng-11687	442	18	-	-	PUNCT
fumecheng-11687	442	19	scale	scale	NOUN
fumecheng-11687	442	20	mathematical	mathematical	ADJ
fumecheng-11687	442	21	model	model	NOUN
fumecheng-11687	442	22	for	for	ADP
fumecheng-11687	442	23	tsunami	tsunami	NOUN
fumecheng-11687	442	24	wave	wave	NOUN
fumecheng-11687	442	25	,	,	PUNCT
fumecheng-11687	442	26	gem	gem	PROPN
fumecheng-11687	442	27	international	international	ADJ
fumecheng-11687	442	28	journal	journal	NOUN
fumecheng-11687	442	29	on	on	ADP
fumecheng-11687	442	30	geomathematics	geomathematic	NOUN
fumecheng-11687	442	31	,	,	PUNCT
fumecheng-11687	442	32	12(1	12(1	NUM
fumecheng-11687	442	33	)	)	PUNCT
fumecheng-11687	442	34	,	,	PUNCT
fumecheng-11687	442	35	10	10	NUM
fumecheng-11687	442	36	.	.	X
fumecheng-11687	442	37	16	16	NUM
fumecheng-11687	442	38	.	.	PUNCT
fumecheng-11687	443	1	nayfeh	nayfeh	PROPN
fumecheng-11687	443	2	,	,	PUNCT
fumecheng-11687	443	3	a.h	a.h	PROPN
fumecheng-11687	443	4	.	.	PROPN
fumecheng-11687	443	5	,	,	PUNCT
fumecheng-11687	443	6	2011	2011	NUM
fumecheng-11687	443	7	,	,	PUNCT
fumecheng-11687	443	8	introduction	introduction	NOUN
fumecheng-11687	443	9	to	to	ADP
fumecheng-11687	443	10	perturbation	perturbation	NOUN
fumecheng-11687	443	11	techniques	technique	NOUN
fumecheng-11687	443	12	,	,	PUNCT
fumecheng-11687	443	13	john	john	PROPN
fumecheng-11687	443	14	wiley	wiley	PROPN
fumecheng-11687	443	15	&	&	CCONJ
fumecheng-11687	443	16	sons	son	NOUN
fumecheng-11687	443	17	.	.	PUNCT
fumecheng-11687	444	1	the	the	DET
fumecheng-11687	444	2	up	up	ADV
fumecheng-11687	444	3	-	-	PUNCT
fumecheng-11687	444	4	grating	grate	VERB
fumecheng-11687	444	5	rank	rank	NOUN
fumecheng-11687	444	6	approach	approach	NOUN
fumecheng-11687	444	7	to	to	PART
fumecheng-11687	444	8	solve	solve	VERB
fumecheng-11687	444	9	a	a	DET
fumecheng-11687	444	10	forced	force	VERB
fumecheng-11687	444	11	fractal	fractal	ADJ
fumecheng-11687	444	12	duffing	duffing	NOUN
fumecheng-11687	444	13	oscillator	oscillator	NOUN
fumecheng-11687	444	14	by	by	ADP
fumecheng-11687	444	15	the	the	DET
fumecheng-11687	444	16	np	np	PROPN
fumecheng-11687	444	17	technique	technique	NOUN
fumecheng-11687	444	18	215	215	NUM
fumecheng-11687	444	19	17	17	NUM
fumecheng-11687	444	20	.	.	PUNCT
fumecheng-11687	445	1	he	he	PRON
fumecheng-11687	445	2	,	,	PUNCT
fumecheng-11687	445	3	j.-h	j.-h	PROPN
fumecheng-11687	445	4	.	.	PROPN
fumecheng-11687	445	5	,	,	PUNCT
fumecheng-11687	445	6	1999	1999	NUM
fumecheng-11687	445	7	,	,	PUNCT
fumecheng-11687	445	8	homotopy	homotopy	VERB
fumecheng-11687	445	9	perturbation	perturbation	NOUN
fumecheng-11687	445	10	technique	technique	NOUN
fumecheng-11687	445	11	,	,	PUNCT
fumecheng-11687	445	12	computer	computer	NOUN
fumecheng-11687	445	13	methods	method	NOUN
fumecheng-11687	445	14	in	in	ADP
fumecheng-11687	445	15	applied	applied	ADJ
fumecheng-11687	445	16	mechanics	mechanic	NOUN
fumecheng-11687	445	17	and	and	CCONJ
fumecheng-11687	445	18	engineering	engineering	NOUN
fumecheng-11687	445	19	,	,	PUNCT
fumecheng-11687	445	20	178(3	178(3	NUM
fumecheng-11687	445	21	-	-	SYM
fumecheng-11687	445	22	4	4	NUM
fumecheng-11687	445	23	)	)	PUNCT
fumecheng-11687	445	24	,	,	PUNCT
fumecheng-11687	445	25	pp	pp	ADP
fumecheng-11687	445	26	.	.	PUNCT
fumecheng-11687	446	1	257–262	257–262	NUM
fumecheng-11687	446	2	.	.	NOUN
fumecheng-11687	447	1	18	18	NUM
fumecheng-11687	447	2	.	.	X
fumecheng-11687	448	1	wang	wang	PROPN
fumecheng-11687	448	2	,	,	PUNCT
fumecheng-11687	448	3	k.-l	k.-l	PROPN
fumecheng-11687	448	4	.	.	PROPN
fumecheng-11687	448	5	,	,	PUNCT
fumecheng-11687	448	6	2021	2021	NUM
fumecheng-11687	448	7	,	,	PUNCT
fumecheng-11687	448	8	a	a	DET
fumecheng-11687	448	9	new	new	ADJ
fumecheng-11687	448	10	fractal	fractal	ADJ
fumecheng-11687	448	11	transform	transform	NOUN
fumecheng-11687	448	12	frequency	frequency	NOUN
fumecheng-11687	448	13	formulation	formulation	NOUN
fumecheng-11687	448	14	for	for	ADP
fumecheng-11687	448	15	fractal	fractal	ADJ
fumecheng-11687	448	16	nonlinear	nonlinear	ADJ
fumecheng-11687	448	17	oscillators	oscillator	NOUN
fumecheng-11687	448	18	,	,	PUNCT
fumecheng-11687	448	19	fractals	fractal	NOUN
fumecheng-11687	448	20	,	,	PUNCT
fumecheng-11687	448	21	29(3	29(3	NUM
fumecheng-11687	448	22	)	)	PUNCT
fumecheng-11687	448	23	,	,	PUNCT
fumecheng-11687	448	24	2150062	2150062	NUM
fumecheng-11687	448	25	.	.	PUNCT
fumecheng-11687	449	1	19	19	NUM
fumecheng-11687	449	2	.	.	X
fumecheng-11687	449	3	wang	wang	PROPN
fumecheng-11687	449	4	,	,	PUNCT
fumecheng-11687	449	5	k.-l	k.-l	PROPN
fumecheng-11687	449	6	.	.	PROPN
fumecheng-11687	449	7	,	,	PUNCT
fumecheng-11687	449	8	2021	2021	NUM
fumecheng-11687	449	9	,	,	PUNCT
fumecheng-11687	449	10	he	he	PRON
fumecheng-11687	449	11	’s	’	VERB
fumecheng-11687	449	12	frequency	frequency	NOUN
fumecheng-11687	449	13	formulation	formulation	NOUN
fumecheng-11687	449	14	for	for	ADP
fumecheng-11687	449	15	fractal	fractal	ADJ
fumecheng-11687	449	16	nonlinear	nonlinear	ADJ
fumecheng-11687	449	17	oscillator	oscillator	NOUN
fumecheng-11687	449	18	arising	arise	VERB
fumecheng-11687	449	19	in	in	ADP
fumecheng-11687	449	20	a	a	DET
fumecheng-11687	449	21	microgravity	microgravity	NOUN
fumecheng-11687	449	22	space	space	NOUN
fumecheng-11687	449	23	,	,	PUNCT
fumecheng-11687	449	24	numerical	numerical	ADJ
fumecheng-11687	449	25	methods	method	NOUN
fumecheng-11687	449	26	for	for	ADP
fumecheng-11687	449	27	partial	partial	ADJ
fumecheng-11687	449	28	differential	differential	NOUN
fumecheng-11687	449	29	equations	equation	NOUN
fumecheng-11687	449	30	,	,	PUNCT
fumecheng-11687	449	31	37(2	37(2	PRON
fumecheng-11687	449	32	)	)	PUNCT
fumecheng-11687	449	33	,	,	PUNCT
fumecheng-11687	449	34	pp	pp	ADJ
fumecheng-11687	449	35	.	.	PUNCT
fumecheng-11687	450	1	1374	1374	NUM
fumecheng-11687	450	2	-	-	SYM
fumecheng-11687	450	3	1384	1384	NUM
fumecheng-11687	450	4	.	.	PUNCT
fumecheng-11687	451	1	20	20	NUM
fumecheng-11687	451	2	.	.	X
fumecheng-11687	452	1	wang	wang	PROPN
fumecheng-11687	452	2	,	,	PUNCT
fumecheng-11687	452	3	k.-l	k.-l	PROPN
fumecheng-11687	452	4	.	.	PUNCT
fumecheng-11687	452	5	,	,	PUNCT
fumecheng-11687	452	6	wei	wei	PROPN
fumecheng-11687	452	7	,	,	PUNCT
fumecheng-11687	452	8	c.-f	c.-f	NOUN
fumecheng-11687	452	9	.	.	PUNCT
fumecheng-11687	452	10	,	,	PUNCT
fumecheng-11687	452	11	2021	2021	NUM
fumecheng-11687	452	12	,	,	PUNCT
fumecheng-11687	452	13	a	a	DET
fumecheng-11687	452	14	powerful	powerful	ADJ
fumecheng-11687	452	15	and	and	CCONJ
fumecheng-11687	452	16	simple	simple	ADJ
fumecheng-11687	452	17	frequency	frequency	NOUN
fumecheng-11687	452	18	formula	formula	NOUN
fumecheng-11687	452	19	to	to	PART
fumecheng-11687	452	20	nonlinear	nonlinear	ADJ
fumecheng-11687	452	21	fractal	fractal	ADJ
fumecheng-11687	452	22	oscillators	oscillator	NOUN
fumecheng-11687	452	23	,	,	PUNCT
fumecheng-11687	452	24	journal	journal	NOUN
fumecheng-11687	452	25	of	of	ADP
fumecheng-11687	452	26	low	low	ADJ
fumecheng-11687	452	27	frequency	frequency	NOUN
fumecheng-11687	452	28	noise	noise	NOUN
fumecheng-11687	452	29	,	,	PUNCT
fumecheng-11687	452	30	vibration	vibration	NOUN
fumecheng-11687	452	31	and	and	CCONJ
fumecheng-11687	452	32	active	active	ADJ
fumecheng-11687	452	33	control	control	NOUN
fumecheng-11687	452	34	,	,	PUNCT
fumecheng-11687	452	35	40(3	40(3	NUM
fumecheng-11687	452	36	)	)	PUNCT
fumecheng-11687	452	37	,	,	PUNCT
fumecheng-11687	452	38	pp	pp	ADP
fumecheng-11687	452	39	.	.	PUNCT
fumecheng-11687	453	1	1373	1373	NUM
fumecheng-11687	453	2	-	-	SYM
fumecheng-11687	453	3	1379	1379	NUM
fumecheng-11687	453	4	21	21	NUM
fumecheng-11687	453	5	.	.	PUNCT
fumecheng-11687	454	1	lu	lu	PROPN
fumecheng-11687	454	2	,	,	PUNCT
fumecheng-11687	454	3	j.	j.	PROPN
fumecheng-11687	454	4	,	,	PUNCT
fumecheng-11687	454	5	chen	chen	PROPN
fumecheng-11687	454	6	,	,	PUNCT
fumecheng-11687	454	7	l.	l.	PROPN
fumecheng-11687	454	8	,	,	PUNCT
fumecheng-11687	454	9	2022	2022	NUM
fumecheng-11687	454	10	,	,	PUNCT
fumecheng-11687	454	11	numerical	numerical	ADJ
fumecheng-11687	454	12	analysis	analysis	NOUN
fumecheng-11687	454	13	of	of	ADP
fumecheng-11687	454	14	a	a	DET
fumecheng-11687	454	15	fractal	fractal	ADJ
fumecheng-11687	454	16	modification	modification	NOUN
fumecheng-11687	454	17	of	of	ADP
fumecheng-11687	454	18	yao	yao	PROPN
fumecheng-11687	454	19	-	-	PUNCT
fumecheng-11687	454	20	cheng	cheng	PROPN
fumecheng-11687	454	21	oscillator	oscillator	PROPN
fumecheng-11687	454	22	,	,	PUNCT
fumecheng-11687	454	23	results	result	NOUN
fumecheng-11687	454	24	in	in	ADP
fumecheng-11687	454	25	physics	physics	NOUN
fumecheng-11687	454	26	,	,	PUNCT
fumecheng-11687	454	27	105602	105602	NUM
fumecheng-11687	454	28	.	.	PUNCT
fumecheng-11687	455	1	22	22	NUM
fumecheng-11687	455	2	.	.	PUNCT
fumecheng-11687	456	1	elías	elías	PROPN
fumecheng-11687	456	2	-	-	PUNCT
fumecheng-11687	456	3	zúñiga	zúñiga	PROPN
fumecheng-11687	456	4	,	,	PUNCT
fumecheng-11687	456	5	a.	a.	NOUN
fumecheng-11687	456	6	,	,	PUNCT
fumecheng-11687	456	7	martínez	martínez	PROPN
fumecheng-11687	456	8	-	-	PUNCT
fumecheng-11687	456	9	romero	romero	PROPN
fumecheng-11687	456	10	,	,	PUNCT
fumecheng-11687	456	11	o.	o.	PROPN
fumecheng-11687	456	12	,	,	PUNCT
fumecheng-11687	456	13	olvera	olvera	PROPN
fumecheng-11687	456	14	-	-	PUNCT
fumecheng-11687	456	15	trejo	trejo	PROPN
fumecheng-11687	456	16	,	,	PUNCT
fumecheng-11687	456	17	d.	d.	PROPN
fumecheng-11687	456	18	,	,	PUNCT
fumecheng-11687	456	19	palacios	palacio	NOUN
fumecheng-11687	456	20	-	-	PUNCT
fumecheng-11687	456	21	pineda	pineda	PROPN
fumecheng-11687	456	22	,	,	PUNCT
fumecheng-11687	456	23	l.m	l.m	PROPN
fumecheng-11687	456	24	.	.	PROPN
fumecheng-11687	456	25	,	,	PUNCT
fumecheng-11687	456	26	2021	2021	NUM
fumecheng-11687	456	27	,	,	PUNCT
fumecheng-11687	456	28	an	an	DET
fumecheng-11687	456	29	efficient	efficient	ADJ
fumecheng-11687	456	30	ancient	ancient	ADJ
fumecheng-11687	456	31	chinese	chinese	ADJ
fumecheng-11687	456	32	algorithm	algorithm	NOUN
fumecheng-11687	456	33	to	to	PART
fumecheng-11687	456	34	investigate	investigate	VERB
fumecheng-11687	456	35	the	the	DET
fumecheng-11687	456	36	dynamics	dynamic	NOUN
fumecheng-11687	456	37	response	response	NOUN
fumecheng-11687	456	38	of	of	ADP
fumecheng-11687	456	39	a	a	DET
fumecheng-11687	456	40	fractal	fractal	ADJ
fumecheng-11687	456	41	microgravity	microgravity	NOUN
fumecheng-11687	456	42	forced	force	VERB
fumecheng-11687	456	43	oscillator	oscillator	NOUN
fumecheng-11687	456	44	,	,	PUNCT
fumecheng-11687	456	45	fractals	fractal	NOUN
fumecheng-11687	456	46	,	,	PUNCT
fumecheng-11687	456	47	29(6	29(6	NUM
fumecheng-11687	456	48	)	)	PUNCT
fumecheng-11687	456	49	,	,	PUNCT
fumecheng-11687	456	50	2150144	2150144	NUM
fumecheng-11687	456	51	.	.	PUNCT
fumecheng-11687	457	1	23	23	NUM
fumecheng-11687	457	2	.	.	PUNCT
fumecheng-11687	458	1	elías	elías	PROPN
fumecheng-11687	458	2	-	-	PUNCT
fumecheng-11687	458	3	zúñiga	zúñiga	PROPN
fumecheng-11687	458	4	,	,	PUNCT
fumecheng-11687	458	5	a.	a.	NOUN
fumecheng-11687	458	6	,	,	PUNCT
fumecheng-11687	458	7	martínez	martínez	PROPN
fumecheng-11687	458	8	-	-	PUNCT
fumecheng-11687	458	9	romero	romero	PROPN
fumecheng-11687	458	10	,	,	PUNCT
fumecheng-11687	458	11	o.	o.	PROPN
fumecheng-11687	458	12	,	,	PUNCT
fumecheng-11687	458	13	olvera	olvera	PROPN
fumecheng-11687	458	14	-	-	PUNCT
fumecheng-11687	458	15	trejo	trejo	PROPN
fumecheng-11687	458	16	,	,	PUNCT
fumecheng-11687	458	17	d.	d.	PROPN
fumecheng-11687	458	18	,	,	PUNCT
fumecheng-11687	458	19	palacios	palacio	NOUN
fumecheng-11687	458	20	-	-	PUNCT
fumecheng-11687	458	21	pineda	pineda	PROPN
fumecheng-11687	458	22	,	,	PUNCT
fumecheng-11687	458	23	l.m	l.m	PROPN
fumecheng-11687	458	24	.	.	PROPN
fumecheng-11687	458	25	,	,	PUNCT
fumecheng-11687	458	26	2021	2021	NUM
fumecheng-11687	458	27	,	,	PUNCT
fumecheng-11687	458	28	investigation	investigation	NOUN
fumecheng-11687	458	29	of	of	ADP
fumecheng-11687	458	30	the	the	DET
fumecheng-11687	458	31	steady	steady	ADJ
fumecheng-11687	458	32	-	-	PUNCT
fumecheng-11687	458	33	state	state	NOUN
fumecheng-11687	458	34	solution	solution	NOUN
fumecheng-11687	458	35	of	of	ADP
fumecheng-11687	458	36	the	the	DET
fumecheng-11687	458	37	fractal	fractal	ADJ
fumecheng-11687	458	38	forced	force	VERB
fumecheng-11687	458	39	duffing	duffing	NOUN
fumecheng-11687	458	40	’s	’s	PART
fumecheng-11687	458	41	oscillator	oscillator	NOUN
fumecheng-11687	458	42	using	use	VERB
fumecheng-11687	458	43	an	an	DET
fumecheng-11687	458	44	ancient	ancient	ADJ
fumecheng-11687	458	45	chinese	chinese	ADJ
fumecheng-11687	458	46	algorithm	algorithm	NOUN
fumecheng-11687	458	47	,	,	PUNCT
fumecheng-11687	458	48	fractals	fractal	NOUN
fumecheng-11687	458	49	,	,	PUNCT
fumecheng-11687	458	50	29(6	29(6	NUM
fumecheng-11687	458	51	)	)	PUNCT
fumecheng-11687	458	52	,	,	PUNCT
fumecheng-11687	458	53	2150133	2150133	NUM
fumecheng-11687	458	54	.	.	PUNCT
fumecheng-11687	459	1	24	24	NUM
fumecheng-11687	459	2	.	.	PUNCT
fumecheng-11687	460	1	sheng	sheng	PROPN
fumecheng-11687	460	2	,	,	PUNCT
fumecheng-11687	460	3	m.	m.	NOUN
fumecheng-11687	460	4	,	,	PUNCT
fumecheng-11687	460	5	li	li	PROPN
fumecheng-11687	460	6	,	,	PUNCT
fumecheng-11687	460	7	g.	g.	PROPN
fumecheng-11687	460	8	,	,	PUNCT
fumecheng-11687	460	9	tian	tian	PROPN
fumecheng-11687	460	10	,	,	PUNCT
fumecheng-11687	460	11	s.	s.	PROPN
fumecheng-11687	460	12	,	,	PUNCT
fumecheng-11687	460	13	huang	huang	PROPN
fumecheng-11687	460	14	,	,	PUNCT
fumecheng-11687	460	15	z.	z.	PROPN
fumecheng-11687	460	16	,	,	PUNCT
fumecheng-11687	460	17	chen	chen	PROPN
fumecheng-11687	460	18	,	,	PUNCT
fumecheng-11687	460	19	l.	l.	PROPN
fumecheng-11687	460	20	,	,	PUNCT
fumecheng-11687	460	21	2016	2016	NUM
fumecheng-11687	460	22	,	,	PUNCT
fumecheng-11687	460	23	a	a	DET
fumecheng-11687	460	24	fractal	fractal	ADJ
fumecheng-11687	460	25	permeability	permeability	NOUN
fumecheng-11687	460	26	model	model	NOUN
fumecheng-11687	460	27	for	for	ADP
fumecheng-11687	460	28	shale	shale	NOUN
fumecheng-11687	460	29	matrix	matrix	NOUN
fumecheng-11687	460	30	with	with	ADP
fumecheng-11687	460	31	multi	multi	ADJ
fumecheng-11687	460	32	-	-	ADJ
fumecheng-11687	460	33	scale	scale	ADJ
fumecheng-11687	460	34	porous	porous	ADJ
fumecheng-11687	460	35	structure	structure	NOUN
fumecheng-11687	460	36	,	,	PUNCT
fumecheng-11687	460	37	fractals	fractal	NOUN
fumecheng-11687	460	38	,	,	PUNCT
fumecheng-11687	460	39	24(1	24(1	NUM
fumecheng-11687	460	40	)	)	PUNCT
fumecheng-11687	460	41	,	,	PUNCT
fumecheng-11687	460	42	1650002	1650002	NUM
fumecheng-11687	460	43	.	.	PUNCT
fumecheng-11687	461	1	25	25	NUM
fumecheng-11687	461	2	.	.	PUNCT
fumecheng-11687	461	3	miao	miao	NOUN
fumecheng-11687	461	4	,	,	PUNCT
fumecheng-11687	461	5	t.	t.	PROPN
fumecheng-11687	461	6	,	,	PUNCT
fumecheng-11687	461	7	chen	chen	PROPN
fumecheng-11687	461	8	,	,	PUNCT
fumecheng-11687	461	9	a.	a.	PROPN
fumecheng-11687	461	10	,	,	PUNCT
fumecheng-11687	461	11	xu	xu	PROPN
fumecheng-11687	461	12	,	,	PUNCT
fumecheng-11687	461	13	y.	y.	PROPN
fumecheng-11687	461	14	,	,	PUNCT
fumecheng-11687	461	15	cheng	cheng	PROPN
fumecheng-11687	461	16	,	,	PUNCT
fumecheng-11687	461	17	s.	s.	PROPN
fumecheng-11687	461	18	,	,	PUNCT
fumecheng-11687	461	19	yu	yu	PROPN
fumecheng-11687	461	20	,	,	PUNCT
fumecheng-11687	461	21	b.	b.	PROPN
fumecheng-11687	461	22	,	,	PUNCT
fumecheng-11687	461	23	2019	2019	NUM
fumecheng-11687	461	24	,	,	PUNCT
fumecheng-11687	461	25	a	a	DET
fumecheng-11687	461	26	fractal	fractal	ADJ
fumecheng-11687	461	27	permeability	permeability	NOUN
fumecheng-11687	461	28	model	model	NOUN
fumecheng-11687	461	29	for	for	ADP
fumecheng-11687	461	30	porous	porous	ADJ
fumecheng-11687	461	31	–	–	PUNCT
fumecheng-11687	461	32	fracture	fracture	ADJ
fumecheng-11687	461	33	media	medium	NOUN
fumecheng-11687	461	34	with	with	ADP
fumecheng-11687	461	35	the	the	DET
fumecheng-11687	461	36	transfer	transfer	NOUN
fumecheng-11687	461	37	of	of	ADP
fumecheng-11687	461	38	fluids	fluid	NOUN
fumecheng-11687	461	39	from	from	ADP
fumecheng-11687	461	40	porous	porous	ADJ
fumecheng-11687	461	41	matrix	matrix	NOUN
fumecheng-11687	461	42	to	to	ADP
fumecheng-11687	461	43	fracture	fracture	NOUN
fumecheng-11687	461	44	,	,	PUNCT
fumecheng-11687	461	45	fractals	fractal	NOUN
fumecheng-11687	461	46	,	,	PUNCT
fumecheng-11687	461	47	27(6	27(6	NUM
fumecheng-11687	461	48	)	)	PUNCT
fumecheng-11687	461	49	,	,	PUNCT
fumecheng-11687	461	50	1950121	1950121	NUM
fumecheng-11687	461	51	.	.	PUNCT
fumecheng-11687	462	1	26	26	NUM
fumecheng-11687	462	2	.	.	PUNCT
fumecheng-11687	463	1	xu	xu	PROPN
fumecheng-11687	463	2	,	,	PUNCT
fumecheng-11687	463	3	j.	j.	PROPN
fumecheng-11687	463	4	,	,	PUNCT
fumecheng-11687	463	5	wu	wu	PROPN
fumecheng-11687	463	6	,	,	PUNCT
fumecheng-11687	463	7	k.	k.	PROPN
fumecheng-11687	463	8	,	,	PUNCT
fumecheng-11687	463	9	li	li	PROPN
fumecheng-11687	463	10	,	,	PUNCT
fumecheng-11687	463	11	r.	r.	PROPN
fumecheng-11687	463	12	,	,	PUNCT
fumecheng-11687	463	13	li	li	PROPN
fumecheng-11687	463	14	,	,	PUNCT
fumecheng-11687	463	15	z.	z.	PROPN
fumecheng-11687	463	16	,	,	PUNCT
fumecheng-11687	463	17	li	li	PROPN
fumecheng-11687	463	18	,	,	PUNCT
fumecheng-11687	463	19	j.	j.	PROPN
fumecheng-11687	463	20	,	,	PUNCT
fumecheng-11687	463	21	xu	xu	PROPN
fumecheng-11687	463	22	,	,	PUNCT
fumecheng-11687	463	23	q.	q.	PROPN
fumecheng-11687	463	24	,	,	PUNCT
fumecheng-11687	463	25	chen	chen	PROPN
fumecheng-11687	463	26	,	,	PUNCT
fumecheng-11687	463	27	z.	z.	PROPN
fumecheng-11687	463	28	,	,	PUNCT
fumecheng-11687	463	29	2018	2018	NUM
fumecheng-11687	463	30	,	,	PUNCT
fumecheng-11687	463	31	real	real	ADJ
fumecheng-11687	463	32	gas	gas	NOUN
fumecheng-11687	463	33	transport	transport	NOUN
fumecheng-11687	463	34	in	in	ADP
fumecheng-11687	463	35	shale	shale	NOUN
fumecheng-11687	463	36	matrix	matrix	NOUN
fumecheng-11687	463	37	with	with	ADP
fumecheng-11687	463	38	fractal	fractal	ADJ
fumecheng-11687	463	39	structures	structure	NOUN
fumecheng-11687	463	40	,	,	PUNCT
fumecheng-11687	463	41	fuel	fuel	NOUN
fumecheng-11687	463	42	,	,	PUNCT
fumecheng-11687	463	43	219	219	NUM
fumecheng-11687	463	44	,	,	PUNCT
fumecheng-11687	463	45	pp	pp	ADJ
fumecheng-11687	463	46	.	.	PUNCT
fumecheng-11687	464	1	353	353	NUM
fumecheng-11687	464	2	-	-	SYM
fumecheng-11687	464	3	363	363	NUM
fumecheng-11687	464	4	.	.	PUNCT
fumecheng-11687	465	1	27	27	NUM
fumecheng-11687	465	2	.	.	PUNCT
fumecheng-11687	466	1	wang	wang	PROPN
fumecheng-11687	466	2	,	,	PUNCT
fumecheng-11687	466	3	s.	s.	PROPN
fumecheng-11687	466	4	,	,	PUNCT
fumecheng-11687	466	5	wu	wu	PROPN
fumecheng-11687	466	6	,	,	PUNCT
fumecheng-11687	466	7	t.	t.	PROPN
fumecheng-11687	466	8	,	,	PUNCT
fumecheng-11687	466	9	cao	cao	PROPN
fumecheng-11687	466	10	,	,	PUNCT
fumecheng-11687	466	11	x.	x.	PROPN
fumecheng-11687	466	12	,	,	PUNCT
fumecheng-11687	466	13	zheng	zheng	PROPN
fumecheng-11687	466	14	,	,	PUNCT
fumecheng-11687	466	15	q.	q.	PROPN
fumecheng-11687	466	16	,	,	PUNCT
fumecheng-11687	466	17	ai	ai	VERB
fumecheng-11687	466	18	,	,	PUNCT
fumecheng-11687	466	19	m.	m.	NOUN
fumecheng-11687	466	20	,	,	PUNCT
fumecheng-11687	466	21	2017	2017	NUM
fumecheng-11687	466	22	,	,	PUNCT
fumecheng-11687	466	23	a	a	DET
fumecheng-11687	466	24	fractal	fractal	ADJ
fumecheng-11687	466	25	model	model	NOUN
fumecheng-11687	466	26	for	for	ADP
fumecheng-11687	466	27	gas	gas	NOUN
fumecheng-11687	466	28	apparent	apparent	ADJ
fumecheng-11687	466	29	permeability	permeability	NOUN
fumecheng-11687	466	30	in	in	ADP
fumecheng-11687	466	31	microfractures	microfracture	NOUN
fumecheng-11687	466	32	of	of	ADP
fumecheng-11687	466	33	tight	tight	ADJ
fumecheng-11687	466	34	/	/	SYM
fumecheng-11687	466	35	shale	shale	NOUN
fumecheng-11687	466	36	reservoirs	reservoir	NOUN
fumecheng-11687	466	37	,	,	PUNCT
fumecheng-11687	466	38	fractals	fractal	NOUN
fumecheng-11687	466	39	,	,	PUNCT
fumecheng-11687	466	40	25(3	25(3	NUM
fumecheng-11687	466	41	)	)	PUNCT
fumecheng-11687	466	42	,	,	PUNCT
fumecheng-11687	466	43	1750036	1750036	NUM
fumecheng-11687	466	44	.	.	PUNCT
fumecheng-11687	467	1	28	28	NUM
fumecheng-11687	467	2	.	.	PUNCT
fumecheng-11687	467	3	wu	wu	PROPN
fumecheng-11687	467	4	,	,	PUNCT
fumecheng-11687	467	5	t.	t.	PROPN
fumecheng-11687	467	6	,	,	PUNCT
fumecheng-11687	467	7	wang	wang	PROPN
fumecheng-11687	467	8	,	,	PUNCT
fumecheng-11687	467	9	s.	s.	PROPN
fumecheng-11687	467	10	,	,	PUNCT
fumecheng-11687	467	11	2020	2020	NUM
fumecheng-11687	467	12	,	,	PUNCT
fumecheng-11687	467	13	a	a	DET
fumecheng-11687	467	14	fractal	fractal	ADJ
fumecheng-11687	467	15	permeability	permeability	NOUN
fumecheng-11687	467	16	model	model	NOUN
fumecheng-11687	467	17	for	for	ADP
fumecheng-11687	467	18	real	real	ADJ
fumecheng-11687	467	19	gas	gas	NOUN
fumecheng-11687	467	20	in	in	ADP
fumecheng-11687	467	21	shale	shale	NOUN
fumecheng-11687	467	22	reservoirs	reservoir	NOUN
fumecheng-11687	467	23	coupled	couple	VERB
fumecheng-11687	467	24	with	with	ADP
fumecheng-11687	467	25	knudsen	knudsen	PROPN
fumecheng-11687	467	26	diffusion	diffusion	PROPN
fumecheng-11687	467	27	and	and	CCONJ
fumecheng-11687	467	28	surface	surface	NOUN
fumecheng-11687	467	29	diffusion	diffusion	NOUN
fumecheng-11687	467	30	effects	effect	NOUN
fumecheng-11687	467	31	,	,	PUNCT
fumecheng-11687	467	32	fractals	fractal	NOUN
fumecheng-11687	467	33	,	,	PUNCT
fumecheng-11687	467	34	28(1	28(1	NOUN
fumecheng-11687	467	35	)	)	PUNCT
fumecheng-11687	467	36	,	,	PUNCT
fumecheng-11687	467	37	2050017	2050017	NUM
fumecheng-11687	467	38	.	.	PUNCT
fumecheng-11687	468	1	29	29	NUM
fumecheng-11687	468	2	.	.	X
fumecheng-11687	468	3	yang	yang	PROPN
fumecheng-11687	468	4	,	,	PUNCT
fumecheng-11687	468	5	c.-y	c.-y	NOUN
fumecheng-11687	468	6	.	.	PUNCT
fumecheng-11687	468	7	,	,	PUNCT
fumecheng-11687	468	8	zhang	zhang	PROPN
fumecheng-11687	468	9	,	,	PUNCT
fumecheng-11687	468	10	y.-d	y.-d	PROPN
fumecheng-11687	468	11	.	.	PROPN
fumecheng-11687	468	12	,	,	PUNCT
fumecheng-11687	468	13	yang	yang	PROPN
fumecheng-11687	468	14	,	,	PUNCT
fumecheng-11687	468	15	x.-j	x.-j	PROPN
fumecheng-11687	468	16	.	.	PROPN
fumecheng-11687	468	17	,	,	PUNCT
fumecheng-11687	468	18	2016	2016	NUM
fumecheng-11687	468	19	,	,	PUNCT
fumecheng-11687	468	20	exact	exact	ADJ
fumecheng-11687	468	21	solutions	solution	NOUN
fumecheng-11687	468	22	for	for	ADP
fumecheng-11687	468	23	the	the	DET
fumecheng-11687	468	24	differential	differential	ADJ
fumecheng-11687	468	25	equations	equation	NOUN
fumecheng-11687	468	26	in	in	ADP
fumecheng-11687	468	27	fractal	fractal	ADJ
fumecheng-11687	468	28	heat	heat	NOUN
fumecheng-11687	468	29	transfer	transfer	NOUN
fumecheng-11687	468	30	,	,	PUNCT
fumecheng-11687	468	31	thermal	thermal	ADJ
fumecheng-11687	468	32	science	science	NOUN
fumecheng-11687	468	33	,	,	PUNCT
fumecheng-11687	468	34	20(suppl	20(suppl	NUM
fumecheng-11687	468	35	.	.	NOUN
fumecheng-11687	468	36	3	3	NUM
fumecheng-11687	468	37	)	)	PUNCT
fumecheng-11687	468	38	,	,	PUNCT
fumecheng-11687	468	39	pp	pp	ADP
fumecheng-11687	468	40	.	.	PUNCT
fumecheng-11687	469	1	747	747	NUM
fumecheng-11687	469	2	-	-	SYM
fumecheng-11687	469	3	750	750	NUM
fumecheng-11687	469	4	.	.	PUNCT
fumecheng-11687	470	1	30	30	NUM
fumecheng-11687	470	2	.	.	PUNCT
fumecheng-11687	471	1	el	el	PROPN
fumecheng-11687	471	2	-	-	PUNCT
fumecheng-11687	471	3	dib	dib	PROPN
fumecheng-11687	471	4	,	,	PUNCT
fumecheng-11687	471	5	y.o	y.o	PROPN
fumecheng-11687	471	6	.	.	PROPN
fumecheng-11687	471	7	,	,	PUNCT
fumecheng-11687	471	8	elgazery	elgazery	PROPN
fumecheng-11687	471	9	,	,	PUNCT
fumecheng-11687	471	10	n.s	n.s	PROPN
fumecheng-11687	471	11	.	.	PROPN
fumecheng-11687	471	12	,	,	PUNCT
fumecheng-11687	471	13	2022	2022	NUM
fumecheng-11687	471	14	,	,	PUNCT
fumecheng-11687	471	15	a	a	DET
fumecheng-11687	471	16	novel	novel	ADJ
fumecheng-11687	471	17	pattern	pattern	NOUN
fumecheng-11687	471	18	in	in	ADP
fumecheng-11687	471	19	a	a	DET
fumecheng-11687	471	20	class	class	NOUN
fumecheng-11687	471	21	of	of	ADP
fumecheng-11687	471	22	fractal	fractal	ADJ
fumecheng-11687	471	23	models	model	NOUN
fumecheng-11687	471	24	with	with	ADP
fumecheng-11687	471	25	the	the	DET
fumecheng-11687	471	26	non	non	ADJ
fumecheng-11687	471	27	-	-	ADJ
fumecheng-11687	471	28	perturbative	perturbative	ADJ
fumecheng-11687	471	29	approach	approach	NOUN
fumecheng-11687	471	30	,	,	PUNCT
fumecheng-11687	471	31	chaos	chaos	NOUN
fumecheng-11687	471	32	,	,	PUNCT
fumecheng-11687	471	33	solitons	soliton	NOUN
fumecheng-11687	471	34	&	&	CCONJ
fumecheng-11687	471	35	fractals	fractal	NOUN
fumecheng-11687	471	36	,	,	PUNCT
fumecheng-11687	471	37	164	164	NUM
fumecheng-11687	471	38	,	,	PUNCT
fumecheng-11687	471	39	112694	112694	NUM
fumecheng-11687	471	40	.	.	PUNCT
fumecheng-11687	472	1	31	31	NUM
fumecheng-11687	472	2	.	.	PUNCT
fumecheng-11687	473	1	el	el	PROPN
fumecheng-11687	473	2	-	-	PUNCT
fumecheng-11687	473	3	dib	dib	PROPN
fumecheng-11687	473	4	,	,	PUNCT
fumecheng-11687	473	5	y.o	y.o	PROPN
fumecheng-11687	473	6	.	.	PROPN
fumecheng-11687	473	7	,	,	PUNCT
fumecheng-11687	473	8	elgazery	elgazery	PROPN
fumecheng-11687	473	9	,	,	PUNCT
fumecheng-11687	473	10	n.s	n.s	PROPN
fumecheng-11687	473	11	.	.	PROPN
fumecheng-11687	473	12	,	,	PUNCT
fumecheng-11687	473	13	2023	2023	NUM
fumecheng-11687	473	14	,	,	PUNCT
fumecheng-11687	473	15	an	an	DET
fumecheng-11687	473	16	efficient	efficient	ADJ
fumecheng-11687	473	17	approach	approach	NOUN
fumecheng-11687	473	18	to	to	ADP
fumecheng-11687	473	19	converting	convert	VERB
fumecheng-11687	473	20	the	the	DET
fumecheng-11687	473	21	damping	damp	VERB
fumecheng-11687	473	22	fractal	fractal	ADJ
fumecheng-11687	473	23	models	model	NOUN
fumecheng-11687	473	24	to	to	ADP
fumecheng-11687	473	25	the	the	DET
fumecheng-11687	473	26	traditional	traditional	ADJ
fumecheng-11687	473	27	system	system	NOUN
fumecheng-11687	473	28	,	,	PUNCT
fumecheng-11687	473	29	communications	communication	NOUN
fumecheng-11687	473	30	in	in	ADP
fumecheng-11687	473	31	nonlinear	nonlinear	ADJ
fumecheng-11687	473	32	science	science	NOUN
fumecheng-11687	473	33	and	and	CCONJ
fumecheng-11687	473	34	numerical	numerical	PROPN
fumecheng-11687	473	35	simulation	simulation	PROPN
fumecheng-11687	473	36	,	,	PUNCT
fumecheng-11687	473	37	118	118	NUM
fumecheng-11687	473	38	,	,	PUNCT
fumecheng-11687	473	39	107036	107036	NUM
fumecheng-11687	473	40	.	.	PUNCT
fumecheng-11687	474	1	32	32	NUM
fumecheng-11687	474	2	.	.	X
fumecheng-11687	475	1	selivanov	selivanov	PROPN
fumecheng-11687	475	2	,	,	PUNCT
fumecheng-11687	475	3	m.f	m.f	PROPN
fumecheng-11687	475	4	.	.	PROPN
fumecheng-11687	475	5	,	,	PUNCT
fumecheng-11687	475	6	chornoivan	chornoivan	PROPN
fumecheng-11687	475	7	,	,	PUNCT
fumecheng-11687	475	8	y.o	y.o	PROPN
fumecheng-11687	475	9	.	.	PROPN
fumecheng-11687	475	10	,	,	PUNCT
fumecheng-11687	475	11	2018	2018	NUM
fumecheng-11687	475	12	,	,	PUNCT
fumecheng-11687	475	13	a	a	DET
fumecheng-11687	475	14	semi	semi	ADJ
fumecheng-11687	475	15	-	-	ADJ
fumecheng-11687	475	16	analytical	analytical	ADJ
fumecheng-11687	475	17	solution	solution	NOUN
fumecheng-11687	475	18	method	method	NOUN
fumecheng-11687	475	19	for	for	ADP
fumecheng-11687	475	20	problems	problem	NOUN
fumecheng-11687	475	21	of	of	ADP
fumecheng-11687	475	22	cohesive	cohesive	ADJ
fumecheng-11687	475	23	fracture	fracture	NOUN
fumecheng-11687	475	24	and	and	CCONJ
fumecheng-11687	475	25	some	some	PRON
fumecheng-11687	475	26	of	of	ADP
fumecheng-11687	475	27	its	its	PRON
fumecheng-11687	475	28	applications	application	NOUN
fumecheng-11687	475	29	,	,	PUNCT
fumecheng-11687	475	30	international	international	ADJ
fumecheng-11687	475	31	journal	journal	NOUN
fumecheng-11687	475	32	of	of	ADP
fumecheng-11687	475	33	fracture	fracture	NOUN
fumecheng-11687	475	34	,	,	PUNCT
fumecheng-11687	475	35	212	212	NUM
fumecheng-11687	475	36	,	,	PUNCT
fumecheng-11687	475	37	pp	pp	ADJ
fumecheng-11687	475	38	.	.	PUNCT
fumecheng-11687	476	1	113	113	NUM
fumecheng-11687	476	2	-	-	SYM
fumecheng-11687	476	3	121	121	NUM
fumecheng-11687	476	4	.	.	PUNCT
fumecheng-11687	477	1	33	33	NUM
fumecheng-11687	477	2	.	.	PUNCT
fumecheng-11687	478	1	khater	khater	PROPN
fumecheng-11687	478	2	,	,	PUNCT
fumecheng-11687	478	3	m.m.a	m.m.a	NOUN
fumecheng-11687	478	4	.	.	PROPN
fumecheng-11687	478	5	,	,	PUNCT
fumecheng-11687	478	6	mousa	mousa	PROPN
fumecheng-11687	478	7	,	,	PUNCT
fumecheng-11687	478	8	a.a	a.a	PROPN
fumecheng-11687	478	9	.	.	PROPN
fumecheng-11687	478	10	,	,	PUNCT
fumecheng-11687	478	11	el	el	PROPN
fumecheng-11687	478	12	-	-	ADJ
fumecheng-11687	478	13	shorbagy	shorbagy	ADJ
fumecheng-11687	478	14	,	,	PUNCT
fumecheng-11687	478	15	m.a	m.a	PROPN
fumecheng-11687	478	16	.	.	PROPN
fumecheng-11687	478	17	,	,	PUNCT
fumecheng-11687	478	18	attia	attia	PROPN
fumecheng-11687	478	19	,	,	PUNCT
fumecheng-11687	478	20	r.a.m	r.a.m	PROPN
fumecheng-11687	478	21	.	.	PROPN
fumecheng-11687	478	22	,	,	PUNCT
fumecheng-11687	478	23	2021	2021	NUM
fumecheng-11687	478	24	,	,	PUNCT
fumecheng-11687	478	25	analytical	analytical	ADJ
fumecheng-11687	478	26	and	and	CCONJ
fumecheng-11687	478	27	semi	semi	ADJ
fumecheng-11687	478	28	-	-	ADJ
fumecheng-11687	478	29	analytical	analytical	ADJ
fumecheng-11687	478	30	solutions	solution	NOUN
fumecheng-11687	478	31	for	for	ADP
fumecheng-11687	478	32	phi	phi	ADJ
fumecheng-11687	478	33	-	-	PUNCT
fumecheng-11687	478	34	four	four	NUM
fumecheng-11687	478	35	equation	equation	NOUN
fumecheng-11687	478	36	through	through	ADP
fumecheng-11687	478	37	three	three	NUM
fumecheng-11687	478	38	recent	recent	ADJ
fumecheng-11687	478	39	schemes	scheme	NOUN
fumecheng-11687	478	40	,	,	PUNCT
fumecheng-11687	478	41	results	result	NOUN
fumecheng-11687	478	42	in	in	ADP
fumecheng-11687	478	43	physics	physics	NOUN
fumecheng-11687	478	44	,	,	PUNCT
fumecheng-11687	478	45	22	22	NUM
fumecheng-11687	478	46	,	,	PUNCT
fumecheng-11687	478	47	103954	103954	NUM
fumecheng-11687	478	48	.	.	PUNCT
fumecheng-11687	479	1	34	34	NUM
fumecheng-11687	479	2	.	.	PUNCT
fumecheng-11687	479	3	moshtaghi	moshtaghi	PROPN
fumecheng-11687	479	4	,	,	PUNCT
fumecheng-11687	479	5	n.	n.	NOUN
fumecheng-11687	479	6	,	,	PUNCT
fumecheng-11687	479	7	saadatmandi	saadatmandi	PROPN
fumecheng-11687	479	8	,	,	PUNCT
fumecheng-11687	479	9	a.	a.	NOUN
fumecheng-11687	479	10	,	,	PUNCT
fumecheng-11687	479	11	2021	2021	NUM
fumecheng-11687	479	12	,	,	PUNCT
fumecheng-11687	479	13	numerical	numerical	ADJ
fumecheng-11687	479	14	solution	solution	NOUN
fumecheng-11687	479	15	of	of	ADP
fumecheng-11687	479	16	time	time	NOUN
fumecheng-11687	479	17	fractional	fractional	ADJ
fumecheng-11687	479	18	cable	cable	NOUN
fumecheng-11687	479	19	equation	equation	NOUN
fumecheng-11687	479	20	via	via	ADP
fumecheng-11687	479	21	the	the	DET
fumecheng-11687	479	22	sincbernoulli	sincbernoulli	NOUN
fumecheng-11687	479	23	collocation	collocation	NOUN
fumecheng-11687	479	24	method	method	NOUN
fumecheng-11687	479	25	,	,	PUNCT
fumecheng-11687	479	26	journal	journal	NOUN
fumecheng-11687	479	27	of	of	ADP
fumecheng-11687	479	28	applied	applied	ADJ
fumecheng-11687	479	29	and	and	CCONJ
fumecheng-11687	479	30	computational	computational	ADJ
fumecheng-11687	479	31	mechanics	mechanic	NOUN
fumecheng-11687	479	32	,	,	PUNCT
fumecheng-11687	479	33	7(4	7(4	NUM
fumecheng-11687	479	34	)	)	PUNCT
fumecheng-11687	479	35	,	,	PUNCT
fumecheng-11687	479	36	pp	pp	ADJ
fumecheng-11687	479	37	.	.	PUNCT
fumecheng-11687	480	1	1916	1916	NUM
fumecheng-11687	480	2	-	-	SYM
fumecheng-11687	480	3	1924	1924	NUM
fumecheng-11687	480	4	.	.	PUNCT
fumecheng-11687	481	1	35	35	NUM
fumecheng-11687	481	2	.	.	PUNCT
fumecheng-11687	482	1	elías	elías	PROPN
fumecheng-11687	482	2	-	-	PUNCT
fumecheng-11687	482	3	zúñiga	zúñiga	PROPN
fumecheng-11687	482	4	,	,	PUNCT
fumecheng-11687	482	5	a.	a.	NOUN
fumecheng-11687	482	6	,	,	PUNCT
fumecheng-11687	482	7	martínez	martínez	PROPN
fumecheng-11687	482	8	-	-	PUNCT
fumecheng-11687	482	9	romero	romero	PROPN
fumecheng-11687	482	10	,	,	PUNCT
fumecheng-11687	482	11	o.	o.	PROPN
fumecheng-11687	482	12	,	,	PUNCT
fumecheng-11687	482	13	olvera	olvera	PROPN
fumecheng-11687	482	14	-	-	PUNCT
fumecheng-11687	482	15	trejo	trejo	PROPN
fumecheng-11687	482	16	,	,	PUNCT
fumecheng-11687	482	17	d.	d.	PROPN
fumecheng-11687	482	18	,	,	PUNCT
fumecheng-11687	482	19	palacios	palacio	NOUN
fumecheng-11687	482	20	-	-	PUNCT
fumecheng-11687	482	21	pineda	pineda	PROPN
fumecheng-11687	482	22	,	,	PUNCT
fumecheng-11687	482	23	l.m	l.m	PROPN
fumecheng-11687	482	24	.	.	PROPN
fumecheng-11687	482	25	,	,	PUNCT
fumecheng-11687	482	26	2021	2021	NUM
fumecheng-11687	482	27	,	,	PUNCT
fumecheng-11687	482	28	exact	exact	ADJ
fumecheng-11687	482	29	steady	steady	ADJ
fumecheng-11687	482	30	-	-	PUNCT
fumecheng-11687	482	31	state	state	NOUN
fumecheng-11687	482	32	solution	solution	NOUN
fumecheng-11687	482	33	of	of	ADP
fumecheng-11687	482	34	fractals	fractal	NOUN
fumecheng-11687	482	35	damped	damp	VERB
fumecheng-11687	482	36	,	,	PUNCT
fumecheng-11687	482	37	and	and	CCONJ
fumecheng-11687	482	38	forced	force	VERB
fumecheng-11687	482	39	systems	system	NOUN
fumecheng-11687	482	40	,	,	PUNCT
fumecheng-11687	482	41	results	result	NOUN
fumecheng-11687	482	42	in	in	ADP
fumecheng-11687	482	43	physics	physics	NOUN
fumecheng-11687	482	44	,	,	PUNCT
fumecheng-11687	482	45	28	28	NUM
fumecheng-11687	482	46	,	,	PUNCT
fumecheng-11687	482	47	104580	104580	NUM
fumecheng-11687	482	48	.	.	PUNCT
fumecheng-11687	483	1	36	36	NUM
fumecheng-11687	483	2	.	.	PUNCT
fumecheng-11687	484	1	he	he	PRON
fumecheng-11687	484	2	,	,	PUNCT
fumecheng-11687	484	3	j.-h	j.-h	PROPN
fumecheng-11687	484	4	.	.	PROPN
fumecheng-11687	484	5	,	,	PUNCT
fumecheng-11687	484	6	2019	2019	NUM
fumecheng-11687	484	7	,	,	PUNCT
fumecheng-11687	484	8	the	the	DET
fumecheng-11687	484	9	simplest	simple	ADJ
fumecheng-11687	484	10	approach	approach	NOUN
fumecheng-11687	484	11	to	to	ADP
fumecheng-11687	484	12	nonlinear	nonlinear	ADJ
fumecheng-11687	484	13	oscillators	oscillator	NOUN
fumecheng-11687	484	14	,	,	PUNCT
fumecheng-11687	484	15	results	result	NOUN
fumecheng-11687	484	16	in	in	ADP
fumecheng-11687	484	17	physics	physics	NOUN
fumecheng-11687	484	18	,	,	PUNCT
fumecheng-11687	484	19	15(2019	15(2019	NUM
fumecheng-11687	484	20	)	)	PUNCT
fumecheng-11687	484	21	,	,	PUNCT
fumecheng-11687	484	22	102546	102546	NUM
fumecheng-11687	484	23	.	.	PUNCT
fumecheng-11687	485	1	37	37	NUM
fumecheng-11687	485	2	.	.	PUNCT
fumecheng-11687	486	1	he	he	PRON
fumecheng-11687	486	2	,	,	PUNCT
fumecheng-11687	486	3	j.-h	j.-h	PROPN
fumecheng-11687	486	4	.	.	PROPN
fumecheng-11687	486	5	,	,	PUNCT
fumecheng-11687	486	6	2019	2019	NUM
fumecheng-11687	486	7	,	,	PUNCT
fumecheng-11687	486	8	the	the	PRON
fumecheng-11687	486	9	simpler	simple	ADJ
fumecheng-11687	486	10	,	,	PUNCT
fumecheng-11687	486	11	the	the	PRON
fumecheng-11687	486	12	better	well	ADJ
fumecheng-11687	486	13	:	:	PUNCT
fumecheng-11687	486	14	analytical	analytical	ADJ
fumecheng-11687	486	15	methods	method	NOUN
fumecheng-11687	486	16	for	for	ADP
fumecheng-11687	486	17	nonlinear	nonlinear	ADJ
fumecheng-11687	486	18	oscillators	oscillator	NOUN
fumecheng-11687	486	19	and	and	CCONJ
fumecheng-11687	486	20	fractional	fractional	ADJ
fumecheng-11687	486	21	oscillators	oscillator	NOUN
fumecheng-11687	486	22	,	,	PUNCT
fumecheng-11687	486	23	journal	journal	NOUN
fumecheng-11687	486	24	of	of	ADP
fumecheng-11687	486	25	low	low	ADJ
fumecheng-11687	486	26	frequency	frequency	NOUN
fumecheng-11687	486	27	noise	noise	NOUN
fumecheng-11687	486	28	,	,	PUNCT
fumecheng-11687	486	29	vibration	vibration	NOUN
fumecheng-11687	486	30	and	and	CCONJ
fumecheng-11687	486	31	active	active	ADJ
fumecheng-11687	486	32	control	control	NOUN
fumecheng-11687	486	33	,	,	PUNCT
fumecheng-11687	486	34	38(3	38(3	NUM
fumecheng-11687	486	35	-	-	SYM
fumecheng-11687	486	36	4	4	NUM
fumecheng-11687	486	37	)	)	PUNCT
fumecheng-11687	486	38	,	,	PUNCT
fumecheng-11687	486	39	pp	pp	ADJ
fumecheng-11687	486	40	.	.	PUNCT
fumecheng-11687	486	41	1252	1252	NUM
fumecheng-11687	486	42	-	-	SYM
fumecheng-11687	486	43	1260	1260	NUM
fumecheng-11687	486	44	.	.	PUNCT
fumecheng-11687	487	1	38	38	NUM
fumecheng-11687	487	2	.	.	PUNCT
fumecheng-11687	488	1	el	el	PROPN
fumecheng-11687	488	2	-	-	PUNCT
fumecheng-11687	488	3	dib	dib	PROPN
fumecheng-11687	488	4	,	,	PUNCT
fumecheng-11687	488	5	y.o	y.o	PROPN
fumecheng-11687	488	6	.	.	PROPN
fumecheng-11687	488	7	,	,	PUNCT
fumecheng-11687	488	8	2023	2023	NUM
fumecheng-11687	488	9	,	,	PUNCT
fumecheng-11687	488	10	insightful	insightful	ADJ
fumecheng-11687	488	11	and	and	CCONJ
fumecheng-11687	488	12	comprehensive	comprehensive	ADJ
fumecheng-11687	488	13	formularization	formularization	NOUN
fumecheng-11687	488	14	of	of	ADP
fumecheng-11687	488	15	frequency	frequency	NOUN
fumecheng-11687	488	16	amplitude	amplitude	NOUN
fumecheng-11687	488	17	formula	formula	NOUN
fumecheng-11687	488	18	for	for	ADP
fumecheng-11687	488	19	strong	strong	ADJ
fumecheng-11687	488	20	or	or	CCONJ
fumecheng-11687	488	21	singular	singular	ADJ
fumecheng-11687	488	22	nonlinear	nonlinear	ADJ
fumecheng-11687	488	23	oscillators	oscillator	NOUN
fumecheng-11687	488	24	,	,	PUNCT
fumecheng-11687	488	25	journal	journal	NOUN
fumecheng-11687	488	26	of	of	ADP
fumecheng-11687	488	27	low	low	ADJ
fumecheng-11687	488	28	frequency	frequency	NOUN
fumecheng-11687	488	29	noise	noise	NOUN
fumecheng-11687	488	30	,	,	PUNCT
fumecheng-11687	488	31	vibration	vibration	NOUN
fumecheng-11687	488	32	and	and	CCONJ
fumecheng-11687	488	33	active	active	ADJ
fumecheng-11687	488	34	control	control	NOUN
fumecheng-11687	488	35	,	,	PUNCT
fumecheng-11687	488	36	42(1	42(1	NOUN
fumecheng-11687	488	37	)	)	PUNCT
fumecheng-11687	488	38	,	,	PUNCT
fumecheng-11687	488	39	pp	pp	PROPN
fumecheng-11687	488	40	.	.	PUNCT
fumecheng-11687	489	1	89	89	NUM
fumecheng-11687	489	2	-	-	SYM
fumecheng-11687	489	3	109	109	NUM
fumecheng-11687	489	4	.	.	NOUN
fumecheng-11687	490	1	39	39	NUM
fumecheng-11687	490	2	.	.	PUNCT
fumecheng-11687	491	1	el	el	PROPN
fumecheng-11687	491	2	-	-	PUNCT
fumecheng-11687	491	3	dib	dib	PROPN
fumecheng-11687	491	4	,	,	PUNCT
fumecheng-11687	491	5	y.o	y.o	PROPN
fumecheng-11687	491	6	.	.	PROPN
fumecheng-11687	491	7	,	,	PUNCT
fumecheng-11687	491	8	alyousef	alyousef	PROPN
fumecheng-11687	491	9	,	,	PUNCT
fumecheng-11687	491	10	h.a	h.a	PROPN
fumecheng-11687	491	11	.	.	PROPN
fumecheng-11687	491	12	,	,	PUNCT
fumecheng-11687	491	13	2023	2023	NUM
fumecheng-11687	491	14	,	,	PUNCT
fumecheng-11687	491	15	successive	successive	ADJ
fumecheng-11687	491	16	approximate	approximate	ADJ
fumecheng-11687	491	17	solutions	solution	NOUN
fumecheng-11687	491	18	for	for	ADP
fumecheng-11687	491	19	nonlinear	nonlinear	ADJ
fumecheng-11687	491	20	oscillation	oscillation	NOUN
fumecheng-11687	491	21	and	and	CCONJ
fumecheng-11687	491	22	improvement	improvement	NOUN
fumecheng-11687	491	23	of	of	ADP
fumecheng-11687	491	24	the	the	DET
fumecheng-11687	491	25	solution	solution	NOUN
fumecheng-11687	491	26	accuracy	accuracy	NOUN
fumecheng-11687	491	27	with	with	ADP
fumecheng-11687	491	28	efficient	efficient	ADJ
fumecheng-11687	491	29	non	non	ADJ
fumecheng-11687	491	30	-	-	ADJ
fumecheng-11687	491	31	perturbative	perturbative	ADJ
fumecheng-11687	491	32	technique	technique	NOUN
fumecheng-11687	491	33	,	,	PUNCT
fumecheng-11687	491	34	journal	journal	NOUN
fumecheng-11687	491	35	of	of	ADP
fumecheng-11687	491	36	low	low	ADJ
fumecheng-11687	491	37	frequency	frequency	NOUN
fumecheng-11687	491	38	noise	noise	NOUN
fumecheng-11687	491	39	,	,	PUNCT
fumecheng-11687	491	40	vibration	vibration	NOUN
fumecheng-11687	491	41	and	and	CCONJ
fumecheng-11687	491	42	active	active	ADJ
fumecheng-11687	491	43	control	control	NOUN
fumecheng-11687	491	44	,	,	PUNCT
fumecheng-11687	491	45	doi	doi	NOUN
fumecheng-11687	491	46	:	:	PUNCT
fumecheng-11687	491	47	10.1177/14613484231161425	10.1177/14613484231161425	NUM
fumecheng-11687	491	48	.	.	NOUN
fumecheng-11687	491	49	40	40	NUM
fumecheng-11687	491	50	.	.	PUNCT
fumecheng-11687	492	1	feng	feng	PROPN
fumecheng-11687	492	2	,	,	PUNCT
fumecheng-11687	492	3	g.-q	g.-q	PROPN
fumecheng-11687	492	4	.	.	PUNCT
fumecheng-11687	492	5	,	,	PUNCT
fumecheng-11687	492	6	2021	2021	NUM
fumecheng-11687	492	7	,	,	PUNCT
fumecheng-11687	492	8	he	he	PRON
fumecheng-11687	492	9	’s	’	VERB
fumecheng-11687	492	10	frequency	frequency	NOUN
fumecheng-11687	492	11	formula	formula	NOUN
fumecheng-11687	492	12	to	to	ADP
fumecheng-11687	492	13	fractal	fractal	ADJ
fumecheng-11687	492	14	undamped	undampe	VERB
fumecheng-11687	492	15	duffing	duffing	NOUN
fumecheng-11687	492	16	equation	equation	NOUN
fumecheng-11687	492	17	,	,	PUNCT
fumecheng-11687	492	18	journal	journal	NOUN
fumecheng-11687	492	19	of	of	ADP
fumecheng-11687	492	20	low	low	ADJ
fumecheng-11687	492	21	frequency	frequency	NOUN
fumecheng-11687	492	22	noise	noise	NOUN
fumecheng-11687	492	23	,	,	PUNCT
fumecheng-11687	492	24	vibration	vibration	NOUN
fumecheng-11687	492	25	and	and	CCONJ
fumecheng-11687	492	26	active	active	ADJ
fumecheng-11687	492	27	control	control	NOUN
fumecheng-11687	492	28	,	,	PUNCT
fumecheng-11687	492	29	40(4	40(4	NUM
fumecheng-11687	492	30	)	)	PUNCT
fumecheng-11687	492	31	,	,	PUNCT
fumecheng-11687	492	32	pp	pp	ADP
fumecheng-11687	492	33	.	.	PUNCT
fumecheng-11687	493	1	1671	1671	NUM
fumecheng-11687	493	2	-	-	SYM
fumecheng-11687	493	3	1676	1676	NUM
fumecheng-11687	493	4	.	.	PUNCT
fumecheng-11687	494	1	41	41	NUM
fumecheng-11687	494	2	.	.	PUNCT
fumecheng-11687	495	1	elías	elías	PROPN
fumecheng-11687	495	2	-	-	PUNCT
fumecheng-11687	495	3	zúñiga	zúñiga	PROPN
fumecheng-11687	495	4	,	,	PUNCT
fumecheng-11687	495	5	a.	a.	NOUN
fumecheng-11687	495	6	,	,	PUNCT
fumecheng-11687	495	7	palacios	palacio	NOUN
fumecheng-11687	495	8	-	-	PUNCT
fumecheng-11687	495	9	pineda	pineda	PROPN
fumecheng-11687	495	10	,	,	PUNCT
fumecheng-11687	495	11	l.m	l.m	PROPN
fumecheng-11687	495	12	.	.	PROPN
fumecheng-11687	495	13	,	,	PUNCT
fumecheng-11687	495	14	jimenez	jimenez	PROPN
fumecheng-11687	495	15	-	-	PUNCT
fumecheng-11687	495	16	cedeno	cedeno	PROPN
fumecheng-11687	495	17	,	,	PUNCT
fumecheng-11687	495	18	i.	i.	PROPN
fumecheng-11687	495	19	h.	h.	PROPN
fumecheng-11687	495	20	,	,	PUNCT
fumecheng-11687	495	21	martínez	martínez	PROPN
fumecheng-11687	495	22	-	-	PUNCT
fumecheng-11687	495	23	romero	romero	PROPN
fumecheng-11687	495	24	,	,	PUNCT
fumecheng-11687	495	25	o.	o.	PROPN
fumecheng-11687	495	26	,	,	PUNCT
fumecheng-11687	495	27	olvera	olvera	PROPN
fumecheng-11687	495	28	-	-	PUNCT
fumecheng-11687	495	29	trejo	trejo	PROPN
fumecheng-11687	495	30	,	,	PUNCT
fumecheng-11687	495	31	d.	d.	PROPN
fumecheng-11687	495	32	,	,	PUNCT
fumecheng-11687	495	33	2021	2021	NUM
fumecheng-11687	495	34	,	,	PUNCT
fumecheng-11687	495	35	analytical	analytical	ADJ
fumecheng-11687	495	36	solution	solution	NOUN
fumecheng-11687	495	37	of	of	ADP
fumecheng-11687	495	38	the	the	DET
fumecheng-11687	495	39	fractal	fractal	ADJ
fumecheng-11687	495	40	cubic	cubic	ADJ
fumecheng-11687	495	41	–	–	PUNCT
fumecheng-11687	495	42	quintic	quintic	ADJ
fumecheng-11687	495	43	duffing	duffing	NOUN
fumecheng-11687	495	44	equation	equation	NOUN
fumecheng-11687	495	45	,	,	PUNCT
fumecheng-11687	495	46	fractals	fractal	NOUN
fumecheng-11687	495	47	,	,	PUNCT
fumecheng-11687	495	48	29(4	29(4	NOUN
fumecheng-11687	495	49	)	)	PUNCT
fumecheng-11687	495	50	,	,	PUNCT
fumecheng-11687	495	51	2150080	2150080	NUM
fumecheng-11687	495	52	.	.	PUNCT
fumecheng-11687	496	1	42	42	NUM
fumecheng-11687	496	2	.	.	PUNCT
fumecheng-11687	497	1	elías	elías	PROPN
fumecheng-11687	497	2	-	-	PUNCT
fumecheng-11687	497	3	zúñiga	zúñiga	PROPN
fumecheng-11687	497	4	,	,	PUNCT
fumecheng-11687	497	5	a.	a.	NOUN
fumecheng-11687	497	6	,	,	PUNCT
fumecheng-11687	497	7	palacios	palacio	NOUN
fumecheng-11687	497	8	-	-	PUNCT
fumecheng-11687	497	9	pineda	pineda	PROPN
fumecheng-11687	497	10	,	,	PUNCT
fumecheng-11687	497	11	l.m	l.m	PROPN
fumecheng-11687	497	12	.	.	PROPN
fumecheng-11687	497	13	,	,	PUNCT
fumecheng-11687	497	14	martínez	martínez	PROPN
fumecheng-11687	497	15	-	-	PUNCT
fumecheng-11687	497	16	romero	romero	PROPN
fumecheng-11687	497	17	,	,	PUNCT
fumecheng-11687	497	18	o.	o.	PROPN
fumecheng-11687	497	19	,	,	PUNCT
fumecheng-11687	497	20	olvera	olvera	PROPN
fumecheng-11687	497	21	-	-	PUNCT
fumecheng-11687	497	22	trejo	trejo	PROPN
fumecheng-11687	497	23	,	,	PUNCT
fumecheng-11687	497	24	d.	d.	PROPN
fumecheng-11687	497	25	,	,	PUNCT
fumecheng-11687	497	26	2021	2021	NUM
fumecheng-11687	497	27	,	,	PUNCT
fumecheng-11687	497	28	dynamics	dynamic	NOUN
fumecheng-11687	497	29	response	response	NOUN
fumecheng-11687	497	30	of	of	ADP
fumecheng-11687	497	31	the	the	DET
fumecheng-11687	497	32	forced	force	VERB
fumecheng-11687	497	33	fangzhu	fangzhu	NOUN
fumecheng-11687	497	34	fractal	fractal	ADJ
fumecheng-11687	497	35	device	device	NOUN
fumecheng-11687	497	36	for	for	ADP
fumecheng-11687	497	37	water	water	NOUN
fumecheng-11687	497	38	collection	collection	NOUN
fumecheng-11687	497	39	from	from	ADP
fumecheng-11687	497	40	air	air	NOUN
fumecheng-11687	497	41	,	,	PUNCT
fumecheng-11687	497	42	fractals	fractal	NOUN
fumecheng-11687	497	43	,	,	PUNCT
fumecheng-11687	497	44	29(7	29(7	NUM
fumecheng-11687	497	45	)	)	PUNCT
fumecheng-11687	497	46	,	,	PUNCT
fumecheng-11687	497	47	2150186	2150186	NUM
fumecheng-11687	497	48	.	.	PUNCT
fumecheng-11687	498	1	43	43	NUM
fumecheng-11687	498	2	.	.	PUNCT
fumecheng-11687	498	3	podlubny	podlubny	PROPN
fumecheng-11687	498	4	,	,	PUNCT
fumecheng-11687	498	5	i.	i.	NOUN
fumecheng-11687	498	6	,	,	PUNCT
fumecheng-11687	498	7	1998	1998	NUM
fumecheng-11687	498	8	,	,	PUNCT
fumecheng-11687	498	9	fractional	fractional	ADJ
fumecheng-11687	498	10	differential	differential	ADJ
fumecheng-11687	498	11	equations	equation	NOUN
fumecheng-11687	498	12	:	:	PUNCT
fumecheng-11687	498	13	an	an	DET
fumecheng-11687	498	14	introduction	introduction	NOUN
fumecheng-11687	498	15	to	to	ADP
fumecheng-11687	498	16	fractional	fractional	ADJ
fumecheng-11687	498	17	derivatives	derivative	NOUN
fumecheng-11687	498	18	,	,	PUNCT
fumecheng-11687	498	19	fractional	fractional	ADJ
fumecheng-11687	498	20	differential	differential	ADJ
fumecheng-11687	498	21	equations	equation	NOUN
fumecheng-11687	498	22	,	,	PUNCT
fumecheng-11687	498	23	to	to	ADP
fumecheng-11687	498	24	methods	method	NOUN
fumecheng-11687	498	25	of	of	ADP
fumecheng-11687	498	26	their	their	PRON
fumecheng-11687	498	27	solution	solution	NOUN
fumecheng-11687	498	28	and	and	CCONJ
fumecheng-11687	498	29	some	some	PRON
fumecheng-11687	498	30	of	of	ADP
fumecheng-11687	498	31	their	their	PRON
fumecheng-11687	498	32	applications	application	NOUN
fumecheng-11687	498	33	,	,	PUNCT
fumecheng-11687	498	34	elsevier	elsevier	NOUN
fumecheng-11687	498	35	.	.	PUNCT
fumecheng-11687	499	1	44	44	NUM
fumecheng-11687	499	2	.	.	PUNCT
fumecheng-11687	499	3	abbas	abbas	PROPN
fumecheng-11687	499	4	,	,	PUNCT
fumecheng-11687	499	5	s.	s.	PROPN
fumecheng-11687	499	6	,	,	PUNCT
fumecheng-11687	499	7	benchohra	benchohra	NOUN
fumecheng-11687	499	8	,	,	PUNCT
fumecheng-11687	499	9	m.	m.	NOUN
fumecheng-11687	499	10	,	,	PUNCT
fumecheng-11687	499	11	n'guérékata	n'guérékata	PROPN
fumecheng-11687	499	12	,	,	PUNCT
fumecheng-11687	499	13	g.m	g.m	PROPN
fumecheng-11687	499	14	.	.	PROPN
fumecheng-11687	499	15	,	,	PUNCT
fumecheng-11687	499	16	2012	2012	NUM
fumecheng-11687	499	17	,	,	PUNCT
fumecheng-11687	499	18	topics	topic	NOUN
fumecheng-11687	499	19	in	in	ADP
fumecheng-11687	499	20	fractional	fractional	ADJ
fumecheng-11687	499	21	differential	differential	ADJ
fumecheng-11687	499	22	equations	equation	NOUN
fumecheng-11687	499	23	,	,	PUNCT
fumecheng-11687	499	24	springer	springer	NOUN
fumecheng-11687	499	25	science	science	PROPN
fumecheng-11687	499	26	&	&	CCONJ
fumecheng-11687	499	27	business	business	NOUN
fumecheng-11687	499	28	media	medium	NOUN
fumecheng-11687	499	29	.	.	PUNCT
fumecheng-11687	500	1	216	216	NUM
fumecheng-11687	500	2	y.o	y.o	PROPN
fumecheng-11687	500	3	.	.	PROPN
fumecheng-11687	500	4	el	el	PROPN
fumecheng-11687	500	5	-	-	PUNCT
fumecheng-11687	500	6	dib	dib	PROPN
fumecheng-11687	500	7	,	,	PUNCT
fumecheng-11687	500	8	n.s	n.s	PROPN
fumecheng-11687	500	9	.	.	PROPN
fumecheng-11687	500	10	elgazery	elgazery	PROPN
fumecheng-11687	500	11	,	,	PUNCT
fumecheng-11687	500	12	h.a	h.a	PROPN
fumecheng-11687	500	13	.	.	PROPN
fumecheng-11687	500	14	alyousef	alyousef	PROPN
fumecheng-11687	500	15	45	45	NUM
fumecheng-11687	500	16	.	.	PUNCT
fumecheng-11687	501	1	wang	wang	PROPN
fumecheng-11687	501	2	,	,	PUNCT
fumecheng-11687	501	3	k.-l	k.-l	PROPN
fumecheng-11687	501	4	.	.	PROPN
fumecheng-11687	501	5	,	,	PUNCT
fumecheng-11687	501	6	liu	liu	PROPN
fumecheng-11687	501	7	,	,	PUNCT
fumecheng-11687	501	8	s.-y	s.-y	NOUN
fumecheng-11687	501	9	.	.	PUNCT
fumecheng-11687	501	10	,	,	PUNCT
fumecheng-11687	501	11	2016	2016	NUM
fumecheng-11687	501	12	,	,	PUNCT
fumecheng-11687	501	13	he	he	PRON
fumecheng-11687	501	14	’s	’	VERB
fumecheng-11687	501	15	fractional	fractional	ADJ
fumecheng-11687	501	16	derivative	derivative	NOUN
fumecheng-11687	501	17	for	for	ADP
fumecheng-11687	501	18	non	non	ADJ
fumecheng-11687	501	19	-	-	ADJ
fumecheng-11687	501	20	linear	linear	ADJ
fumecheng-11687	501	21	fractional	fractional	ADJ
fumecheng-11687	501	22	heat	heat	NOUN
fumecheng-11687	501	23	transfer	transfer	NOUN
fumecheng-11687	501	24	equation	equation	NOUN
fumecheng-11687	501	25	,	,	PUNCT
fumecheng-11687	501	26	thermal	thermal	ADJ
fumecheng-11687	501	27	science	science	NOUN
fumecheng-11687	501	28	,	,	PUNCT
fumecheng-11687	501	29	20(3	20(3	NOUN
fumecheng-11687	501	30	)	)	PUNCT
fumecheng-11687	501	31	,	,	PUNCT
fumecheng-11687	501	32	pp	pp	ADP
fumecheng-11687	501	33	.	.	PUNCT
fumecheng-11687	502	1	793	793	NUM
fumecheng-11687	502	2	-	-	SYM
fumecheng-11687	502	3	796	796	NUM
fumecheng-11687	502	4	.	.	PUNCT
fumecheng-11687	503	1	46	46	NUM
fumecheng-11687	503	2	.	.	PUNCT
fumecheng-11687	504	1	wang	wang	PROPN
fumecheng-11687	504	2	,	,	PUNCT
fumecheng-11687	504	3	k.-l	k.-l	PROPN
fumecheng-11687	504	4	.	.	PROPN
fumecheng-11687	504	5	,	,	PUNCT
fumecheng-11687	504	6	liu	liu	PROPN
fumecheng-11687	504	7	,	,	PUNCT
fumecheng-11687	504	8	s.-y	s.-y	NOUN
fumecheng-11687	504	9	.	.	PUNCT
fumecheng-11687	504	10	,	,	PUNCT
fumecheng-11687	504	11	2017	2017	NUM
fumecheng-11687	504	12	,	,	PUNCT
fumecheng-11687	504	13	he	he	PRON
fumecheng-11687	504	14	’s	’	VERB
fumecheng-11687	504	15	fractional	fractional	ADJ
fumecheng-11687	504	16	derivative	derivative	NOUN
fumecheng-11687	504	17	and	and	CCONJ
fumecheng-11687	504	18	its	its	PRON
fumecheng-11687	504	19	application	application	NOUN
fumecheng-11687	504	20	for	for	ADP
fumecheng-11687	504	21	fractional	fractional	ADJ
fumecheng-11687	504	22	fornbergwhitham	fornbergwhitham	PROPN
fumecheng-11687	504	23	equation	equation	NOUN
fumecheng-11687	504	24	,	,	PUNCT
fumecheng-11687	504	25	thermal	thermal	ADJ
fumecheng-11687	504	26	science	science	NOUN
fumecheng-11687	504	27	,	,	PUNCT
fumecheng-11687	504	28	21(5	21(5	NUM
fumecheng-11687	504	29	)	)	PUNCT
fumecheng-11687	504	30	,	,	PUNCT
fumecheng-11687	504	31	pp	pp	PROPN
fumecheng-11687	504	32	.	.	PUNCT
fumecheng-11687	505	1	2049	2049	NUM
fumecheng-11687	505	2	-	-	SYM
fumecheng-11687	505	3	2055	2055	NUM
fumecheng-11687	505	4	.	.	PUNCT
fumecheng-11687	506	1	47	47	NUM
fumecheng-11687	506	2	.	.	PUNCT
fumecheng-11687	506	3	wu	wu	PROPN
fumecheng-11687	506	4	,	,	PUNCT
fumecheng-11687	506	5	y.	y.	PROPN
fumecheng-11687	506	6	,	,	PUNCT
fumecheng-11687	506	7	liu	liu	PROPN
fumecheng-11687	506	8	,	,	PUNCT
fumecheng-11687	506	9	y.-p	y.-p	PROPN
fumecheng-11687	506	10	.	.	PROPN
fumecheng-11687	506	11	,	,	PUNCT
fumecheng-11687	506	12	2021	2021	NUM
fumecheng-11687	506	13	,	,	PUNCT
fumecheng-11687	506	14	residual	residual	ADJ
fumecheng-11687	506	15	calculation	calculation	NOUN
fumecheng-11687	506	16	in	in	ADP
fumecheng-11687	506	17	he	he	PRON
fumecheng-11687	506	18	’s	’s	PART
fumecheng-11687	506	19	frequency	frequency	NOUN
fumecheng-11687	506	20	–	–	PUNCT
fumecheng-11687	506	21	amplitude	amplitude	NOUN
fumecheng-11687	506	22	formulation	formulation	NOUN
fumecheng-11687	506	23	,	,	PUNCT
fumecheng-11687	506	24	journal	journal	NOUN
fumecheng-11687	506	25	of	of	ADP
fumecheng-11687	506	26	low	low	ADJ
fumecheng-11687	506	27	frequency	frequency	NOUN
fumecheng-11687	506	28	noise	noise	NOUN
fumecheng-11687	506	29	,	,	PUNCT
fumecheng-11687	506	30	vibration	vibration	NOUN
fumecheng-11687	506	31	and	and	CCONJ
fumecheng-11687	506	32	active	active	ADJ
fumecheng-11687	506	33	control	control	NOUN
fumecheng-11687	506	34	,	,	PUNCT
fumecheng-11687	506	35	40(2	40(2	NUM
fumecheng-11687	506	36	)	)	PUNCT
fumecheng-11687	506	37	,	,	PUNCT
fumecheng-11687	506	38	pp	pp	PROPN
fumecheng-11687	506	39	.	.	PUNCT
fumecheng-11687	507	1	1040	1040	NUM
fumecheng-11687	507	2	-	-	SYM
fumecheng-11687	507	3	1047	1047	NUM
fumecheng-11687	507	4	.	.	PUNCT
fumecheng-11687	508	1	48	48	NUM
fumecheng-11687	508	2	.	.	PUNCT
fumecheng-11687	509	1	he	he	PRON
fumecheng-11687	509	2	,	,	PUNCT
fumecheng-11687	509	3	j.-h	j.-h	PROPN
fumecheng-11687	509	4	.	.	PROPN
fumecheng-11687	509	5	,	,	PUNCT
fumecheng-11687	509	6	ain	ain	PROPN
fumecheng-11687	509	7	,	,	PUNCT
fumecheng-11687	509	8	q.t	q.t	PROPN
fumecheng-11687	509	9	.	.	PROPN
fumecheng-11687	509	10	,	,	PUNCT
fumecheng-11687	509	11	2020	2020	NUM
fumecheng-11687	509	12	,	,	PUNCT
fumecheng-11687	509	13	new	new	ADJ
fumecheng-11687	509	14	promises	promise	NOUN
fumecheng-11687	509	15	and	and	CCONJ
fumecheng-11687	509	16	future	future	ADJ
fumecheng-11687	509	17	challenges	challenge	NOUN
fumecheng-11687	509	18	of	of	ADP
fumecheng-11687	509	19	fractal	fractal	ADJ
fumecheng-11687	509	20	calculus	calculus	NOUN
fumecheng-11687	509	21	:	:	PUNCT
fumecheng-11687	509	22	from	from	ADP
fumecheng-11687	509	23	two	two	NUM
fumecheng-11687	509	24	-	-	PUNCT
fumecheng-11687	509	25	scale	scale	NOUN
fumecheng-11687	509	26	thermodynamics	thermodynamic	NOUN
fumecheng-11687	509	27	to	to	ADP
fumecheng-11687	509	28	fractal	fractal	ADJ
fumecheng-11687	509	29	variational	variational	ADJ
fumecheng-11687	509	30	principle	principle	NOUN
fumecheng-11687	509	31	,	,	PUNCT
fumecheng-11687	509	32	thermal	thermal	ADJ
fumecheng-11687	509	33	science	science	NOUN
fumecheng-11687	509	34	,	,	PUNCT
fumecheng-11687	509	35	24(2	24(2	NUM
fumecheng-11687	509	36	)	)	PUNCT
fumecheng-11687	509	37	,	,	PUNCT
fumecheng-11687	509	38	pp	pp	PROPN
fumecheng-11687	509	39	.	.	PUNCT
fumecheng-11687	510	1	659	659	NUM
fumecheng-11687	510	2	-	-	SYM
fumecheng-11687	510	3	681	681	NUM
fumecheng-11687	510	4	.	.	PUNCT
fumecheng-11687	511	1	49	49	NUM
fumecheng-11687	511	2	.	.	PUNCT
fumecheng-11687	512	1	el	el	PROPN
fumecheng-11687	512	2	-	-	PUNCT
fumecheng-11687	512	3	dib	dib	PROPN
fumecheng-11687	512	4	,	,	PUNCT
fumecheng-11687	512	5	y.o	y.o	PROPN
fumecheng-11687	512	6	.	.	PROPN
fumecheng-11687	512	7	,	,	PUNCT
fumecheng-11687	512	8	elgazery	elgazery	PROPN
fumecheng-11687	512	9	,	,	PUNCT
fumecheng-11687	512	10	n.s	n.s	PROPN
fumecheng-11687	512	11	.	.	PROPN
fumecheng-11687	512	12	,	,	PUNCT
fumecheng-11687	512	13	alyousef	alyousef	PROPN
fumecheng-11687	512	14	,	,	PUNCT
fumecheng-11687	512	15	h.a	h.a	PROPN
fumecheng-11687	512	16	.	.	PROPN
fumecheng-11687	512	17	,	,	PUNCT
fumecheng-11687	512	18	2023	2023	NUM
fumecheng-11687	512	19	,	,	PUNCT
fumecheng-11687	512	20	galerkin	galerkin	X
fumecheng-11687	512	21	’s	’s	PART
fumecheng-11687	512	22	method	method	NOUN
fumecheng-11687	512	23	to	to	PART
fumecheng-11687	512	24	solve	solve	VERB
fumecheng-11687	512	25	a	a	DET
fumecheng-11687	512	26	fractional	fractional	ADJ
fumecheng-11687	512	27	time	time	NOUN
fumecheng-11687	512	28	-	-	PUNCT
fumecheng-11687	512	29	delayed	delay	VERB
fumecheng-11687	512	30	jerk	jerk	NOUN
fumecheng-11687	512	31	oscillator	oscillator	NOUN
fumecheng-11687	512	32	,	,	PUNCT
fumecheng-11687	512	33	archive	archive	NOUN
fumecheng-11687	512	34	of	of	ADP
fumecheng-11687	512	35	applied	apply	VERB
fumecheng-11687	512	36	mechanics	mechanic	NOUN
fumecheng-11687	512	37	,	,	PUNCT
fumecheng-11687	512	38	93	93	NUM
fumecheng-11687	512	39	,	,	PUNCT
fumecheng-11687	512	40	pp	pp	ADJ
fumecheng-11687	512	41	.	.	PUNCT
fumecheng-11687	513	1	3597	3597	NUM
fumecheng-11687	513	2	-	-	SYM
fumecheng-11687	513	3	3607	3607	NUM
fumecheng-11687	513	4	.	.	PUNCT
fumecheng-11687	514	1	50	50	NUM
fumecheng-11687	514	2	.	.	X
fumecheng-11687	515	1	el	el	PROPN
fumecheng-11687	515	2	-	-	PUNCT
fumecheng-11687	515	3	dib	dib	PROPN
fumecheng-11687	515	4	,	,	PUNCT
fumecheng-11687	515	5	y.o	y.o	PROPN
fumecheng-11687	515	6	.	.	PROPN
fumecheng-11687	515	7	,	,	PUNCT
fumecheng-11687	515	8	elgazery	elgazery	PROPN
fumecheng-11687	515	9	,	,	PUNCT
fumecheng-11687	515	10	n.s	n.s	PROPN
fumecheng-11687	515	11	.	.	PROPN
fumecheng-11687	515	12	,	,	PUNCT
fumecheng-11687	515	13	alyousef	alyousef	PROPN
fumecheng-11687	515	14	,	,	PUNCT
fumecheng-11687	515	15	h.a	h.a	PROPN
fumecheng-11687	515	16	.	.	PROPN
fumecheng-11687	515	17	,	,	PUNCT
fumecheng-11687	515	18	2023	2023	NUM
fumecheng-11687	515	19	,	,	PUNCT
fumecheng-11687	515	20	an	an	DET
fumecheng-11687	515	21	instrumental	instrumental	ADJ
fumecheng-11687	515	22	insight	insight	NOUN
fumecheng-11687	515	23	for	for	ADP
fumecheng-11687	515	24	a	a	DET
fumecheng-11687	515	25	periodic	periodic	ADJ
fumecheng-11687	515	26	solution	solution	NOUN
fumecheng-11687	515	27	of	of	ADP
fumecheng-11687	515	28	a	a	DET
fumecheng-11687	515	29	fractal	fractal	ADJ
fumecheng-11687	515	30	mathieu	mathieu	PROPN
fumecheng-11687	515	31	–	–	PUNCT
fumecheng-11687	515	32	duffing	duffing	NOUN
fumecheng-11687	515	33	equation	equation	NOUN
fumecheng-11687	515	34	,	,	PUNCT
fumecheng-11687	515	35	journal	journal	NOUN
fumecheng-11687	515	36	of	of	ADP
fumecheng-11687	515	37	low	low	ADJ
fumecheng-11687	515	38	frequency	frequency	NOUN
fumecheng-11687	515	39	noise	noise	NOUN
fumecheng-11687	515	40	,	,	PUNCT
fumecheng-11687	515	41	vibration	vibration	NOUN
fumecheng-11687	515	42	and	and	CCONJ
fumecheng-11687	515	43	active	active	ADJ
fumecheng-11687	515	44	control	control	NOUN
fumecheng-11687	515	45	,	,	PUNCT
fumecheng-11687	515	46	doi	doi	NOUN
fumecheng-11687	515	47	:	:	PUNCT
fumecheng-11687	515	48	10.1177/14613484231185907	10.1177/14613484231185907	NUM
fumecheng-11687	515	49	.	.	PUNCT
fumecheng-11687	516	1	51	51	NUM
fumecheng-11687	516	2	.	.	PUNCT
fumecheng-11687	517	1	he	he	PRON
fumecheng-11687	517	2	,	,	PUNCT
fumecheng-11687	517	3	j.-h	j.-h	PROPN
fumecheng-11687	517	4	.	.	PROPN
fumecheng-11687	517	5	,	,	PUNCT
fumecheng-11687	517	6	2018	2018	NUM
fumecheng-11687	517	7	,	,	PUNCT
fumecheng-11687	517	8	fractal	fractal	ADJ
fumecheng-11687	517	9	calculus	calculus	NOUN
fumecheng-11687	517	10	and	and	CCONJ
fumecheng-11687	517	11	its	its	PRON
fumecheng-11687	517	12	geometrical	geometrical	ADJ
fumecheng-11687	517	13	explanation	explanation	NOUN
fumecheng-11687	517	14	,	,	PUNCT
fumecheng-11687	517	15	results	result	NOUN
fumecheng-11687	517	16	in	in	ADP
fumecheng-11687	517	17	physics	physics	NOUN
fumecheng-11687	517	18	,	,	PUNCT
fumecheng-11687	517	19	10	10	NUM
fumecheng-11687	517	20	,	,	PUNCT
fumecheng-11687	517	21	pp	pp	ADJ
fumecheng-11687	517	22	.	.	PUNCT
fumecheng-11687	518	1	272	272	NUM
fumecheng-11687	518	2	-	-	SYM
fumecheng-11687	518	3	276	276	NUM
fumecheng-11687	518	4	.	.	PUNCT
fumecheng-11687	519	1	52	52	NUM
fumecheng-11687	519	2	.	.	PUNCT
fumecheng-11687	520	1	el	el	PROPN
fumecheng-11687	520	2	-	-	PUNCT
fumecheng-11687	520	3	dib	dib	PROPN
fumecheng-11687	520	4	,	,	PUNCT
fumecheng-11687	520	5	y.o	y.o	PROPN
fumecheng-11687	520	6	.	.	PROPN
fumecheng-11687	520	7	,	,	PUNCT
fumecheng-11687	520	8	2022	2022	NUM
fumecheng-11687	520	9	,	,	PUNCT
fumecheng-11687	520	10	an	an	DET
fumecheng-11687	520	11	efficient	efficient	ADJ
fumecheng-11687	520	12	approach	approach	NOUN
fumecheng-11687	520	13	to	to	ADP
fumecheng-11687	520	14	solving	solve	VERB
fumecheng-11687	520	15	fractional	fractional	ADJ
fumecheng-11687	520	16	van	van	PROPN
fumecheng-11687	520	17	der	der	PROPN
fumecheng-11687	520	18	pol	pol	PROPN
fumecheng-11687	520	19	–	–	PUNCT
fumecheng-11687	520	20	duffing	duffe	VERB
fumecheng-11687	520	21	jerk	jerk	NOUN
fumecheng-11687	520	22	oscillator	oscillator	NOUN
fumecheng-11687	520	23	,	,	PUNCT
fumecheng-11687	520	24	communications	communication	NOUN
fumecheng-11687	520	25	in	in	ADP
fumecheng-11687	520	26	theoretical	theoretical	ADJ
fumecheng-11687	520	27	physics	physics	NOUN
fumecheng-11687	520	28	.	.	PUNCT
fumecheng-11687	520	29	,	,	PUNCT
fumecheng-11687	520	30	74	74	NUM
fumecheng-11687	520	31	,	,	PUNCT
fumecheng-11687	520	32	105006	105006	NUM
fumecheng-11687	520	33	.	.	PUNCT
fumecheng-11687	521	1	53	53	NUM
fumecheng-11687	521	2	.	.	X
fumecheng-11687	522	1	el	el	PROPN
fumecheng-11687	522	2	-	-	PUNCT
fumecheng-11687	522	3	dib	dib	PROPN
fumecheng-11687	522	4	,	,	PUNCT
fumecheng-11687	522	5	y.o	y.o	PROPN
fumecheng-11687	522	6	.	.	PROPN
fumecheng-11687	522	7	,	,	PUNCT
fumecheng-11687	522	8	2022	2022	NUM
fumecheng-11687	522	9	,	,	PUNCT
fumecheng-11687	522	10	the	the	DET
fumecheng-11687	522	11	simplest	simple	ADJ
fumecheng-11687	522	12	approach	approach	NOUN
fumecheng-11687	522	13	to	to	ADP
fumecheng-11687	522	14	solving	solve	VERB
fumecheng-11687	522	15	the	the	DET
fumecheng-11687	522	16	cubic	cubic	ADJ
fumecheng-11687	522	17	nonlinear	nonlinear	PROPN
fumecheng-11687	522	18	jerk	jerk	PROPN
fumecheng-11687	522	19	oscillator	oscillator	NOUN
fumecheng-11687	522	20	with	with	ADP
fumecheng-11687	522	21	the	the	DET
fumecheng-11687	522	22	nonperturbative	nonperturbative	ADJ
fumecheng-11687	522	23	method	method	NOUN
fumecheng-11687	522	24	,	,	PUNCT
fumecheng-11687	522	25	mathematical	mathematical	ADJ
fumecheng-11687	522	26	methods	method	NOUN
fumecheng-11687	522	27	in	in	ADP
fumecheng-11687	522	28	the	the	DET
fumecheng-11687	522	29	applied	apply	VERB
fumecheng-11687	522	30	sciences	science	NOUN
fumecheng-11687	522	31	,	,	PUNCT
fumecheng-11687	522	32	45(9	45(9	NUM
fumecheng-11687	522	33	)	)	PUNCT
fumecheng-11687	522	34	,	,	PUNCT
fumecheng-11687	522	35	pp	pp	ADP
fumecheng-11687	522	36	.	.	PUNCT
fumecheng-11687	523	1	5165	5165	NUM
fumecheng-11687	523	2	-	-	SYM
fumecheng-11687	523	3	5183	5183	NUM
fumecheng-11687	523	4	.	.	PUNCT
fumecheng-11687	524	1	54	54	NUM
fumecheng-11687	524	2	.	.	X
fumecheng-11687	525	1	el	el	PROPN
fumecheng-11687	525	2	-	-	PUNCT
fumecheng-11687	525	3	dib	dib	PROPN
fumecheng-11687	525	4	,	,	PUNCT
fumecheng-11687	525	5	y.o	y.o	PROPN
fumecheng-11687	525	6	.	.	PROPN
fumecheng-11687	525	7	,	,	PUNCT
fumecheng-11687	525	8	elgazery	elgazery	PROPN
fumecheng-11687	525	9	,	,	PUNCT
fumecheng-11687	525	10	n.s	n.s	PROPN
fumecheng-11687	525	11	.	.	PROPN
fumecheng-11687	525	12	,	,	PUNCT
fumecheng-11687	525	13	khattab	khattab	PROPN
fumecheng-11687	525	14	,	,	PUNCT
fumecheng-11687	525	15	y.m	y.m	PROPN
fumecheng-11687	525	16	.	.	PROPN
fumecheng-11687	525	17	,	,	PUNCT
fumecheng-11687	525	18	alyousef	alyousef	PROPN
fumecheng-11687	525	19	,	,	PUNCT
fumecheng-11687	525	20	h.a	h.a	PROPN
fumecheng-11687	525	21	.	.	PROPN
fumecheng-11687	525	22	,	,	PUNCT
fumecheng-11687	525	23	2023	2023	NUM
fumecheng-11687	525	24	,	,	PUNCT
fumecheng-11687	525	25	an	an	DET
fumecheng-11687	525	26	innovative	innovative	ADJ
fumecheng-11687	525	27	technique	technique	NOUN
fumecheng-11687	525	28	to	to	PART
fumecheng-11687	525	29	solve	solve	VERB
fumecheng-11687	525	30	a	a	DET
fumecheng-11687	525	31	fractal	fractal	ADJ
fumecheng-11687	525	32	damping	damp	VERB
fumecheng-11687	525	33	duffing	duffing	NOUN
fumecheng-11687	525	34	-	-	PUNCT
fumecheng-11687	525	35	jerk	jerk	NOUN
fumecheng-11687	525	36	oscillator	oscillator	NOUN
fumecheng-11687	525	37	,	,	PUNCT
fumecheng-11687	525	38	communications	communication	NOUN
fumecheng-11687	525	39	in	in	ADP
fumecheng-11687	525	40	theoretical	theoretical	ADJ
fumecheng-11687	525	41	physics	physics	NOUN
fumecheng-11687	525	42	,	,	PUNCT
fumecheng-11687	525	43	75	75	NUM
fumecheng-11687	525	44	,	,	PUNCT
fumecheng-11687	525	45	055001	055001	NUM
fumecheng-11687	525	46	.	.	PUNCT