id	sid	tid	token	lemma	pos
ejpam-5140	1	1	european	european	PROPN
ejpam-5140	1	2	journal	journal	PROPN
ejpam-5140	1	3	of	of	ADP
ejpam-5140	1	4	pure	pure	ADJ
ejpam-5140	1	5	and	and	CCONJ
ejpam-5140	1	6	applied	apply	VERB
ejpam-5140	1	7	mathematics	mathematic	NOUN
ejpam-5140	1	8	vol	vol	NOUN
ejpam-5140	1	9	.	.	PROPN
ejpam-5140	2	1	17	17	NUM
ejpam-5140	2	2	,	,	PUNCT
ejpam-5140	2	3	no	no	INTJ
ejpam-5140	2	4	.	.	NOUN
ejpam-5140	2	5	2	2	NUM
ejpam-5140	2	6	,	,	PUNCT
ejpam-5140	2	7	2024	2024	NUM
ejpam-5140	2	8	,	,	PUNCT
ejpam-5140	2	9	1254	1254	NUM
ejpam-5140	2	10	-	-	SYM
ejpam-5140	2	11	1264	1264	NUM
ejpam-5140	2	12	issn	issn	PROPN
ejpam-5140	2	13	1307	1307	NUM
ejpam-5140	2	14	-	-	SYM
ejpam-5140	2	15	5543	5543	NUM
ejpam-5140	2	16	–	–	PUNCT
ejpam-5140	3	1	ejpam.com	ejpam.com	X
ejpam-5140	3	2	published	publish	VERB
ejpam-5140	3	3	by	by	ADP
ejpam-5140	3	4	new	new	PROPN
ejpam-5140	3	5	york	york	PROPN
ejpam-5140	3	6	business	business	PROPN
ejpam-5140	3	7	global	global	PROPN
ejpam-5140	3	8	twodimensional	twodimensional	ADJ
ejpam-5140	3	9	coupled	couple	VERB
ejpam-5140	3	10	asymmetric	asymmetric	PROPN
ejpam-5140	3	11	van	van	PROPN
ejpam-5140	3	12	der	der	PROPN
ejpam-5140	3	13	pol	pol	PROPN
ejpam-5140	3	14	oscillator	oscillator	NOUN
ejpam-5140	3	15	v.	v.	PROPN
ejpam-5140	3	16	s.	s.	PROPN
ejpam-5140	3	17	erturk1	erturk1	PROPN
ejpam-5140	3	18	,	,	PUNCT
ejpam-5140	3	19	b.	b.	PROPN
ejpam-5140	3	20	rath2	rath2	PROPN
ejpam-5140	3	21	,	,	PUNCT
ejpam-5140	3	22	taqwa	taqwa	PROPN
ejpam-5140	3	23	m.	m.	NOUN
ejpam-5140	3	24	al	al	PROPN
ejpam-5140	3	25	-	-	PUNCT
ejpam-5140	3	26	khader3	khader3	PROPN
ejpam-5140	3	27	,	,	PUNCT
ejpam-5140	3	28	noorhan	noorhan	ADP
ejpam-5140	3	29	alshaikh4	alshaikh4	PROPN
ejpam-5140	3	30	,	,	PUNCT
ejpam-5140	3	31	p.	p.	PROPN
ejpam-5140	3	32	mallick2	mallick2	PROPN
ejpam-5140	3	33	,	,	PUNCT
ejpam-5140	3	34	jihad	jihad	VERB
ejpam-5140	3	35	asad4,∗	asad4,∗	PROPN
ejpam-5140	3	36	1	1	NUM
ejpam-5140	3	37	department	department	NOUN
ejpam-5140	3	38	of	of	ADP
ejpam-5140	3	39	mathematics	mathematic	NOUN
ejpam-5140	3	40	,	,	PUNCT
ejpam-5140	3	41	faculty	faculty	NOUN
ejpam-5140	3	42	of	of	ADP
ejpam-5140	3	43	arts	art	NOUN
ejpam-5140	3	44	and	and	CCONJ
ejpam-5140	3	45	sciences	science	NOUN
ejpam-5140	3	46	,	,	PUNCT
ejpam-5140	3	47	ondokuz	ondokuz	NOUN
ejpam-5140	3	48	mayis	mayis	PROPN
ejpam-5140	3	49	university	university	PROPN
ejpam-5140	3	50	,	,	PUNCT
ejpam-5140	3	51	55139	55139	NUM
ejpam-5140	3	52	samsun	samsun	NOUN
ejpam-5140	3	53	,	,	PUNCT
ejpam-5140	3	54	turkey	turkey	PROPN
ejpam-5140	3	55	2	2	NUM
ejpam-5140	3	56	department	department	NOUN
ejpam-5140	3	57	of	of	ADP
ejpam-5140	3	58	physics	physics	PROPN
ejpam-5140	3	59	,	,	PUNCT
ejpam-5140	3	60	maharaja	maharaja	PROPN
ejpam-5140	3	61	sriram	sriram	PROPN
ejpam-5140	3	62	chandra	chandra	PROPN
ejpam-5140	3	63	bhanja	bhanja	PROPN
ejpam-5140	3	64	deo	deo	PROPN
ejpam-5140	3	65	university	university	PROPN
ejpam-5140	3	66	,	,	PUNCT
ejpam-5140	3	67	baripada757003	baripada757003	PROPN
ejpam-5140	3	68	,	,	PUNCT
ejpam-5140	3	69	odisha	odisha	PROPN
ejpam-5140	3	70	,	,	PUNCT
ejpam-5140	3	71	india	india	PROPN
ejpam-5140	3	72	3	3	PROPN
ejpam-5140	3	73	department	department	NOUN
ejpam-5140	3	74	of	of	ADP
ejpam-5140	3	75	applied	apply	VERB
ejpam-5140	3	76	mathematics	mathematic	NOUN
ejpam-5140	3	77	,	,	PUNCT
ejpam-5140	3	78	faculty	faculty	NOUN
ejpam-5140	3	79	of	of	ADP
ejpam-5140	3	80	applied	apply	VERB
ejpam-5140	3	81	sciences	science	NOUN
ejpam-5140	3	82	,	,	PUNCT
ejpam-5140	3	83	palestine	palestine	PROPN
ejpam-5140	3	84	technical	technical	PROPN
ejpam-5140	3	85	universitykadoorie	universitykadoorie	PROPN
ejpam-5140	3	86	,	,	PUNCT
ejpam-5140	3	87	tulkarm	tulkarm	NOUN
ejpam-5140	3	88	p	p	PROPN
ejpam-5140	3	89	305	305	NUM
ejpam-5140	3	90	,	,	PUNCT
ejpam-5140	3	91	palestine	palestine	PROPN
ejpam-5140	3	92	4	4	NUM
ejpam-5140	3	93	department	department	PROPN
ejpam-5140	3	94	of	of	ADP
ejpam-5140	3	95	physics	physics	PROPN
ejpam-5140	3	96	,	,	PUNCT
ejpam-5140	3	97	faculty	faculty	NOUN
ejpam-5140	3	98	of	of	ADP
ejpam-5140	3	99	applied	apply	VERB
ejpam-5140	3	100	sciences	science	NOUN
ejpam-5140	3	101	,	,	PUNCT
ejpam-5140	3	102	palestine	palestine	PROPN
ejpam-5140	3	103	technical	technical	PROPN
ejpam-5140	3	104	universitykadoorie	universitykadoorie	PROPN
ejpam-5140	3	105	,	,	PUNCT
ejpam-5140	3	106	tulkarm	tulkarm	NOUN
ejpam-5140	3	107	p	p	PROPN
ejpam-5140	3	108	305	305	NUM
ejpam-5140	3	109	,	,	PUNCT
ejpam-5140	3	110	palestine	palestine	PROPN
ejpam-5140	3	111	abstract	abstract	NOUN
ejpam-5140	3	112	.	.	PUNCT
ejpam-5140	4	1	a	a	DET
ejpam-5140	4	2	reliable	reliable	ADJ
ejpam-5140	4	3	algorithm	algorithm	NOUN
ejpam-5140	4	4	based	base	VERB
ejpam-5140	4	5	on	on	ADP
ejpam-5140	4	6	an	an	DET
ejpam-5140	4	7	adaptation	adaptation	NOUN
ejpam-5140	4	8	of	of	ADP
ejpam-5140	4	9	the	the	DET
ejpam-5140	4	10	standard	standard	ADJ
ejpam-5140	4	11	differential	differential	ADJ
ejpam-5140	4	12	transform	transform	NOUN
ejpam-5140	4	13	method	method	NOUN
ejpam-5140	4	14	(	(	PUNCT
ejpam-5140	4	15	dtm	dtm	PROPN
ejpam-5140	4	16	)	)	PUNCT
ejpam-5140	4	17	is	be	AUX
ejpam-5140	4	18	presented	present	VERB
ejpam-5140	4	19	,	,	PUNCT
ejpam-5140	4	20	which	which	PRON
ejpam-5140	4	21	is	be	AUX
ejpam-5140	4	22	the	the	DET
ejpam-5140	4	23	multi	multi	ADJ
ejpam-5140	4	24	-	-	ADJ
ejpam-5140	4	25	step	step	ADJ
ejpam-5140	4	26	differential	differential	NOUN
ejpam-5140	4	27	transform	transform	NOUN
ejpam-5140	4	28	method	method	NOUN
ejpam-5140	4	29	(	(	PUNCT
ejpam-5140	4	30	ms	ms	PROPN
ejpam-5140	4	31	-	-	PUNCT
ejpam-5140	4	32	dtm	dtm	NOUN
ejpam-5140	4	33	)	)	PUNCT
ejpam-5140	4	34	since	since	SCONJ
ejpam-5140	4	35	it	it	PRON
ejpam-5140	4	36	may	may	AUX
ejpam-5140	4	37	be	be	AUX
ejpam-5140	4	38	difficult	difficult	ADJ
ejpam-5140	4	39	to	to	PART
ejpam-5140	4	40	directly	directly	ADV
ejpam-5140	4	41	apply	apply	VERB
ejpam-5140	4	42	differential	differential	ADJ
ejpam-5140	4	43	transform	transform	NOUN
ejpam-5140	4	44	method	method	NOUN
ejpam-5140	4	45	(	(	PUNCT
ejpam-5140	4	46	dtm	dtm	PROPN
ejpam-5140	4	47	)	)	PUNCT
ejpam-5140	4	48	to	to	PART
ejpam-5140	4	49	obtain	obtain	VERB
ejpam-5140	4	50	the	the	DET
ejpam-5140	4	51	series	series	NOUN
ejpam-5140	4	52	solutions	solution	NOUN
ejpam-5140	4	53	for	for	ADP
ejpam-5140	4	54	the	the	DET
ejpam-5140	4	55	present	present	ADJ
ejpam-5140	4	56	twodimensional	twodimensional	ADJ
ejpam-5140	4	57	coupled	couple	VERB
ejpam-5140	4	58	asymmetric	asymmetric	ADJ
ejpam-5140	4	59	van	van	PROPN
ejpam-5140	4	60	der	der	PROPN
ejpam-5140	4	61	pol	pol	PROPN
ejpam-5140	4	62	oscillator	oscillator	NOUN
ejpam-5140	4	63	.	.	PUNCT
ejpam-5140	5	1	the	the	DET
ejpam-5140	5	2	solutions	solution	NOUN
ejpam-5140	5	3	of	of	ADP
ejpam-5140	5	4	a	a	DET
ejpam-5140	5	5	twodimensional	twodimensional	ADJ
ejpam-5140	5	6	coupled	couple	VERB
ejpam-5140	5	7	asymmetric	asymmetric	ADJ
ejpam-5140	5	8	van	van	PROPN
ejpam-5140	5	9	der	der	PROPN
ejpam-5140	5	10	pol	pol	PROPN
ejpam-5140	5	11	oscillator	oscillator	NOUN
ejpam-5140	5	12	were	be	AUX
ejpam-5140	5	13	obtained	obtain	VERB
ejpam-5140	5	14	by	by	ADP
ejpam-5140	5	15	msdtm	msdtm	VERB
ejpam-5140	5	16	.	.	PUNCT
ejpam-5140	6	1	figurative	figurative	ADJ
ejpam-5140	6	2	comparisons	comparison	NOUN
ejpam-5140	6	3	between	between	ADP
ejpam-5140	6	4	the	the	DET
ejpam-5140	6	5	ms	ms	PROPN
ejpam-5140	6	6	-	-	PUNCT
ejpam-5140	6	7	dtm	dtm	PROPN
ejpam-5140	6	8	and	and	CCONJ
ejpam-5140	6	9	the	the	DET
ejpam-5140	6	10	classical	classical	ADJ
ejpam-5140	6	11	fourth	fourth	ADJ
ejpam-5140	6	12	order	order	NOUN
ejpam-5140	6	13	runge	runge	NOUN
ejpam-5140	6	14	-	-	PUNCT
ejpam-5140	6	15	kutta	kutta	NOUN
ejpam-5140	6	16	method	method	NOUN
ejpam-5140	6	17	(	(	PUNCT
ejpam-5140	6	18	rk4	rk4	NOUN
ejpam-5140	6	19	)	)	PUNCT
ejpam-5140	6	20	are	be	AUX
ejpam-5140	6	21	given	give	VERB
ejpam-5140	6	22	.	.	PUNCT
ejpam-5140	7	1	the	the	DET
ejpam-5140	7	2	obtained	obtain	VERB
ejpam-5140	7	3	results	result	NOUN
ejpam-5140	7	4	reveal	reveal	VERB
ejpam-5140	7	5	that	that	SCONJ
ejpam-5140	7	6	the	the	DET
ejpam-5140	7	7	proposed	propose	VERB
ejpam-5140	7	8	technique	technique	NOUN
ejpam-5140	7	9	is	be	AUX
ejpam-5140	7	10	a	a	DET
ejpam-5140	7	11	promising	promising	ADJ
ejpam-5140	7	12	tool	tool	NOUN
ejpam-5140	7	13	to	to	PART
ejpam-5140	7	14	solve	solve	VERB
ejpam-5140	7	15	the	the	DET
ejpam-5140	7	16	considered	consider	VERB
ejpam-5140	7	17	van	van	PROPN
ejpam-5140	7	18	der	der	ADJ
ejpam-5140	7	19	pol	pol	PROPN
ejpam-5140	7	20	oscillator	oscillator	NOUN
ejpam-5140	7	21	and	and	CCONJ
ejpam-5140	7	22	yield	yield	VERB
ejpam-5140	7	23	same	same	ADJ
ejpam-5140	7	24	information	information	NOUN
ejpam-5140	7	25	on	on	ADP
ejpam-5140	7	26	the	the	DET
ejpam-5140	7	27	phase	phase	NOUN
ejpam-5140	7	28	portrait	portrait	NOUN
ejpam-5140	7	29	confirming	confirm	VERB
ejpam-5140	7	30	the	the	DET
ejpam-5140	7	31	stability	stability	NOUN
ejpam-5140	7	32	of	of	ADP
ejpam-5140	7	33	the	the	DET
ejpam-5140	7	34	system	system	NOUN
ejpam-5140	7	35	,	,	PUNCT
ejpam-5140	7	36	effectively	effectively	ADV
ejpam-5140	7	37	.	.	PUNCT
ejpam-5140	8	1	it	it	PRON
ejpam-5140	8	2	can	can	AUX
ejpam-5140	8	3	be	be	AUX
ejpam-5140	8	4	said	say	VERB
ejpam-5140	8	5	that	that	SCONJ
ejpam-5140	8	6	the	the	DET
ejpam-5140	8	7	considered	consider	VERB
ejpam-5140	8	8	approach	approach	NOUN
ejpam-5140	8	9	can	can	AUX
ejpam-5140	8	10	be	be	AUX
ejpam-5140	8	11	easily	easily	ADV
ejpam-5140	8	12	extended	extend	VERB
ejpam-5140	8	13	to	to	ADP
ejpam-5140	8	14	other	other	ADJ
ejpam-5140	8	15	nonlinear	nonlinear	ADJ
ejpam-5140	8	16	van	van	PROPN
ejpam-5140	8	17	der	der	ADJ
ejpam-5140	8	18	pol	pol	PROPN
ejpam-5140	8	19	oscillator	oscillator	NOUN
ejpam-5140	8	20	systems	system	NOUN
ejpam-5140	8	21	and	and	CCONJ
ejpam-5140	8	22	therefore	therefore	ADV
ejpam-5140	8	23	is	be	AUX
ejpam-5140	8	24	widely	widely	ADV
ejpam-5140	8	25	applicable	applicable	ADJ
ejpam-5140	8	26	in	in	ADP
ejpam-5140	8	27	engineering	engineering	NOUN
ejpam-5140	8	28	and	and	CCONJ
ejpam-5140	8	29	other	other	ADJ
ejpam-5140	8	30	sciences	science	NOUN
ejpam-5140	8	31	.	.	PUNCT
ejpam-5140	9	1	2020	2020	NUM
ejpam-5140	9	2	mathematics	mathematic	NOUN
ejpam-5140	9	3	subject	subject	NOUN
ejpam-5140	9	4	classifications	classification	NOUN
ejpam-5140	9	5	:	:	PUNCT
ejpam-5140	9	6	34a45	34a45	NUM
ejpam-5140	9	7	,	,	PUNCT
ejpam-5140	9	8	34c05	34c05	NUM
ejpam-5140	9	9	,	,	PUNCT
ejpam-5140	9	10	65l05	65l05	NUM
ejpam-5140	9	11	,	,	PUNCT
ejpam-5140	9	12	34c15	34c15	NUM
ejpam-5140	9	13	,	,	PUNCT
ejpam-5140	9	14	34c25	34c25	NUM
ejpam-5140	9	15	key	key	ADJ
ejpam-5140	9	16	words	word	NOUN
ejpam-5140	9	17	and	and	CCONJ
ejpam-5140	9	18	phrases	phrase	NOUN
ejpam-5140	9	19	:	:	PUNCT
ejpam-5140	9	20	coupled	couple	VERB
ejpam-5140	9	21	van	van	PROPN
ejpam-5140	9	22	der	der	PROPN
ejpam-5140	9	23	pol	pol	PROPN
ejpam-5140	9	24	,	,	PUNCT
ejpam-5140	9	25	twodimension	twodimension	NOUN
ejpam-5140	9	26	,	,	PUNCT
ejpam-5140	9	27	phase	phase	NOUN
ejpam-5140	9	28	portrait	portrait	NOUN
ejpam-5140	9	29	,	,	PUNCT
ejpam-5140	9	30	semi	semi	ADV
ejpam-5140	9	31	analytical	analytical	ADJ
ejpam-5140	9	32	1	1	NUM
ejpam-5140	9	33	.	.	PUNCT
ejpam-5140	10	1	introduction	introduction	NOUN
ejpam-5140	10	2	the	the	DET
ejpam-5140	10	3	study	study	NOUN
ejpam-5140	10	4	of	of	ADP
ejpam-5140	10	5	nonlinear	nonlinear	ADJ
ejpam-5140	10	6	oscillations	oscillation	NOUN
ejpam-5140	10	7	is	be	AUX
ejpam-5140	10	8	a	a	DET
ejpam-5140	10	9	crucial	crucial	ADJ
ejpam-5140	10	10	area	area	NOUN
ejpam-5140	10	11	of	of	ADP
ejpam-5140	10	12	research	research	NOUN
ejpam-5140	10	13	in	in	ADP
ejpam-5140	10	14	various	various	ADJ
ejpam-5140	10	15	fields	field	NOUN
ejpam-5140	10	16	of	of	ADP
ejpam-5140	10	17	mechanical	mechanical	ADJ
ejpam-5140	10	18	structures	structure	NOUN
ejpam-5140	10	19	,	,	PUNCT
ejpam-5140	10	20	physical	physical	ADJ
ejpam-5140	10	21	science	science	NOUN
ejpam-5140	10	22	,	,	PUNCT
ejpam-5140	10	23	and	and	CCONJ
ejpam-5140	10	24	other	other	ADJ
ejpam-5140	10	25	mathematical	mathematical	ADJ
ejpam-5140	10	26	sciences	science	NOUN
ejpam-5140	10	27	.	.	PUNCT
ejpam-5140	11	1	since	since	SCONJ
ejpam-5140	11	2	most	most	ADJ
ejpam-5140	11	3	real	real	ADJ
ejpam-5140	11	4	-	-	PUNCT
ejpam-5140	11	5	world	world	NOUN
ejpam-5140	11	6	systems	system	NOUN
ejpam-5140	11	7	are	be	AUX
ejpam-5140	11	8	described	describe	VERB
ejpam-5140	11	9	by	by	ADP
ejpam-5140	11	10	nonlinear	nonlinear	ADJ
ejpam-5140	11	11	differential	differential	ADJ
ejpam-5140	11	12	equations	equation	NOUN
ejpam-5140	11	13	,	,	PUNCT
ejpam-5140	11	14	mechanical	mechanical	ADJ
ejpam-5140	11	15	systems	system	NOUN
ejpam-5140	11	16	,	,	PUNCT
ejpam-5140	11	17	∗corresponding	∗corresponde	VERB
ejpam-5140	11	18	author	author	NOUN
ejpam-5140	11	19	.	.	PUNCT
ejpam-5140	12	1	doi	doi	NOUN
ejpam-5140	12	2	:	:	PUNCT
ejpam-5140	12	3	https://doi.org/10.29020/nybg.ejpam.v17i2.5140	https://doi.org/10.29020/nybg.ejpam.v17i2.5140	PROPN
ejpam-5140	12	4	email	email	NOUN
ejpam-5140	12	5	addresses	address	VERB
ejpam-5140	12	6	:	:	PUNCT
ejpam-5140	12	7	vserturk@omu.edu.tr	vserturk@omu.edu.tr	PROPN
ejpam-5140	12	8	(	(	PUNCT
ejpam-5140	12	9	v.	v.	ADP
ejpam-5140	12	10	s.	s.	PROPN
ejpam-5140	12	11	erturk	erturk	PROPN
ejpam-5140	12	12	)	)	PUNCT
ejpam-5140	12	13	,	,	PUNCT
ejpam-5140	12	14	biswanathrath10@gmail.com	biswanathrath10@gmail.com	PROPN
ejpam-5140	12	15	(	(	PUNCT
ejpam-5140	12	16	b.	b.	PROPN
ejpam-5140	12	17	rath	rath	PROPN
ejpam-5140	12	18	)	)	PUNCT
ejpam-5140	12	19	,	,	PUNCT
ejpam-5140	12	20	t.alkhader@ptuk.edu.ps	t.alkhader@ptuk.edu.ps	NOUN
ejpam-5140	12	21	(	(	PUNCT
ejpam-5140	12	22	t.	t.	PROPN
ejpam-5140	12	23	m.	m.	PROPN
ejpam-5140	12	24	al	al	PROPN
ejpam-5140	12	25	-	-	PUNCT
ejpam-5140	12	26	khader	khader	PROPN
ejpam-5140	12	27	)	)	PUNCT
ejpam-5140	12	28	,	,	PUNCT
ejpam-5140	12	29	pravanjanphy@gmail.com	pravanjanphy@gmail.com	X
ejpam-5140	12	30	(	(	PUNCT
ejpam-5140	12	31	p.	p.	PROPN
ejpam-5140	12	32	mallick	mallick	PROPN
ejpam-5140	12	33	)	)	PUNCT
ejpam-5140	12	34	,	,	PUNCT
ejpam-5140	12	35	j.asad@ptuk.edu.ps	j.asad@ptuk.edu.ps	NOUN
ejpam-5140	12	36	(	(	PUNCT
ejpam-5140	12	37	j.	j.	PROPN
ejpam-5140	12	38	asad	asad	PROPN
ejpam-5140	12	39	)	)	PUNCT
ejpam-5140	12	40	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5140	12	41	1254	1254	NUM
ejpam-5140	12	42	©	©	PROPN
ejpam-5140	12	43	2024	2024	NUM
ejpam-5140	12	44	ejpam	ejpam	NOUN
ejpam-5140	12	45	all	all	DET
ejpam-5140	12	46	rights	right	NOUN
ejpam-5140	12	47	reserved	reserve	VERB
ejpam-5140	12	48	.	.	PUNCT
ejpam-5140	13	1	j.	j.	PROPN
ejpam-5140	13	2	asad	asad	PROPN
ejpam-5140	13	3	et	et	PROPN
ejpam-5140	13	4	al	al	PROPN
ejpam-5140	13	5	.	.	PUNCT
ejpam-5140	13	6	/	/	SYM
ejpam-5140	13	7	eur	eur	PROPN
ejpam-5140	13	8	.	.	PUNCT
ejpam-5140	14	1	j.	j.	PROPN
ejpam-5140	14	2	pure	pure	PROPN
ejpam-5140	14	3	appl	appl	PROPN
ejpam-5140	14	4	.	.	PROPN
ejpam-5140	14	5	math	math	PROPN
ejpam-5140	14	6	,	,	PUNCT
ejpam-5140	14	7	17	17	NUM
ejpam-5140	14	8	(	(	PUNCT
ejpam-5140	14	9	2	2	NUM
ejpam-5140	14	10	)	)	PUNCT
ejpam-5140	14	11	(	(	PUNCT
ejpam-5140	14	12	2024	2024	NUM
ejpam-5140	14	13	)	)	PUNCT
ejpam-5140	14	14	,	,	PUNCT
ejpam-5140	14	15	1254	1254	NUM
ejpam-5140	14	16	-	-	SYM
ejpam-5140	14	17	1264	1264	NUM
ejpam-5140	14	18	1255	1255	NUM
ejpam-5140	14	19	mathematical	mathematical	ADJ
ejpam-5140	14	20	physics	physics	NOUN
ejpam-5140	14	21	,	,	PUNCT
ejpam-5140	14	22	and	and	CCONJ
ejpam-5140	14	23	engineering	engineering	NOUN
ejpam-5140	14	24	face	face	VERB
ejpam-5140	14	25	several	several	ADJ
ejpam-5140	14	26	difficulties	difficulty	NOUN
ejpam-5140	14	27	.	.	PUNCT
ejpam-5140	15	1	understanding	understand	VERB
ejpam-5140	15	2	the	the	DET
ejpam-5140	15	3	characteristics	characteristic	NOUN
ejpam-5140	15	4	and	and	CCONJ
ejpam-5140	15	5	methods	method	NOUN
ejpam-5140	15	6	for	for	ADP
ejpam-5140	15	7	resolving	resolve	VERB
ejpam-5140	15	8	nonlinear	nonlinear	ADJ
ejpam-5140	15	9	equations	equation	NOUN
ejpam-5140	15	10	in	in	ADP
ejpam-5140	15	11	mechanical	mechanical	ADJ
ejpam-5140	15	12	systems	system	NOUN
ejpam-5140	15	13	has	have	AUX
ejpam-5140	15	14	drawn	draw	VERB
ejpam-5140	15	15	more	more	ADJ
ejpam-5140	15	16	attention	attention	NOUN
ejpam-5140	15	17	in	in	ADP
ejpam-5140	15	18	recent	recent	ADJ
ejpam-5140	15	19	years	year	NOUN
ejpam-5140	15	20	,	,	PUNCT
ejpam-5140	15	21	with	with	ADP
ejpam-5140	15	22	the	the	DET
ejpam-5140	15	23	aim	aim	NOUN
ejpam-5140	15	24	of	of	ADP
ejpam-5140	15	25	developing	develop	VERB
ejpam-5140	15	26	more	more	ADV
ejpam-5140	15	27	accurate	accurate	ADJ
ejpam-5140	15	28	and	and	CCONJ
ejpam-5140	15	29	efficient	efficient	ADJ
ejpam-5140	15	30	methods	method	NOUN
ejpam-5140	15	31	for	for	ADP
ejpam-5140	15	32	analyzing	analyze	VERB
ejpam-5140	15	33	and	and	CCONJ
ejpam-5140	15	34	predicting	predict	VERB
ejpam-5140	15	35	their	their	PRON
ejpam-5140	15	36	behavior	behavior	NOUN
ejpam-5140	15	37	.	.	PUNCT
ejpam-5140	16	1	nonlinear	nonlinear	ADJ
ejpam-5140	16	2	oscillator	oscillator	NOUN
ejpam-5140	16	3	problems	problem	NOUN
ejpam-5140	16	4	have	have	AUX
ejpam-5140	16	5	recently	recently	ADV
ejpam-5140	16	6	been	be	AUX
ejpam-5140	16	7	solved	solve	VERB
ejpam-5140	16	8	using	use	VERB
ejpam-5140	16	9	a	a	DET
ejpam-5140	16	10	variety	variety	NOUN
ejpam-5140	16	11	of	of	ADP
ejpam-5140	16	12	analytical	analytical	ADJ
ejpam-5140	16	13	and	and	CCONJ
ejpam-5140	16	14	numerical	numerical	ADJ
ejpam-5140	16	15	techniques	technique	NOUN
ejpam-5140	16	16	,	,	PUNCT
ejpam-5140	16	17	including	include	VERB
ejpam-5140	16	18	homotopy	homotopy	NOUN
ejpam-5140	16	19	perturbation	perturbation	NOUN
ejpam-5140	16	20	method	method	NOUN
ejpam-5140	16	21	[	[	X
ejpam-5140	16	22	7−−10	7−−10	NUM
ejpam-5140	16	23	]	]	PUNCT
ejpam-5140	16	24	,	,	PUNCT
ejpam-5140	16	25	energy	energy	NOUN
ejpam-5140	16	26	balance	balance	NOUN
ejpam-5140	16	27	method	method	NOUN
ejpam-5140	16	28	[	[	X
ejpam-5140	16	29	2	2	NUM
ejpam-5140	16	30	,	,	PUNCT
ejpam-5140	16	31	16	16	NUM
ejpam-5140	16	32	,	,	PUNCT
ejpam-5140	16	33	27	27	NUM
ejpam-5140	16	34	]	]	PUNCT
ejpam-5140	16	35	,	,	PUNCT
ejpam-5140	16	36	frequencyamplitude	frequencyamplitude	VERB
ejpam-5140	16	37	formulation	formulation	NOUN
ejpam-5140	16	38	[	[	X
ejpam-5140	16	39	5	5	NUM
ejpam-5140	16	40	,	,	PUNCT
ejpam-5140	16	41	12	12	NUM
ejpam-5140	16	42	,	,	PUNCT
ejpam-5140	16	43	13	13	NUM
ejpam-5140	16	44	]	]	PUNCT
ejpam-5140	16	45	,	,	PUNCT
ejpam-5140	16	46	parameter	parameter	NOUN
ejpam-5140	16	47	expanding	expand	VERB
ejpam-5140	16	48	method	method	NOUN
ejpam-5140	16	49	[	[	X
ejpam-5140	16	50	11	11	NUM
ejpam-5140	16	51	,	,	PUNCT
ejpam-5140	16	52	25	25	NUM
ejpam-5140	16	53	,	,	PUNCT
ejpam-5140	16	54	26	26	NUM
ejpam-5140	16	55	]	]	PUNCT
ejpam-5140	16	56	,	,	PUNCT
ejpam-5140	16	57	and	and	CCONJ
ejpam-5140	16	58	variational	variational	ADJ
ejpam-5140	16	59	iteration	iteration	NOUN
ejpam-5140	16	60	method	method	NOUN
ejpam-5140	16	61	[	[	X
ejpam-5140	16	62	14	14	NUM
ejpam-5140	16	63	,	,	PUNCT
ejpam-5140	16	64	15	15	NUM
ejpam-5140	16	65	]	]	PUNCT
ejpam-5140	16	66	,	,	PUNCT
ejpam-5140	16	67	and	and	CCONJ
ejpam-5140	16	68	recently	recently	ADV
ejpam-5140	16	69	accurate	accurate	ADJ
ejpam-5140	16	70	technique	technique	NOUN
ejpam-5140	16	71	is	be	AUX
ejpam-5140	16	72	used	use	VERB
ejpam-5140	16	73	to	to	PART
ejpam-5140	16	74	find	find	VERB
ejpam-5140	16	75	an	an	DET
ejpam-5140	16	76	approximate	approximate	ADJ
ejpam-5140	16	77	solution	solution	NOUN
ejpam-5140	16	78	to	to	ADP
ejpam-5140	16	79	the	the	DET
ejpam-5140	16	80	fractional	fractional	ADJ
ejpam-5140	16	81	-	-	PUNCT
ejpam-5140	16	82	order	order	NOUN
ejpam-5140	16	83	duffing	duffing	NOUN
ejpam-5140	16	84	-	-	PUNCT
ejpam-5140	16	85	van	van	PROPN
ejpam-5140	16	86	der	der	ADJ
ejpam-5140	16	87	pol	pol	PROPN
ejpam-5140	16	88	oscillators	oscillator	NOUN
ejpam-5140	17	1	[	[	X
ejpam-5140	17	2	18	18	NUM
ejpam-5140	17	3	]	]	PUNCT
ejpam-5140	17	4	.	.	PUNCT
ejpam-5140	18	1	in	in	ADP
ejpam-5140	18	2	chaos	chaos	NOUN
ejpam-5140	18	3	theory	theory	NOUN
ejpam-5140	18	4	,	,	PUNCT
ejpam-5140	18	5	the	the	DET
ejpam-5140	18	6	van	van	PROPN
ejpam-5140	18	7	der	der	ADJ
ejpam-5140	18	8	pol	pol	NOUN
ejpam-5140	18	9	equation	equation	NOUN
ejpam-5140	18	10	is	be	AUX
ejpam-5140	18	11	a	a	DET
ejpam-5140	18	12	typical	typical	ADJ
ejpam-5140	18	13	reference	reference	NOUN
ejpam-5140	18	14	.	.	PUNCT
ejpam-5140	19	1	early	early	ADV
ejpam-5140	19	2	on	on	ADV
ejpam-5140	19	3	in	in	ADP
ejpam-5140	19	4	the	the	DET
ejpam-5140	19	5	model	model	NOUN
ejpam-5140	19	6	’s	’s	PART
ejpam-5140	19	7	creation	creation	NOUN
ejpam-5140	19	8	,	,	PUNCT
ejpam-5140	19	9	researchers	researcher	NOUN
ejpam-5140	19	10	in	in	ADP
ejpam-5140	19	11	the	the	DET
ejpam-5140	19	12	biological	biological	ADJ
ejpam-5140	19	13	and	and	CCONJ
ejpam-5140	19	14	physical	physical	ADJ
ejpam-5140	19	15	sciences	science	NOUN
ejpam-5140	19	16	made	make	VERB
ejpam-5140	19	17	use	use	NOUN
ejpam-5140	19	18	of	of	ADP
ejpam-5140	19	19	it	it	PRON
ejpam-5140	19	20	.	.	PUNCT
ejpam-5140	20	1	this	this	DET
ejpam-5140	20	2	formula	formula	NOUN
ejpam-5140	20	3	is	be	AUX
ejpam-5140	20	4	considered	consider	VERB
ejpam-5140	20	5	to	to	PART
ejpam-5140	20	6	be	be	AUX
ejpam-5140	20	7	an	an	DET
ejpam-5140	20	8	example	example	NOUN
ejpam-5140	20	9	of	of	ADP
ejpam-5140	20	10	an	an	DET
ejpam-5140	20	11	oscillator	oscillator	NOUN
ejpam-5140	20	12	that	that	PRON
ejpam-5140	20	13	damps	damp	VERB
ejpam-5140	20	14	nonlinearly	nonlinearly	ADV
ejpam-5140	20	15	.	.	PUNCT
ejpam-5140	21	1	several	several	ADJ
ejpam-5140	21	2	authors	author	NOUN
ejpam-5140	21	3	and	and	CCONJ
ejpam-5140	21	4	scholars	scholar	NOUN
ejpam-5140	21	5	set	set	VERB
ejpam-5140	21	6	out	out	ADP
ejpam-5140	21	7	to	to	PART
ejpam-5140	21	8	find	find	VERB
ejpam-5140	21	9	an	an	DET
ejpam-5140	21	10	analytical	analytical	ADJ
ejpam-5140	21	11	answer	answer	NOUN
ejpam-5140	21	12	to	to	ADP
ejpam-5140	21	13	the	the	DET
ejpam-5140	21	14	van	van	PROPN
ejpam-5140	21	15	der	der	ADJ
ejpam-5140	21	16	pol	pol	PROPN
ejpam-5140	21	17	dilemma	dilemma	PROPN
ejpam-5140	21	18	.	.	PUNCT
ejpam-5140	22	1	the	the	DET
ejpam-5140	22	2	first	first	ADJ
ejpam-5140	22	3	person	person	NOUN
ejpam-5140	22	4	to	to	PART
ejpam-5140	22	5	simulate	simulate	VERB
ejpam-5140	22	6	electrical	electrical	ADJ
ejpam-5140	22	7	circuits	circuit	NOUN
ejpam-5140	22	8	in	in	ADP
ejpam-5140	22	9	a	a	DET
ejpam-5140	22	10	vacuum	vacuum	NOUN
ejpam-5140	22	11	was	be	AUX
ejpam-5140	22	12	van	van	PROPN
ejpam-5140	22	13	der	der	ADJ
ejpam-5140	22	14	pol	pol	NOUN
ejpam-5140	22	15	[	[	X
ejpam-5140	22	16	6	6	NUM
ejpam-5140	22	17	]	]	PUNCT
ejpam-5140	22	18	.	.	PUNCT
ejpam-5140	23	1	the	the	DET
ejpam-5140	23	2	equation	equation	NOUN
ejpam-5140	23	3	is	be	AUX
ejpam-5140	23	4	often	often	ADV
ejpam-5140	23	5	researched	research	VERB
ejpam-5140	23	6	as	as	ADP
ejpam-5140	23	7	a	a	DET
ejpam-5140	23	8	template	template	NOUN
ejpam-5140	23	9	for	for	ADP
ejpam-5140	23	10	testing	test	VERB
ejpam-5140	23	11	numerical	numerical	ADJ
ejpam-5140	23	12	techniques	technique	NOUN
ejpam-5140	23	13	and	and	CCONJ
ejpam-5140	23	14	for	for	ADP
ejpam-5140	23	15	its	its	PRON
ejpam-5140	23	16	extensive	extensive	ADJ
ejpam-5140	23	17	collection	collection	NOUN
ejpam-5140	23	18	of	of	ADP
ejpam-5140	23	19	chaotic	chaotic	ADJ
ejpam-5140	23	20	solutions	solution	NOUN
ejpam-5140	23	21	[	[	X
ejpam-5140	23	22	3	3	NUM
ejpam-5140	23	23	]	]	PUNCT
ejpam-5140	23	24	.	.	PUNCT
ejpam-5140	24	1	deriving	derive	VERB
ejpam-5140	24	2	the	the	DET
ejpam-5140	24	3	closed	closed	ADJ
ejpam-5140	24	4	-	-	PUNCT
ejpam-5140	24	5	form	form	NOUN
ejpam-5140	24	6	solutions	solution	NOUN
ejpam-5140	24	7	of	of	ADP
ejpam-5140	24	8	a	a	DET
ejpam-5140	24	9	nonlinear	nonlinear	ADJ
ejpam-5140	24	10	differential	differential	ADJ
ejpam-5140	24	11	equation	equation	NOUN
ejpam-5140	24	12	lacks	lack	VERB
ejpam-5140	24	13	a	a	DET
ejpam-5140	24	14	general	general	ADJ
ejpam-5140	24	15	framework	framework	NOUN
ejpam-5140	24	16	.	.	PUNCT
ejpam-5140	25	1	as	as	ADP
ejpam-5140	25	2	a	a	DET
ejpam-5140	25	3	result	result	NOUN
ejpam-5140	25	4	,	,	PUNCT
ejpam-5140	25	5	there	there	PRON
ejpam-5140	25	6	has	have	AUX
ejpam-5140	25	7	been	be	AUX
ejpam-5140	25	8	a	a	DET
ejpam-5140	25	9	growing	grow	VERB
ejpam-5140	25	10	emphasis	emphasis	NOUN
ejpam-5140	25	11	on	on	ADP
ejpam-5140	25	12	numerical	numerical	ADJ
ejpam-5140	25	13	techniques	technique	NOUN
ejpam-5140	25	14	to	to	PART
ejpam-5140	25	15	get	get	VERB
ejpam-5140	25	16	solutions	solution	NOUN
ejpam-5140	25	17	(	(	PUNCT
ejpam-5140	25	18	some	some	PRON
ejpam-5140	25	19	of	of	ADP
ejpam-5140	25	20	which	which	PRON
ejpam-5140	25	21	are	be	AUX
ejpam-5140	25	22	provided	provide	VERB
ejpam-5140	25	23	in	in	ADP
ejpam-5140	25	24	[	[	X
ejpam-5140	25	25	19	19	NUM
ejpam-5140	25	26	]	]	NUM
ejpam-5140	25	27	)	)	PUNCT
ejpam-5140	25	28	,	,	PUNCT
ejpam-5140	25	29	perturbative	perturbative	ADJ
ejpam-5140	25	30	approaches	approach	NOUN
ejpam-5140	25	31	,	,	PUNCT
ejpam-5140	25	32	approximated	approximate	VERB
ejpam-5140	25	33	analytical	analytical	ADJ
ejpam-5140	25	34	approaches	approach	NOUN
ejpam-5140	25	35	based	base	VERB
ejpam-5140	25	36	on	on	ADP
ejpam-5140	25	37	linearization	linearization	NOUN
ejpam-5140	25	38	[	[	X
ejpam-5140	25	39	20	20	NUM
ejpam-5140	25	40	]	]	PUNCT
ejpam-5140	25	41	,	,	PUNCT
ejpam-5140	25	42	or	or	CCONJ
ejpam-5140	26	1	adomian	adomian	NOUN
ejpam-5140	26	2	decomposition	decomposition	NOUN
ejpam-5140	26	3	[	[	X
ejpam-5140	26	4	17	17	NUM
ejpam-5140	26	5	]	]	PUNCT
ejpam-5140	26	6	.	.	PUNCT
ejpam-5140	27	1	in	in	ADP
ejpam-5140	27	2	order	order	NOUN
ejpam-5140	27	3	to	to	PART
ejpam-5140	27	4	examine	examine	VERB
ejpam-5140	27	5	the	the	DET
ejpam-5140	27	6	oscillatory	oscillatory	ADJ
ejpam-5140	27	7	behavior	behavior	NOUN
ejpam-5140	27	8	,	,	PUNCT
ejpam-5140	27	9	the	the	DET
ejpam-5140	27	10	parameter	parameter	NOUN
ejpam-5140	27	11	is	be	AUX
ejpam-5140	27	12	crucial	crucial	ADJ
ejpam-5140	27	13	.	.	PUNCT
ejpam-5140	28	1	these	these	DET
ejpam-5140	28	2	parameters	parameter	NOUN
ejpam-5140	28	3	can	can	AUX
ejpam-5140	28	4	be	be	AUX
ejpam-5140	28	5	computed	compute	VERB
ejpam-5140	28	6	in	in	ADP
ejpam-5140	28	7	a	a	DET
ejpam-5140	28	8	variety	variety	NOUN
ejpam-5140	28	9	of	of	ADP
ejpam-5140	28	10	ways	way	NOUN
ejpam-5140	28	11	[	[	X
ejpam-5140	28	12	27	27	NUM
ejpam-5140	28	13	]	]	PUNCT
ejpam-5140	28	14	.	.	PUNCT
ejpam-5140	29	1	among	among	ADP
ejpam-5140	29	2	of	of	ADP
ejpam-5140	29	3	these	these	DET
ejpam-5140	29	4	techniques	technique	NOUN
ejpam-5140	29	5	,	,	PUNCT
ejpam-5140	29	6	the	the	DET
ejpam-5140	29	7	approximation	approximation	NOUN
ejpam-5140	29	8	lie	lie	NOUN
ejpam-5140	29	9	theorem	theorem	NOUN
ejpam-5140	29	10	was	be	AUX
ejpam-5140	29	11	given	give	VERB
ejpam-5140	29	12	by	by	ADP
ejpam-5140	29	13	baikov	baikov	NOUN
ejpam-5140	29	14	[	[	X
ejpam-5140	29	15	5	5	NUM
ejpam-5140	29	16	,	,	PUNCT
ejpam-5140	29	17	12	12	NUM
ejpam-5140	29	18	,	,	PUNCT
ejpam-5140	29	19	13	13	NUM
ejpam-5140	29	20	]	]	PUNCT
ejpam-5140	29	21	.	.	PUNCT
ejpam-5140	30	1	for	for	ADP
ejpam-5140	30	2	the	the	DET
ejpam-5140	30	3	perturbed	perturb	VERB
ejpam-5140	30	4	odes	ode	NOUN
ejpam-5140	30	5	,	,	PUNCT
ejpam-5140	30	6	naeem	naeem	NOUN
ejpam-5140	30	7	and	and	CCONJ
ejpam-5140	30	8	mahomed	mahome	VERB
ejpam-5140	31	1	[	[	X
ejpam-5140	31	2	11	11	NUM
ejpam-5140	31	3	,	,	PUNCT
ejpam-5140	31	4	26	26	NUM
ejpam-5140	31	5	]	]	PUNCT
ejpam-5140	31	6	proposed	propose	VERB
ejpam-5140	31	7	the	the	DET
ejpam-5140	31	8	partial	partial	ADJ
ejpam-5140	31	9	lagrangian	lagrangian	ADJ
ejpam-5140	31	10	technique	technique	NOUN
ejpam-5140	31	11	[	[	X
ejpam-5140	31	12	14	14	NUM
ejpam-5140	31	13	,	,	PUNCT
ejpam-5140	31	14	25	25	NUM
ejpam-5140	31	15	]	]	PUNCT
ejpam-5140	31	16	.	.	PUNCT
ejpam-5140	32	1	many	many	ADJ
ejpam-5140	32	2	research	research	NOUN
ejpam-5140	32	3	works	work	NOUN
ejpam-5140	32	4	have	have	AUX
ejpam-5140	32	5	been	be	AUX
ejpam-5140	32	6	developed	develop	VERB
ejpam-5140	32	7	for	for	ADP
ejpam-5140	32	8	the	the	DET
ejpam-5140	32	9	systems	system	NOUN
ejpam-5140	32	10	of	of	ADP
ejpam-5140	32	11	approximation	approximation	NOUN
ejpam-5140	32	12	hamiltonians	hamiltonian	NOUN
ejpam-5140	32	13	.	.	PUNCT
ejpam-5140	33	1	the	the	DET
ejpam-5140	33	2	mathematical	mathematical	ADJ
ejpam-5140	33	3	model	model	NOUN
ejpam-5140	33	4	for	for	ADP
ejpam-5140	33	5	the	the	DET
ejpam-5140	33	6	system	system	NOUN
ejpam-5140	33	7	is	be	AUX
ejpam-5140	33	8	a	a	DET
ejpam-5140	33	9	wellknown	wellknown	ADJ
ejpam-5140	33	10	second	second	ADJ
ejpam-5140	33	11	order	order	NOUN
ejpam-5140	33	12	ordinary	ordinary	ADJ
ejpam-5140	33	13	differential	differential	ADJ
ejpam-5140	33	14	equation	equation	NOUN
ejpam-5140	33	15	with	with	ADP
ejpam-5140	33	16	cubic	cubic	ADJ
ejpam-5140	33	17	nonlinearity	nonlinearity	NOUN
ejpam-5140	33	18	–	–	PUNCT
ejpam-5140	33	19	the	the	DET
ejpam-5140	33	20	van	van	PROPN
ejpam-5140	33	21	der	der	ADJ
ejpam-5140	33	22	pol	pol	NOUN
ejpam-5140	33	23	equation	equation	NOUN
ejpam-5140	33	24	.	.	PUNCT
ejpam-5140	34	1	since	since	SCONJ
ejpam-5140	34	2	then	then	ADV
ejpam-5140	34	3	,	,	PUNCT
ejpam-5140	34	4	thousands	thousand	NOUN
ejpam-5140	34	5	of	of	ADP
ejpam-5140	34	6	papers	paper	NOUN
ejpam-5140	34	7	have	have	AUX
ejpam-5140	34	8	been	be	AUX
ejpam-5140	34	9	published	publish	VERB
ejpam-5140	34	10	achieving	achieve	VERB
ejpam-5140	34	11	better	well	ADJ
ejpam-5140	34	12	approximations	approximation	NOUN
ejpam-5140	34	13	to	to	ADP
ejpam-5140	34	14	the	the	DET
ejpam-5140	34	15	solutions	solution	NOUN
ejpam-5140	34	16	occurring	occur	VERB
ejpam-5140	34	17	in	in	ADP
ejpam-5140	34	18	such	such	ADJ
ejpam-5140	34	19	nonlinear	nonlinear	ADJ
ejpam-5140	34	20	systems	system	NOUN
ejpam-5140	34	21	.	.	PUNCT
ejpam-5140	35	1	the	the	DET
ejpam-5140	35	2	van	van	PROPN
ejpam-5140	35	3	der	der	PROPN
ejpam-5140	35	4	pol	pol	PROPN
ejpam-5140	35	5	oscillator	oscillator	NOUN
ejpam-5140	35	6	is	be	AUX
ejpam-5140	35	7	a	a	DET
ejpam-5140	35	8	classic	classic	ADJ
ejpam-5140	35	9	example	example	NOUN
ejpam-5140	35	10	of	of	ADP
ejpam-5140	35	11	self	self	NOUN
ejpam-5140	35	12	-	-	PUNCT
ejpam-5140	35	13	oscillatory	oscillatory	ADJ
ejpam-5140	35	14	system	system	NOUN
ejpam-5140	35	15	and	and	CCONJ
ejpam-5140	35	16	is	be	AUX
ejpam-5140	35	17	now	now	ADV
ejpam-5140	35	18	considered	consider	VERB
ejpam-5140	35	19	as	as	ADP
ejpam-5140	35	20	very	very	ADV
ejpam-5140	35	21	useful	useful	ADJ
ejpam-5140	35	22	mathematical	mathematical	ADJ
ejpam-5140	35	23	model	model	NOUN
ejpam-5140	35	24	that	that	PRON
ejpam-5140	35	25	can	can	AUX
ejpam-5140	35	26	be	be	AUX
ejpam-5140	35	27	used	use	VERB
ejpam-5140	35	28	in	in	ADP
ejpam-5140	35	29	much	much	ADV
ejpam-5140	35	30	more	more	ADV
ejpam-5140	35	31	complicated	complicated	ADJ
ejpam-5140	35	32	and	and	CCONJ
ejpam-5140	35	33	modified	modify	VERB
ejpam-5140	35	34	systems	system	NOUN
ejpam-5140	35	35	.	.	PUNCT
ejpam-5140	36	1	the	the	DET
ejpam-5140	36	2	van	van	PROPN
ejpam-5140	36	3	der	der	PROPN
ejpam-5140	36	4	pol	pol	NOUN
ejpam-5140	36	5	equation	equation	NOUN
ejpam-5140	36	6	is	be	AUX
ejpam-5140	36	7	so	so	ADV
ejpam-5140	36	8	important	important	ADJ
ejpam-5140	36	9	to	to	ADP
ejpam-5140	36	10	mathematicians	mathematician	NOUN
ejpam-5140	36	11	,	,	PUNCT
ejpam-5140	36	12	physicists	physicist	NOUN
ejpam-5140	36	13	and	and	CCONJ
ejpam-5140	36	14	engineers	engineer	NOUN
ejpam-5140	36	15	and	and	CCONJ
ejpam-5140	36	16	is	be	AUX
ejpam-5140	36	17	still	still	ADV
ejpam-5140	36	18	being	be	AUX
ejpam-5140	36	19	extensively	extensively	ADV
ejpam-5140	36	20	studied	study	VERB
ejpam-5140	36	21	[	[	PUNCT
ejpam-5140	36	22	4	4	NUM
ejpam-5140	36	23	,	,	PUNCT
ejpam-5140	36	24	21	21	NUM
ejpam-5140	36	25	−	−	NOUN
ejpam-5140	36	26	−24	−24	ADP
ejpam-5140	36	27	]	]	PUNCT
ejpam-5140	36	28	.	.	PUNCT
ejpam-5140	37	1	since	since	SCONJ
ejpam-5140	37	2	its	its	PRON
ejpam-5140	37	3	introduction	introduction	NOUN
ejpam-5140	37	4	in	in	ADP
ejpam-5140	37	5	the	the	DET
ejpam-5140	37	6	1920	1920	NUM
ejpam-5140	37	7	’s	’s	NOUN
ejpam-5140	37	8	,	,	PUNCT
ejpam-5140	37	9	the	the	DET
ejpam-5140	37	10	van	van	PROPN
ejpam-5140	37	11	der	der	ADJ
ejpam-5140	37	12	pol	pol	NOUN
ejpam-5140	37	13	equation	equation	NOUN
ejpam-5140	37	14	has	have	AUX
ejpam-5140	37	15	been	be	AUX
ejpam-5140	37	16	a	a	DET
ejpam-5140	37	17	prototype	prototype	NOUN
ejpam-5140	37	18	for	for	ADP
ejpam-5140	37	19	systems	system	NOUN
ejpam-5140	37	20	with	with	ADP
ejpam-5140	37	21	self	self	NOUN
ejpam-5140	37	22	-	-	PUNCT
ejpam-5140	37	23	excited	excite	VERB
ejpam-5140	37	24	limit	limit	NOUN
ejpam-5140	37	25	cycle	cycle	NOUN
ejpam-5140	37	26	oscillations	oscillation	NOUN
ejpam-5140	37	27	.	.	PUNCT
ejpam-5140	38	1	the	the	DET
ejpam-5140	38	2	classical	classical	ADJ
ejpam-5140	38	3	experimental	experimental	ADJ
ejpam-5140	38	4	setup	setup	NOUN
ejpam-5140	38	5	of	of	ADP
ejpam-5140	38	6	the	the	DET
ejpam-5140	38	7	system	system	NOUN
ejpam-5140	38	8	is	be	AUX
ejpam-5140	38	9	the	the	DET
ejpam-5140	38	10	oscillator	oscillator	NOUN
ejpam-5140	38	11	with	with	ADP
ejpam-5140	38	12	vacuum	vacuum	PROPN
ejpam-5140	38	13	triode	triode	NOUN
ejpam-5140	38	14	.	.	PUNCT
ejpam-5140	39	1	the	the	DET
ejpam-5140	39	2	investigations	investigation	NOUN
ejpam-5140	39	3	of	of	ADP
ejpam-5140	39	4	the	the	DET
ejpam-5140	39	5	forced	force	VERB
ejpam-5140	39	6	van	van	PROPN
ejpam-5140	39	7	der	der	PROPN
ejpam-5140	39	8	pol	pol	PROPN
ejpam-5140	39	9	oscillator	oscillator	NOUN
ejpam-5140	39	10	behaviour	behaviour	NOUN
ejpam-5140	39	11	have	have	AUX
ejpam-5140	39	12	carried	carry	VERB
ejpam-5140	39	13	out	out	ADP
ejpam-5140	39	14	by	by	ADP
ejpam-5140	39	15	many	many	ADJ
ejpam-5140	39	16	researchers	researcher	NOUN
ejpam-5140	39	17	.	.	PUNCT
ejpam-5140	40	1	the	the	DET
ejpam-5140	40	2	equation	equation	NOUN
ejpam-5140	40	3	has	have	AUX
ejpam-5140	40	4	been	be	AUX
ejpam-5140	40	5	studied	study	VERB
ejpam-5140	40	6	over	over	ADP
ejpam-5140	40	7	wide	wide	ADJ
ejpam-5140	40	8	parameter	parameter	NOUN
ejpam-5140	40	9	regimes	regime	NOUN
ejpam-5140	40	10	,	,	PUNCT
ejpam-5140	40	11	from	from	ADP
ejpam-5140	40	12	perturbations	perturbation	NOUN
ejpam-5140	40	13	of	of	ADP
ejpam-5140	40	14	harmonic	harmonic	ADJ
ejpam-5140	40	15	motion	motion	NOUN
ejpam-5140	40	16	to	to	ADP
ejpam-5140	40	17	relaxation	relaxation	NOUN
ejpam-5140	40	18	oscillations	oscillation	NOUN
ejpam-5140	40	19	[	[	X
ejpam-5140	40	20	1	1	NUM
ejpam-5140	40	21	]	]	PUNCT
ejpam-5140	40	22	.	.	PUNCT
ejpam-5140	41	1	let	let	VERB
ejpam-5140	41	2	us	we	PRON
ejpam-5140	41	3	discuss	discuss	VERB
ejpam-5140	41	4	the	the	DET
ejpam-5140	41	5	exact	exact	ADJ
ejpam-5140	41	6	solution	solution	NOUN
ejpam-5140	41	7	of	of	ADP
ejpam-5140	41	8	a	a	DET
ejpam-5140	41	9	van	van	PROPN
ejpam-5140	41	10	der	der	ADJ
ejpam-5140	41	11	pol	pol	NOUN
ejpam-5140	41	12	like	like	ADP
ejpam-5140	41	13	equation	equation	NOUN
ejpam-5140	41	14	in	in	ADP
ejpam-5140	41	15	two	two	NUM
ejpam-5140	41	16	dimensions	dimension	NOUN
ejpam-5140	41	17	[	[	X
ejpam-5140	41	18	8	8	NUM
ejpam-5140	41	19	]	]	PUNCT
ejpam-5140	41	20	as	as	ADP
ejpam-5140	41	21	:	:	PUNCT
ejpam-5140	41	22	x′′	x′′	PROPN
ejpam-5140	42	1	+	+	CCONJ
ejpam-5140	42	2	ω2x+	ω2x+	ADV
ejpam-5140	42	3	ε	ε	PROPN
ejpam-5140	42	4	(	(	PUNCT
ejpam-5140	42	5	αx2	αx2	NOUN
ejpam-5140	42	6	+	+	CCONJ
ejpam-5140	42	7	βy2	βy2	NUM
ejpam-5140	42	8	−	−	NOUN
ejpam-5140	42	9	1	1	NUM
ejpam-5140	42	10	)	)	PUNCT
ejpam-5140	42	11	x′	x′	PROPN
ejpam-5140	43	1	=	=	SYM
ejpam-5140	43	2	0	0	NUM
ejpam-5140	43	3	(	(	PUNCT
ejpam-5140	43	4	1	1	X
ejpam-5140	43	5	)	)	PUNCT
ejpam-5140	43	6	y′′	y′′	NOUN
ejpam-5140	43	7	+	+	CCONJ
ejpam-5140	43	8	ω2y	ω2y	PROPN
ejpam-5140	43	9	−	−	PROPN
ejpam-5140	43	10	ε	ε	PROPN
ejpam-5140	43	11	(	(	PUNCT
ejpam-5140	43	12	αx2	αx2	NOUN
ejpam-5140	43	13	+	+	CCONJ
ejpam-5140	43	14	βy2	βy2	NUM
ejpam-5140	43	15	−	−	NOUN
ejpam-5140	43	16	1	1	NUM
ejpam-5140	43	17	)	)	PUNCT
ejpam-5140	43	18	y′	y′	NOUN
ejpam-5140	44	1	=	=	SYM
ejpam-5140	44	2	0	0	SYM
ejpam-5140	44	3	(	(	PUNCT
ejpam-5140	44	4	2	2	NUM
ejpam-5140	44	5	)	)	PUNCT
ejpam-5140	45	1	j.	j.	PROPN
ejpam-5140	45	2	asad	asad	PROPN
ejpam-5140	45	3	et	et	PROPN
ejpam-5140	45	4	al	al	PROPN
ejpam-5140	45	5	.	.	PUNCT
ejpam-5140	45	6	/	/	SYM
ejpam-5140	45	7	eur	eur	PROPN
ejpam-5140	45	8	.	.	PUNCT
ejpam-5140	46	1	j.	j.	PROPN
ejpam-5140	46	2	pure	pure	PROPN
ejpam-5140	46	3	appl	appl	PROPN
ejpam-5140	46	4	.	.	PROPN
ejpam-5140	46	5	math	math	PROPN
ejpam-5140	46	6	,	,	PUNCT
ejpam-5140	46	7	17	17	NUM
ejpam-5140	46	8	(	(	PUNCT
ejpam-5140	46	9	2	2	NUM
ejpam-5140	46	10	)	)	PUNCT
ejpam-5140	46	11	(	(	PUNCT
ejpam-5140	46	12	2024	2024	NUM
ejpam-5140	46	13	)	)	PUNCT
ejpam-5140	46	14	,	,	PUNCT
ejpam-5140	46	15	1254	1254	NUM
ejpam-5140	46	16	-	-	SYM
ejpam-5140	46	17	1264	1264	NUM
ejpam-5140	46	18	1256	1256	NUM
ejpam-5140	46	19	for	for	ADP
ejpam-5140	46	20	α	α	NOUN
ejpam-5140	46	21	=	=	SYM
ejpam-5140	46	22	β	β	X
ejpam-5140	46	23	=	=	SYM
ejpam-5140	46	24	1	1	NUM
ejpam-5140	46	25	,	,	PUNCT
ejpam-5140	46	26	the	the	DET
ejpam-5140	46	27	above	above	ADJ
ejpam-5140	46	28	equations	equation	NOUN
ejpam-5140	46	29	reduce	reduce	VERB
ejpam-5140	46	30	to	to	ADP
ejpam-5140	46	31	:	:	PUNCT
ejpam-5140	46	32	x′′	x′′	PROPN
ejpam-5140	47	1	+	+	CCONJ
ejpam-5140	47	2	ω2x+	ω2x+	ADV
ejpam-5140	47	3	ε	ε	PROPN
ejpam-5140	47	4	(	(	PUNCT
ejpam-5140	47	5	x2	x2	PROPN
ejpam-5140	48	1	+	+	CCONJ
ejpam-5140	48	2	y2	y2	INTJ
ejpam-5140	49	1	−	−	NOUN
ejpam-5140	49	2	1	1	NUM
ejpam-5140	49	3	)	)	PUNCT
ejpam-5140	49	4	x′	x′	PROPN
ejpam-5140	50	1	=	=	SYM
ejpam-5140	50	2	0	0	PROPN
ejpam-5140	50	3	.	.	PUNCT
ejpam-5140	51	1	(	(	PUNCT
ejpam-5140	51	2	3	3	X
ejpam-5140	51	3	)	)	PUNCT
ejpam-5140	51	4	y′′	y′′	NOUN
ejpam-5140	51	5	+	+	CCONJ
ejpam-5140	51	6	ω2y	ω2y	PROPN
ejpam-5140	51	7	−	−	PROPN
ejpam-5140	51	8	ε	ε	PROPN
ejpam-5140	51	9	(	(	PUNCT
ejpam-5140	51	10	x2	x2	PROPN
ejpam-5140	52	1	+	+	CCONJ
ejpam-5140	52	2	y2	y2	INTJ
ejpam-5140	53	1	−	−	NOUN
ejpam-5140	53	2	1	1	NUM
ejpam-5140	53	3	)	)	PUNCT
ejpam-5140	53	4	y′	y′	NOUN
ejpam-5140	54	1	=	=	SYM
ejpam-5140	54	2	0	0	X
ejpam-5140	54	3	.	.	PUNCT
ejpam-5140	55	1	(	(	PUNCT
ejpam-5140	55	2	4	4	X
ejpam-5140	55	3	)	)	PUNCT
ejpam-5140	55	4	using	use	VERB
ejpam-5140	55	5	x	x	X
ejpam-5140	55	6	=	=	PUNCT
ejpam-5140	55	7	a	a	DET
ejpam-5140	55	8	sinωt	sinωt	NOUN
ejpam-5140	55	9	and	and	CCONJ
ejpam-5140	55	10	y	y	PROPN
ejpam-5140	55	11	=	=	PROPN
ejpam-5140	55	12	a	a	DET
ejpam-5140	55	13	cosωt	cosωt	NOUN
ejpam-5140	55	14	,	,	PUNCT
ejpam-5140	55	15	we	we	PRON
ejpam-5140	55	16	have	have	VERB
ejpam-5140	55	17	x′′	x′′	PROPN
ejpam-5140	55	18	+	+	PUNCT
ejpam-5140	55	19	ω2x	ω2x	NOUN
ejpam-5140	55	20	=	=	SYM
ejpam-5140	55	21	0	0	PROPN
ejpam-5140	55	22	.	.	PUNCT
ejpam-5140	56	1	(	(	PUNCT
ejpam-5140	56	2	5	5	X
ejpam-5140	56	3	)	)	PUNCT
ejpam-5140	56	4	y′′	y′′	NOUN
ejpam-5140	56	5	+	+	CCONJ
ejpam-5140	56	6	ω2y	ω2y	PROPN
ejpam-5140	56	7	=	=	SYM
ejpam-5140	56	8	0	0	X
ejpam-5140	56	9	.	.	PUNCT
ejpam-5140	57	1	(	(	PUNCT
ejpam-5140	57	2	6	6	NUM
ejpam-5140	57	3	)	)	PUNCT
ejpam-5140	57	4	the	the	DET
ejpam-5140	57	5	solution	solution	NOUN
ejpam-5140	57	6	of	of	ADP
ejpam-5140	57	7	(	(	PUNCT
ejpam-5140	57	8	5&6	5&6	NUM
ejpam-5140	57	9	)	)	PUNCT
ejpam-5140	57	10	remains	remain	VERB
ejpam-5140	57	11	the	the	DET
ejpam-5140	57	12	same	same	ADJ
ejpam-5140	57	13	as	as	ADP
ejpam-5140	57	14	our	our	PRON
ejpam-5140	57	15	assumptions	assumption	NOUN
ejpam-5140	57	16	.	.	PUNCT
ejpam-5140	58	1	however	however	ADV
ejpam-5140	58	2	,	,	PUNCT
ejpam-5140	58	3	for	for	ADP
ejpam-5140	58	4	the	the	DET
ejpam-5140	58	5	case	case	NOUN
ejpam-5140	58	6	α	α	NOUN
ejpam-5140	58	7	̸=	̸=	PROPN
ejpam-5140	58	8	β	β	SYM
ejpam-5140	58	9	̸=	̸=	PROPN
ejpam-5140	58	10	1	1	NUM
ejpam-5140	58	11	one	one	NUM
ejpam-5140	58	12	has	have	VERB
ejpam-5140	58	13	to	to	PART
ejpam-5140	58	14	use	use	VERB
ejpam-5140	58	15	a	a	DET
ejpam-5140	58	16	specific	specific	ADJ
ejpam-5140	58	17	analysis	analysis	NOUN
ejpam-5140	58	18	as	as	SCONJ
ejpam-5140	58	19	given	give	VERB
ejpam-5140	58	20	section	section	NOUN
ejpam-5140	58	21	2	2	NUM
ejpam-5140	58	22	below	below	ADV
ejpam-5140	58	23	.	.	PUNCT
ejpam-5140	59	1	2	2	X
ejpam-5140	59	2	.	.	X
ejpam-5140	59	3	strong	strong	ADJ
ejpam-5140	59	4	coupling	coupling	NOUN
ejpam-5140	59	5	limit	limit	NOUN
ejpam-5140	59	6	for	for	ADP
ejpam-5140	59	7	ω	ω	PROPN
ejpam-5140	59	8	=	=	SYM
ejpam-5140	59	9	1	1	NUM
ejpam-5140	59	10	,	,	PUNCT
ejpam-5140	59	11	α	α	PRON
ejpam-5140	59	12	̸=	̸=	PROPN
ejpam-5140	59	13	β	β	NOUN
ejpam-5140	59	14	,	,	PUNCT
ejpam-5140	59	15	and	and	CCONJ
ejpam-5140	59	16	ε	ε	PROPN
ejpam-5140	59	17	=	=	SYM
ejpam-5140	59	18	1	1	NUM
ejpam-5140	59	19	in	in	ADP
ejpam-5140	59	20	this	this	DET
ejpam-5140	59	21	section	section	NOUN
ejpam-5140	59	22	,	,	PUNCT
ejpam-5140	59	23	we	we	PRON
ejpam-5140	59	24	present	present	VERB
ejpam-5140	59	25	some	some	DET
ejpam-5140	59	26	numerical	numerical	ADJ
ejpam-5140	59	27	analysis	analysis	NOUN
ejpam-5140	59	28	for	for	ADP
ejpam-5140	59	29	the	the	DET
ejpam-5140	59	30	system	system	NOUN
ejpam-5140	59	31	given	give	VERB
ejpam-5140	59	32	in	in	ADP
ejpam-5140	59	33	(	(	PUNCT
ejpam-5140	59	34	1	1	NUM
ejpam-5140	59	35	&	&	CCONJ
ejpam-5140	59	36	2	2	NUM
ejpam-5140	59	37	)	)	PUNCT
ejpam-5140	59	38	for	for	ADP
ejpam-5140	59	39	the	the	DET
ejpam-5140	59	40	following	follow	VERB
ejpam-5140	59	41	case	case	NOUN
ejpam-5140	59	42	consider	consider	VERB
ejpam-5140	59	43	α	α	NOUN
ejpam-5140	59	44	=	=	SYM
ejpam-5140	59	45	1.546	1.546	NUM
ejpam-5140	59	46	,	,	PUNCT
ejpam-5140	59	47	β	β	X
ejpam-5140	59	48	=	=	SYM
ejpam-5140	59	49	1.551	1.551	NUM
ejpam-5140	59	50	,	,	PUNCT
ejpam-5140	59	51	ω	ω	NOUN
ejpam-5140	59	52	=	=	SYM
ejpam-5140	59	53	1	1	NUM
ejpam-5140	59	54	with	with	ADP
ejpam-5140	59	55	ε	ε	PROPN
ejpam-5140	59	56	=	=	SYM
ejpam-5140	59	57	1	1	X
ejpam-5140	59	58	.	.	PUNCT
ejpam-5140	60	1	in	in	ADP
ejpam-5140	60	2	this	this	DET
ejpam-5140	60	3	case	case	NOUN
ejpam-5140	60	4	system	system	NOUN
ejpam-5140	60	5	(	(	PUNCT
ejpam-5140	60	6	1&2	1&2	ADV
ejpam-5140	60	7	)	)	PUNCT
ejpam-5140	60	8	become	become	VERB
ejpam-5140	60	9	:	:	PUNCT
ejpam-5140	60	10	x′′	x′′	PROPN
ejpam-5140	61	1	+	+	CCONJ
ejpam-5140	61	2	x+	x+	NUM
ejpam-5140	61	3	(	(	PUNCT
ejpam-5140	61	4	1.546x2	1.546x2	NUM
ejpam-5140	61	5	+	+	NUM
ejpam-5140	61	6	1.551y2	1.551y2	NUM
ejpam-5140	61	7	−	−	NOUN
ejpam-5140	61	8	1	1	NUM
ejpam-5140	61	9	)	)	PUNCT
ejpam-5140	61	10	x′	x′	PROPN
ejpam-5140	62	1	=	=	SYM
ejpam-5140	62	2	0	0	PROPN
ejpam-5140	62	3	.	.	PUNCT
ejpam-5140	63	1	(	(	PUNCT
ejpam-5140	63	2	7	7	X
ejpam-5140	63	3	)	)	PUNCT
ejpam-5140	63	4	y′′	y′′	NOUN
ejpam-5140	63	5	+	+	CCONJ
ejpam-5140	63	6	y	y	PROPN
ejpam-5140	63	7	−	−	PROPN
ejpam-5140	63	8	(	(	PUNCT
ejpam-5140	63	9	1.546x2	1.546x2	NUM
ejpam-5140	63	10	+	+	NUM
ejpam-5140	63	11	1.551y2	1.551y2	NUM
ejpam-5140	63	12	−	−	NOUN
ejpam-5140	63	13	1	1	NUM
ejpam-5140	63	14	)	)	PUNCT
ejpam-5140	63	15	y′	y′	NOUN
ejpam-5140	64	1	=	=	SYM
ejpam-5140	64	2	0	0	X
ejpam-5140	64	3	.	.	PUNCT
ejpam-5140	65	1	(	(	PUNCT
ejpam-5140	65	2	8)	8)	NUM
ejpam-5140	65	3	the	the	DET
ejpam-5140	65	4	above	above	ADJ
ejpam-5140	65	5	system	system	NOUN
ejpam-5140	65	6	is	be	AUX
ejpam-5140	65	7	a	a	DET
ejpam-5140	65	8	coupled	couple	VERB
ejpam-5140	65	9	nonlinear	nonlinear	ADJ
ejpam-5140	65	10	one	one	NUM
ejpam-5140	65	11	.	.	PUNCT
ejpam-5140	66	1	numerical	numerical	ADJ
ejpam-5140	66	2	technique	technique	NOUN
ejpam-5140	66	3	has	have	VERB
ejpam-5140	66	4	to	to	PART
ejpam-5140	66	5	be	be	AUX
ejpam-5140	66	6	used	use	VERB
ejpam-5140	66	7	to	to	PART
ejpam-5140	66	8	solve	solve	VERB
ejpam-5140	66	9	it	it	PRON
ejpam-5140	66	10	.	.	PUNCT
ejpam-5140	67	1	below	below	ADP
ejpam-5140	67	2	we	we	PRON
ejpam-5140	67	3	use	use	VERB
ejpam-5140	67	4	fourthorder	fourthorder	NOUN
ejpam-5140	67	5	rungekutta	rungekutta	NOUN
ejpam-5140	67	6	technique	technique	NOUN
ejpam-5140	67	7	to	to	PART
ejpam-5140	67	8	simulate	simulate	VERB
ejpam-5140	67	9	x(t	x(t	PROPN
ejpam-5140	67	10	)	)	PUNCT
ejpam-5140	67	11	,	,	PUNCT
ejpam-5140	67	12	y(t	y(t	PROPN
ejpam-5140	67	13	)	)	PUNCT
ejpam-5140	67	14	,	,	PUNCT
ejpam-5140	67	15	x′(t	x′(t	PROPN
ejpam-5140	67	16	)	)	PUNCT
ejpam-5140	67	17	and	and	CCONJ
ejpam-5140	67	18	y′(t	y′(t	NOUN
ejpam-5140	67	19	)	)	PUNCT
ejpam-5140	67	20	vs	vs	ADP
ejpam-5140	67	21	time	time	NOUN
ejpam-5140	67	22	as	as	SCONJ
ejpam-5140	67	23	shown	show	VERB
ejpam-5140	67	24	in	in	ADP
ejpam-5140	67	25	figure	figure	NOUN
ejpam-5140	67	26	1	1	NUM
ejpam-5140	67	27	(	(	PUNCT
ejpam-5140	67	28	ac	ac	PROPN
ejpam-5140	67	29	)	)	PUNCT
ejpam-5140	67	30	.	.	PUNCT
ejpam-5140	68	1	figure	figure	VERB
ejpam-5140	68	2	1	1	NUM
ejpam-5140	68	3	:	:	PUNCT
ejpam-5140	68	4	simulation	simulation	NOUN
ejpam-5140	68	5	of	of	ADP
ejpam-5140	68	6	system	system	NOUN
ejpam-5140	68	7	(	(	PUNCT
ejpam-5140	68	8	7	7	NUM
ejpam-5140	68	9	&	&	CCONJ
ejpam-5140	68	10	8)	8)	NUM
ejpam-5140	68	11	using	use	VERB
ejpam-5140	68	12	forthorder	forthorder	NOUN
ejpam-5140	68	13	rungekutta	rungekutta	NOUN
ejpam-5140	68	14	method	method	NOUN
ejpam-5140	68	15	(	(	PUNCT
ejpam-5140	68	16	a	a	X
ejpam-5140	68	17	)	)	PUNCT
ejpam-5140	68	18	x(t	x(t	PROPN
ejpam-5140	68	19	)	)	PUNCT
ejpam-5140	68	20	vs	vs	ADP
ejpam-5140	68	21	time	time	NOUN
ejpam-5140	68	22	,	,	PUNCT
ejpam-5140	68	23	(	(	PUNCT
ejpam-5140	68	24	b	b	X
ejpam-5140	68	25	)	)	PUNCT
ejpam-5140	68	26	y(t	y(t	NUM
ejpam-5140	68	27	)	)	PUNCT
ejpam-5140	68	28	vs	vs	ADP
ejpam-5140	68	29	time	time	NOUN
ejpam-5140	68	30	(	(	PUNCT
ejpam-5140	68	31	c	c	NOUN
ejpam-5140	68	32	)	)	PUNCT
ejpam-5140	68	33	x′(t	x′(t	NOUN
ejpam-5140	68	34	)	)	PUNCT
ejpam-5140	68	35	vs	vs	ADP
ejpam-5140	68	36	time	time	NOUN
ejpam-5140	68	37	,	,	PUNCT
ejpam-5140	68	38	and	and	CCONJ
ejpam-5140	68	39	(	(	PUNCT
ejpam-5140	68	40	d	d	NOUN
ejpam-5140	68	41	)	)	PUNCT
ejpam-5140	68	42	y′(t	y′(t	NOUN
ejpam-5140	68	43	)	)	PUNCT
ejpam-5140	68	44	vs	vs	ADP
ejpam-5140	68	45	time	time	NOUN
ejpam-5140	68	46	j.	j.	PROPN
ejpam-5140	68	47	asad	asad	PROPN
ejpam-5140	68	48	et	et	PROPN
ejpam-5140	68	49	al	al	PROPN
ejpam-5140	68	50	.	.	PUNCT
ejpam-5140	68	51	/	/	SYM
ejpam-5140	68	52	eur	eur	PROPN
ejpam-5140	68	53	.	.	PUNCT
ejpam-5140	69	1	j.	j.	PROPN
ejpam-5140	69	2	pure	pure	PROPN
ejpam-5140	69	3	appl	appl	PROPN
ejpam-5140	69	4	.	.	PROPN
ejpam-5140	69	5	math	math	PROPN
ejpam-5140	69	6	,	,	PUNCT
ejpam-5140	69	7	17	17	NUM
ejpam-5140	69	8	(	(	PUNCT
ejpam-5140	69	9	2	2	NUM
ejpam-5140	69	10	)	)	PUNCT
ejpam-5140	69	11	(	(	PUNCT
ejpam-5140	69	12	2024	2024	NUM
ejpam-5140	69	13	)	)	PUNCT
ejpam-5140	69	14	,	,	PUNCT
ejpam-5140	69	15	1254	1254	NUM
ejpam-5140	69	16	-	-	SYM
ejpam-5140	69	17	1264	1264	NUM
ejpam-5140	69	18	1257	1257	NUM
ejpam-5140	69	19	the	the	DET
ejpam-5140	69	20	time	time	NOUN
ejpam-5140	69	21	-	-	PUNCT
ejpam-5140	69	22	series	series	NOUN
ejpam-5140	69	23	of	of	ADP
ejpam-5140	69	24	the	the	DET
ejpam-5140	69	25	dynamical	dynamical	ADJ
ejpam-5140	69	26	variables	variable	NOUN
ejpam-5140	69	27	(	(	PUNCT
ejpam-5140	69	28	x(t	x(t	PROPN
ejpam-5140	69	29	)	)	PUNCT
ejpam-5140	69	30	and	and	CCONJ
ejpam-5140	69	31	y(t	y(t	NOUN
ejpam-5140	69	32	)	)	PUNCT
ejpam-5140	69	33	)	)	PUNCT
ejpam-5140	69	34	is	be	AUX
ejpam-5140	69	35	shown	show	VERB
ejpam-5140	69	36	in	in	ADP
ejpam-5140	69	37	figure	figure	NOUN
ejpam-5140	69	38	1	1	NUM
ejpam-5140	69	39	(	(	PUNCT
ejpam-5140	69	40	a	a	PRON
ejpam-5140	69	41	and	and	CCONJ
ejpam-5140	69	42	b	b	NOUN
ejpam-5140	69	43	)	)	PUNCT
ejpam-5140	69	44	.	.	PUNCT
ejpam-5140	70	1	as	as	SCONJ
ejpam-5140	70	2	one	one	PRON
ejpam-5140	70	3	can	can	AUX
ejpam-5140	70	4	see	see	VERB
ejpam-5140	70	5	,	,	PUNCT
ejpam-5140	70	6	these	these	DET
ejpam-5140	70	7	solutions	solution	NOUN
ejpam-5140	70	8	are	be	AUX
ejpam-5140	70	9	periodic	periodic	ADJ
ejpam-5140	70	10	.	.	PUNCT
ejpam-5140	71	1	it	it	PRON
ejpam-5140	71	2	may	may	AUX
ejpam-5140	71	3	be	be	AUX
ejpam-5140	71	4	noted	note	VERB
ejpam-5140	71	5	that	that	SCONJ
ejpam-5140	71	6	the	the	DET
ejpam-5140	71	7	time	time	NOUN
ejpam-5140	71	8	evolution	evolution	NOUN
ejpam-5140	71	9	of	of	ADP
ejpam-5140	71	10	the	the	DET
ejpam-5140	71	11	dynamical	dynamical	ADJ
ejpam-5140	71	12	variables	variable	NOUN
ejpam-5140	71	13	(	(	PUNCT
ejpam-5140	71	14	x(t	x(t	PROPN
ejpam-5140	71	15	)	)	PUNCT
ejpam-5140	71	16	and	and	CCONJ
ejpam-5140	71	17	y(t	y(t	NOUN
ejpam-5140	71	18	)	)	PUNCT
ejpam-5140	71	19	)	)	PUNCT
ejpam-5140	71	20	with	with	ADP
ejpam-5140	71	21	the	the	DET
ejpam-5140	71	22	same	same	ADJ
ejpam-5140	71	23	initial	initial	ADJ
ejpam-5140	71	24	conditions	condition	NOUN
ejpam-5140	71	25	nearly	nearly	ADV
ejpam-5140	71	26	show	show	VERB
ejpam-5140	71	27	similar	similar	ADJ
ejpam-5140	71	28	oscillatory	oscillatory	ADJ
ejpam-5140	71	29	behaviour	behaviour	NOUN
ejpam-5140	71	30	,	,	PUNCT
ejpam-5140	71	31	there	there	PRON
ejpam-5140	71	32	are	be	VERB
ejpam-5140	71	33	also	also	ADV
ejpam-5140	71	34	minute	minute	ADJ
ejpam-5140	71	35	changes	change	NOUN
ejpam-5140	71	36	in	in	ADP
ejpam-5140	71	37	amplitudes	amplitude	NOUN
ejpam-5140	71	38	.	.	PUNCT
ejpam-5140	72	1	the	the	DET
ejpam-5140	72	2	same	same	ADJ
ejpam-5140	72	3	conclusion	conclusion	NOUN
ejpam-5140	72	4	can	can	AUX
ejpam-5140	72	5	be	be	AUX
ejpam-5140	72	6	drawn	draw	VERB
ejpam-5140	72	7	for	for	ADP
ejpam-5140	72	8	figure	figure	NOUN
ejpam-5140	72	9	1	1	NUM
ejpam-5140	72	10	(	(	PUNCT
ejpam-5140	72	11	c	c	NOUN
ejpam-5140	72	12	and	and	CCONJ
ejpam-5140	72	13	d	d	NOUN
ejpam-5140	72	14	)	)	PUNCT
ejpam-5140	72	15	for	for	ADP
ejpam-5140	72	16	the	the	DET
ejpam-5140	72	17	dynamical	dynamical	ADJ
ejpam-5140	72	18	variables	variable	NOUN
ejpam-5140	72	19	(	(	PUNCT
ejpam-5140	72	20	x′(t	x′(t	ADJ
ejpam-5140	72	21	)	)	PUNCT
ejpam-5140	72	22	and	and	CCONJ
ejpam-5140	72	23	y′(t	y′(t	NOUN
ejpam-5140	72	24	)	)	PUNCT
ejpam-5140	72	25	)	)	PUNCT
ejpam-5140	72	26	.	.	PUNCT
ejpam-5140	73	1	furthermore	furthermore	ADV
ejpam-5140	73	2	,	,	PUNCT
ejpam-5140	73	3	in	in	ADP
ejpam-5140	73	4	figure	figure	NOUN
ejpam-5140	73	5	2	2	NUM
ejpam-5140	73	6	(	(	PUNCT
ejpam-5140	73	7	a	a	PRON
ejpam-5140	73	8	&	&	CCONJ
ejpam-5140	73	9	b	b	NOUN
ejpam-5140	73	10	)	)	PUNCT
ejpam-5140	73	11	the	the	DET
ejpam-5140	73	12	phase	phase	NOUN
ejpam-5140	73	13	portrait	portrait	NOUN
ejpam-5140	73	14	of	of	ADP
ejpam-5140	73	15	x′(t)vsx(t	x′(t)vsx(t	NOUN
ejpam-5140	73	16	)	)	PUNCT
ejpam-5140	73	17	,	,	PUNCT
ejpam-5140	73	18	and	and	CCONJ
ejpam-5140	73	19	y′(t	y′(t	X
ejpam-5140	73	20	)	)	PUNCT
ejpam-5140	73	21	vs	vs	ADP
ejpam-5140	73	22	y(t	y(t	PROPN
ejpam-5140	73	23	)	)	PUNCT
ejpam-5140	73	24	has	have	AUX
ejpam-5140	73	25	been	be	AUX
ejpam-5140	73	26	plotted	plot	VERB
ejpam-5140	73	27	.	.	PUNCT
ejpam-5140	74	1	these	these	DET
ejpam-5140	74	2	phase	phase	NOUN
ejpam-5140	74	3	portraits	portrait	NOUN
ejpam-5140	74	4	are	be	AUX
ejpam-5140	74	5	closed	close	VERB
ejpam-5140	74	6	and	and	CCONJ
ejpam-5140	74	7	show	show	VERB
ejpam-5140	74	8	nearly	nearly	ADV
ejpam-5140	74	9	rectangular	rectangular	ADJ
ejpam-5140	74	10	shape	shape	NOUN
ejpam-5140	74	11	.	.	PUNCT
ejpam-5140	75	1	this	this	PRON
ejpam-5140	75	2	implies	imply	VERB
ejpam-5140	75	3	that	that	SCONJ
ejpam-5140	75	4	the	the	DET
ejpam-5140	75	5	suggested	suggest	VERB
ejpam-5140	75	6	system	system	NOUN
ejpam-5140	75	7	a	a	DET
ejpam-5140	75	8	stable	stable	ADJ
ejpam-5140	75	9	one	one	NOUN
ejpam-5140	75	10	.	.	PUNCT
ejpam-5140	76	1	figure	figure	NOUN
ejpam-5140	76	2	2	2	NUM
ejpam-5140	76	3	:	:	PUNCT
ejpam-5140	76	4	phase	phase	NOUN
ejpam-5140	76	5	portrait	portrait	NOUN
ejpam-5140	76	6	of	of	ADP
ejpam-5140	76	7	system	system	NOUN
ejpam-5140	76	8	(	(	PUNCT
ejpam-5140	76	9	7	7	NUM
ejpam-5140	76	10	&	&	CCONJ
ejpam-5140	76	11	8)	8)	NUM
ejpam-5140	76	12	:	:	PUNCT
ejpam-5140	76	13	(	(	PUNCT
ejpam-5140	76	14	a	a	X
ejpam-5140	76	15	)	)	PUNCT
ejpam-5140	76	16	x′(t	x′(t	NOUN
ejpam-5140	76	17	)	)	PUNCT
ejpam-5140	76	18	vs	vs	ADP
ejpam-5140	76	19	x(t	x(t	PROPN
ejpam-5140	76	20	)	)	PUNCT
ejpam-5140	76	21	,	,	PUNCT
ejpam-5140	76	22	and	and	CCONJ
ejpam-5140	76	23	(	(	PUNCT
ejpam-5140	76	24	b	b	NOUN
ejpam-5140	76	25	)	)	PUNCT
ejpam-5140	76	26	y′(t	y′(t	NOUN
ejpam-5140	76	27	)	)	PUNCT
ejpam-5140	76	28	vs	vs	ADP
ejpam-5140	76	29	y(t	y(t	NOUN
ejpam-5140	76	30	)	)	PUNCT
ejpam-5140	76	31	.	.	PUNCT
ejpam-5140	77	1	3	3	X
ejpam-5140	77	2	.	.	X
ejpam-5140	77	3	the	the	DET
ejpam-5140	77	4	msdtm	msdtm	PROPN
ejpam-5140	77	5	method	method	VERB
ejpam-5140	77	6	the	the	DET
ejpam-5140	77	7	multi	multi	ADJ
ejpam-5140	77	8	-	-	ADJ
ejpam-5140	77	9	step	step	ADJ
ejpam-5140	77	10	differential	differential	NOUN
ejpam-5140	77	11	transform	transform	NOUN
ejpam-5140	77	12	technique	technique	NOUN
ejpam-5140	77	13	,	,	PUNCT
ejpam-5140	77	14	or	or	CCONJ
ejpam-5140	77	15	ms	ms	PROPN
ejpam-5140	77	16	-	-	PUNCT
ejpam-5140	77	17	dtm	dtm	PROPN
ejpam-5140	77	18	for	for	ADP
ejpam-5140	77	19	short	short	ADJ
ejpam-5140	77	20	,	,	PUNCT
ejpam-5140	77	21	is	be	AUX
ejpam-5140	77	22	the	the	DET
ejpam-5140	77	23	method	method	NOUN
ejpam-5140	77	24	used	use	VERB
ejpam-5140	77	25	to	to	PART
ejpam-5140	77	26	solve	solve	VERB
ejpam-5140	77	27	odes	ode	NOUN
ejpam-5140	77	28	numerically	numerically	ADV
ejpam-5140	77	29	,	,	PUNCT
ejpam-5140	77	30	and	and	CCONJ
ejpam-5140	77	31	it	it	PRON
ejpam-5140	77	32	is	be	AUX
ejpam-5140	77	33	the	the	DET
ejpam-5140	77	34	sole	sole	ADJ
ejpam-5140	77	35	topic	topic	NOUN
ejpam-5140	77	36	of	of	ADP
ejpam-5140	77	37	this	this	DET
ejpam-5140	77	38	section	section	NOUN
ejpam-5140	77	39	.	.	PUNCT
ejpam-5140	78	1	let	let	VERB
ejpam-5140	78	2	[	[	X
ejpam-5140	78	3	0	0	NUM
ejpam-5140	78	4	,	,	PUNCT
ejpam-5140	78	5	t	t	PROPN
ejpam-5140	78	6	]	]	PUNCT
ejpam-5140	78	7	be	be	AUX
ejpam-5140	78	8	the	the	DET
ejpam-5140	78	9	interval	interval	NOUN
ejpam-5140	78	10	for	for	ADP
ejpam-5140	78	11	the	the	DET
ejpam-5140	78	12	nonlinear	nonlinear	ADJ
ejpam-5140	78	13	initial	initial	ADJ
ejpam-5140	78	14	value	value	NOUN
ejpam-5140	78	15	issue	issue	NOUN
ejpam-5140	78	16	,	,	PUNCT
ejpam-5140	78	17	where	where	SCONJ
ejpam-5140	78	18	a	a	DET
ejpam-5140	78	19	finite	finite	ADJ
ejpam-5140	78	20	series	series	NOUN
ejpam-5140	78	21	may	may	AUX
ejpam-5140	78	22	be	be	AUX
ejpam-5140	78	23	used	use	VERB
ejpam-5140	78	24	to	to	PART
ejpam-5140	78	25	represent	represent	VERB
ejpam-5140	78	26	f	f	PROPN
ejpam-5140	78	27	(	(	PUNCT
ejpam-5140	78	28	t	t	PROPN
ejpam-5140	78	29	,	,	PUNCT
ejpam-5140	78	30	x	x	PROPN
ejpam-5140	78	31	,	,	PUNCT
ejpam-5140	78	32	x′	x′	PROPN
ejpam-5140	78	33	,	,	PUNCT
ejpam-5140	78	34	.	.	PUNCT
ejpam-5140	78	35	.	.	PUNCT
ejpam-5140	79	1	.	.	PUNCT
ejpam-5140	80	1	,	,	PUNCT
ejpam-5140	80	2	x(r	x(r	PROPN
ejpam-5140	80	3	)	)	PUNCT
ejpam-5140	80	4	)	)	PUNCT
ejpam-5140	81	1	=	=	SYM
ejpam-5140	81	2	0	0	NUM
ejpam-5140	81	3	x(t	x(t	PROPN
ejpam-5140	81	4	)	)	PUNCT
ejpam-5140	81	5	=	=	SYM
ejpam-5140	81	6	n∑	n∑	ADJ
ejpam-5140	81	7	n=0	n=0	NUM
ejpam-5140	81	8	ant	ant	NOUN
ejpam-5140	81	9	n	n	CCONJ
ejpam-5140	81	10	,	,	PUNCT
ejpam-5140	81	11	t	t	PROPN
ejpam-5140	81	12	∈	∈	PROPN
ejpam-5140	82	1	[	[	X
ejpam-5140	82	2	0	0	NUM
ejpam-5140	82	3	,	,	PUNCT
ejpam-5140	82	4	t	t	X
ejpam-5140	82	5	]	]	PUNCT
ejpam-5140	82	6	(	(	PUNCT
ejpam-5140	82	7	9	9	NUM
ejpam-5140	82	8	)	)	PUNCT
ejpam-5140	82	9	with	with	ADP
ejpam-5140	82	10	an	an	DET
ejpam-5140	82	11	initial	initial	ADJ
ejpam-5140	82	12	condition	condition	NOUN
ejpam-5140	82	13	x(r)(0	x(r)(0	NUM
ejpam-5140	82	14	)	)	PUNCT
ejpam-5140	82	15	=	=	SYM
ejpam-5140	82	16	ck	ck	PROPN
ejpam-5140	82	17	for	for	ADP
ejpam-5140	82	18	k	k	PROPN
ejpam-5140	82	19	=	=	SYM
ejpam-5140	82	20	0	0	NUM
ejpam-5140	82	21	,	,	PUNCT
ejpam-5140	82	22	1	1	NUM
ejpam-5140	82	23	,	,	PUNCT
ejpam-5140	82	24	.	.	PUNCT
ejpam-5140	82	25	.	.	PUNCT
ejpam-5140	82	26	.	.	PUNCT
ejpam-5140	83	1	,	,	PUNCT
ejpam-5140	83	2	r	r	NOUN
ejpam-5140	83	3	−	−	NOUN
ejpam-5140	83	4	1	1	NUM
ejpam-5140	83	5	.	.	PUNCT
ejpam-5140	84	1	using	use	VERB
ejpam-5140	84	2	the	the	DET
ejpam-5140	84	3	nodes	node	NOUN
ejpam-5140	84	4	tm	tm	PROPN
ejpam-5140	84	5	=	=	PROPN
ejpam-5140	84	6	mh	mh	PROPN
ejpam-5140	84	7	,	,	PUNCT
ejpam-5140	84	8	we	we	PRON
ejpam-5140	84	9	suppose	suppose	VERB
ejpam-5140	84	10	that	that	SCONJ
ejpam-5140	84	11	interval	interval	NOUN
ejpam-5140	84	12	[	[	X
ejpam-5140	84	13	0	0	NUM
ejpam-5140	84	14	,	,	PUNCT
ejpam-5140	84	15	t	t	PROPN
ejpam-5140	84	16	]	]	PUNCT
ejpam-5140	84	17	is	be	AUX
ejpam-5140	84	18	split	split	VERB
ejpam-5140	84	19	into	into	ADP
ejpam-5140	84	20	m	m	PROPN
ejpam-5140	84	21	subintervals	subinterval	NOUN
ejpam-5140	84	22	[	[	X
ejpam-5140	84	23	tm−1	tm−1	NOUN
ejpam-5140	84	24	,	,	PUNCT
ejpam-5140	84	25	tm	tm	NOUN
ejpam-5140	84	26	]	]	X
ejpam-5140	84	27	with	with	ADP
ejpam-5140	84	28	m	m	PROPN
ejpam-5140	84	29	=	=	SYM
ejpam-5140	84	30	1	1	NUM
ejpam-5140	84	31	,	,	PUNCT
ejpam-5140	84	32	2	2	NUM
ejpam-5140	84	33	,	,	PUNCT
ejpam-5140	84	34	.	.	PUNCT
ejpam-5140	84	35	.	.	PUNCT
ejpam-5140	85	1	.	.	PUNCT
ejpam-5140	86	1	,	,	PUNCT
ejpam-5140	86	2	m	m	VERB
ejpam-5140	86	3	and	and	CCONJ
ejpam-5140	86	4	step	step	NOUN
ejpam-5140	86	5	size	size	NOUN
ejpam-5140	86	6	h	h	PROPN
ejpam-5140	86	7	=	=	SYM
ejpam-5140	86	8	t	t	PROPN
ejpam-5140	86	9	/	/	SYM
ejpam-5140	86	10	m	m	PROPN
ejpam-5140	86	11	.	.	PUNCT
ejpam-5140	87	1	ms	ms	PROPN
ejpam-5140	87	2	-	-	PUNCT
ejpam-5140	87	3	dtm	dtm	PROPN
ejpam-5140	87	4	is	be	AUX
ejpam-5140	87	5	a	a	DET
ejpam-5140	87	6	method	method	NOUN
ejpam-5140	87	7	for	for	ADP
ejpam-5140	87	8	computational	computational	ADJ
ejpam-5140	87	9	performance	performance	NOUN
ejpam-5140	87	10	for	for	ADP
ejpam-5140	87	11	values	value	NOUN
ejpam-5140	87	12	of	of	ADP
ejpam-5140	87	13	h.	h.	NOUN
ejpam-5140	87	14	the	the	DET
ejpam-5140	87	15	main	main	ADJ
ejpam-5140	87	16	idea	idea	NOUN
ejpam-5140	87	17	of	of	ADP
ejpam-5140	87	18	ms	ms	PROPN
ejpam-5140	87	19	-	-	PUNCT
ejpam-5140	87	20	dtm	dtm	PROPN
ejpam-5140	87	21	is	be	AUX
ejpam-5140	87	22	we	we	PRON
ejpam-5140	87	23	first	first	ADV
ejpam-5140	87	24	apply	apply	VERB
ejpam-5140	87	25	the	the	DET
ejpam-5140	87	26	differential	differential	ADJ
ejpam-5140	87	27	transform	transform	NOUN
ejpam-5140	87	28	method(in	method(in	NOUN
ejpam-5140	87	29	short	short	ADJ
ejpam-5140	87	30	,	,	PUNCT
ejpam-5140	87	31	dtm	dtm	PROPN
ejpam-5140	87	32	)	)	PUNCT
ejpam-5140	87	33	to	to	PART
ejpam-5140	87	34	ode	ode	VERB
ejpam-5140	87	35	with	with	ADP
ejpam-5140	87	36	initial	initial	ADJ
ejpam-5140	87	37	value	value	NOUN
ejpam-5140	87	38	problem	problem	NOUN
ejpam-5140	87	39	j.	j.	PROPN
ejpam-5140	87	40	asad	asad	PROPN
ejpam-5140	87	41	et	et	PROPN
ejpam-5140	87	42	al	al	PROPN
ejpam-5140	87	43	.	.	PUNCT
ejpam-5140	87	44	/	/	SYM
ejpam-5140	87	45	eur	eur	PROPN
ejpam-5140	87	46	.	.	PUNCT
ejpam-5140	88	1	j.	j.	PROPN
ejpam-5140	88	2	pure	pure	PROPN
ejpam-5140	88	3	appl	appl	PROPN
ejpam-5140	88	4	.	.	PROPN
ejpam-5140	88	5	math	math	PROPN
ejpam-5140	88	6	,	,	PUNCT
ejpam-5140	88	7	17	17	NUM
ejpam-5140	88	8	(	(	PUNCT
ejpam-5140	88	9	2	2	NUM
ejpam-5140	88	10	)	)	PUNCT
ejpam-5140	88	11	(	(	PUNCT
ejpam-5140	88	12	2024	2024	NUM
ejpam-5140	88	13	)	)	PUNCT
ejpam-5140	88	14	,	,	PUNCT
ejpam-5140	88	15	1254	1254	NUM
ejpam-5140	88	16	-	-	SYM
ejpam-5140	88	17	1264	1264	NUM
ejpam-5140	88	18	1258	1258	NUM
ejpam-5140	88	19	f	f	PROPN
ejpam-5140	88	20	(	(	PUNCT
ejpam-5140	88	21	t	t	PROPN
ejpam-5140	88	22	,	,	PUNCT
ejpam-5140	88	23	x	x	PROPN
ejpam-5140	88	24	,	,	PUNCT
ejpam-5140	88	25	x′	x′	PROPN
ejpam-5140	88	26	,	,	PUNCT
ejpam-5140	88	27	.	.	PUNCT
ejpam-5140	88	28	.	.	PUNCT
ejpam-5140	88	29	.	.	PUNCT
ejpam-5140	89	1	,	,	PUNCT
ejpam-5140	89	2	x(r	x(r	PROPN
ejpam-5140	89	3	)	)	PUNCT
ejpam-5140	89	4	)	)	PUNCT
ejpam-5140	90	1	=	=	SYM
ejpam-5140	90	2	0	0	NUM
ejpam-5140	90	3	over	over	ADP
ejpam-5140	90	4	the	the	DET
ejpam-5140	90	5	interval	interval	NOUN
ejpam-5140	91	1	[	[	X
ejpam-5140	91	2	0	0	NUM
ejpam-5140	91	3	,	,	PUNCT
ejpam-5140	91	4	t1	t1	NOUN
ejpam-5140	91	5	]	]	X
ejpam-5140	91	6	.	.	PUNCT
ejpam-5140	92	1	for	for	ADP
ejpam-5140	92	2	initial	initial	ADJ
ejpam-5140	92	3	condition	condition	NOUN
ejpam-5140	92	4	x	x	X
ejpam-5140	92	5	(	(	PUNCT
ejpam-5140	92	6	k	k	NOUN
ejpam-5140	92	7	)	)	PUNCT
ejpam-5140	92	8	1	1	NUM
ejpam-5140	92	9	(	(	PUNCT
ejpam-5140	92	10	0	0	NUM
ejpam-5140	92	11	)	)	PUNCT
ejpam-5140	92	12	=	=	SYM
ejpam-5140	92	13	ck	ck	ADJ
ejpam-5140	92	14	,	,	PUNCT
ejpam-5140	92	15	following	follow	VERB
ejpam-5140	92	16	approximate	approximate	ADJ
ejpam-5140	92	17	solution	solution	NOUN
ejpam-5140	92	18	denoted	denote	VERB
ejpam-5140	92	19	by	by	ADP
ejpam-5140	92	20	x1(t	x1(t	PROPN
ejpam-5140	92	21	)	)	PUNCT
ejpam-5140	92	22	=	=	PRON
ejpam-5140	92	23	k∑	k∑	PROPN
ejpam-5140	92	24	n=0	n=0	X
ejpam-5140	92	25	a1nt	a1nt	PUNCT
ejpam-5140	92	26	n	n	CCONJ
ejpam-5140	92	27	,	,	PUNCT
ejpam-5140	92	28	t	t	PROPN
ejpam-5140	92	29	∈	∈	PROPN
ejpam-5140	93	1	[	[	X
ejpam-5140	93	2	0	0	NUM
ejpam-5140	93	3	,	,	PUNCT
ejpam-5140	93	4	t1	t1	NOUN
ejpam-5140	93	5	]	]	PUNCT
ejpam-5140	93	6	.	.	PUNCT
ejpam-5140	94	1	(	(	PUNCT
ejpam-5140	94	2	10	10	NUM
ejpam-5140	94	3	)	)	PUNCT
ejpam-5140	94	4	for	for	ADP
ejpam-5140	94	5	m	m	PROPN
ejpam-5140	94	6	≥	≥	NUM
ejpam-5140	94	7	2	2	NUM
ejpam-5140	94	8	and	and	CCONJ
ejpam-5140	94	9	subinterval	subinterval	NOUN
ejpam-5140	95	1	[	[	X
ejpam-5140	95	2	tm−1	tm−1	NOUN
ejpam-5140	95	3	,	,	PUNCT
ejpam-5140	95	4	tm	tm	NOUN
ejpam-5140	95	5	]	]	PUNCT
ejpam-5140	95	6	with	with	ADP
ejpam-5140	95	7	initial	initial	ADJ
ejpam-5140	95	8	conditions	condition	NOUN
ejpam-5140	95	9	x	x	SYM
ejpam-5140	95	10	(	(	PUNCT
ejpam-5140	95	11	k	k	NOUN
ejpam-5140	95	12	)	)	PUNCT
ejpam-5140	95	13	m	m	VERB
ejpam-5140	95	14	(	(	PUNCT
ejpam-5140	95	15	tm−1	tm−1	NOUN
ejpam-5140	95	16	)	)	PUNCT
ejpam-5140	96	1	=	=	PUNCT
ejpam-5140	96	2	x	x	X
ejpam-5140	96	3	(	(	PUNCT
ejpam-5140	96	4	k	k	NOUN
ejpam-5140	96	5	)	)	PUNCT
ejpam-5140	96	6	m−1	m−1	PROPN
ejpam-5140	96	7	(	(	PUNCT
ejpam-5140	96	8	tm−1	tm−1	PROPN
ejpam-5140	96	9	)	)	PUNCT
ejpam-5140	96	10	,	,	PUNCT
ejpam-5140	96	11	we	we	PRON
ejpam-5140	96	12	apply	apply	VERB
ejpam-5140	96	13	the	the	DET
ejpam-5140	96	14	dtm	dtm	PROPN
ejpam-5140	96	15	to	to	ADP
ejpam-5140	96	16	f	f	PROPN
ejpam-5140	96	17	(	(	PUNCT
ejpam-5140	96	18	t	t	PROPN
ejpam-5140	96	19	,	,	PUNCT
ejpam-5140	96	20	x	x	PROPN
ejpam-5140	96	21	,	,	PUNCT
ejpam-5140	96	22	x′	x′	PROPN
ejpam-5140	96	23	,	,	PUNCT
ejpam-5140	96	24	.	.	PUNCT
ejpam-5140	96	25	.	.	PUNCT
ejpam-5140	97	1	.	.	PUNCT
ejpam-5140	98	1	,	,	PUNCT
ejpam-5140	98	2	x(r	x(r	PROPN
ejpam-5140	98	3	)	)	PUNCT
ejpam-5140	98	4	)	)	PUNCT
ejpam-5140	99	1	=	=	PUNCT
ejpam-5140	99	2	0	0	NUM
ejpam-5140	99	3	,	,	PUNCT
ejpam-5140	99	4	where	where	SCONJ
ejpam-5140	99	5	t0	t0	PROPN
ejpam-5140	99	6	in	in	ADP
ejpam-5140	99	7	y	y	PROPN
ejpam-5140	99	8	(	(	PUNCT
ejpam-5140	99	9	k	k	NOUN
ejpam-5140	99	10	)	)	PUNCT
ejpam-5140	99	11	=	=	SYM
ejpam-5140	99	12	1	1	NUM
ejpam-5140	99	13	k	k	X
ejpam-5140	99	14	!	!	PUNCT
ejpam-5140	99	15	dky(t	dky(t	PROPN
ejpam-5140	99	16	)	)	PUNCT
ejpam-5140	99	17	dtk	dtk	PROPN
ejpam-5140	99	18	]	]	PUNCT
ejpam-5140	99	19	t	t	PROPN
ejpam-5140	99	20	=	=	SYM
ejpam-5140	99	21	t0	t0	PROPN
ejpam-5140	99	22	,	,	PUNCT
ejpam-5140	99	23	which	which	PRON
ejpam-5140	99	24	is	be	AUX
ejpam-5140	99	25	called	call	VERB
ejpam-5140	99	26	the	the	DET
ejpam-5140	99	27	differential	differential	ADJ
ejpam-5140	99	28	transformation(dt	transformation(dt	NOUN
ejpam-5140	99	29	,	,	PUNCT
ejpam-5140	99	30	in	in	ADP
ejpam-5140	99	31	short	short	ADJ
ejpam-5140	99	32	)	)	PUNCT
ejpam-5140	99	33	of	of	ADP
ejpam-5140	99	34	a	a	DET
ejpam-5140	99	35	function	function	NOUN
ejpam-5140	99	36	y(t	y(t	NUM
ejpam-5140	99	37	)	)	PUNCT
ejpam-5140	99	38	is	be	AUX
ejpam-5140	99	39	replaced	replace	VERB
ejpam-5140	99	40	by	by	ADP
ejpam-5140	99	41	tm−1	tm−1	NOUN
ejpam-5140	99	42	.	.	PUNCT
ejpam-5140	100	1	the	the	DET
ejpam-5140	100	2	process	process	NOUN
ejpam-5140	100	3	is	be	AUX
ejpam-5140	100	4	repeated	repeat	VERB
ejpam-5140	100	5	and	and	CCONJ
ejpam-5140	100	6	generates	generate	VERB
ejpam-5140	100	7	a	a	DET
ejpam-5140	100	8	sequence	sequence	NOUN
ejpam-5140	100	9	of	of	ADP
ejpam-5140	100	10	approximate	approximate	ADJ
ejpam-5140	100	11	solutions	solution	NOUN
ejpam-5140	100	12	xm(t),m	xm(t),m	PROPN
ejpam-5140	100	13	=	=	SYM
ejpam-5140	101	1	1	1	NUM
ejpam-5140	101	2	,	,	PUNCT
ejpam-5140	101	3	2	2	NUM
ejpam-5140	101	4	,	,	PUNCT
ejpam-5140	101	5	.	.	PUNCT
ejpam-5140	101	6	.	.	PUNCT
ejpam-5140	101	7	.	.	PUNCT
ejpam-5140	102	1	,	,	PUNCT
ejpam-5140	102	2	m	m	VERB
ejpam-5140	102	3	with	with	ADP
ejpam-5140	102	4	n	n	PROPN
ejpam-5140	102	5	=	=	PUNCT
ejpam-5140	102	6	k.m	k.m	PROPN
ejpam-5140	102	7	for	for	ADP
ejpam-5140	102	8	the	the	DET
ejpam-5140	102	9	solution	solution	NOUN
ejpam-5140	102	10	x(t	x(t	PROPN
ejpam-5140	102	11	)	)	PUNCT
ejpam-5140	102	12	and	and	CCONJ
ejpam-5140	102	13	denoted	denote	VERB
ejpam-5140	102	14	by	by	ADP
ejpam-5140	102	15	xm(t	xm(t	NOUN
ejpam-5140	102	16	)	)	PUNCT
ejpam-5140	103	1	=	=	PRON
ejpam-5140	103	2	k∑	k∑	VERB
ejpam-5140	103	3	n=0	n=0	ADJ
ejpam-5140	103	4	amn	amn	PROPN
ejpam-5140	103	5	(	(	PUNCT
ejpam-5140	103	6	t−	t−	PROPN
ejpam-5140	103	7	tm−1	tm−1	NOUN
ejpam-5140	103	8	)	)	PUNCT
ejpam-5140	103	9	n	n	PROPN
ejpam-5140	103	10	,	,	PUNCT
ejpam-5140	103	11	t	t	PROPN
ejpam-5140	103	12	∈	∈	PROPN
ejpam-5140	104	1	[	[	X
ejpam-5140	104	2	tm	tm	NOUN
ejpam-5140	104	3	,	,	PUNCT
ejpam-5140	104	4	tm+1	tm+1	X
ejpam-5140	104	5	]	]	PUNCT
ejpam-5140	104	6	.	.	PUNCT
ejpam-5140	105	1	(	(	PUNCT
ejpam-5140	105	2	11	11	NUM
ejpam-5140	105	3	)	)	PUNCT
ejpam-5140	105	4	finally	finally	ADV
ejpam-5140	105	5	,	,	PUNCT
ejpam-5140	105	6	the	the	DET
ejpam-5140	105	7	ms	ms	PROPN
ejpam-5140	105	8	-	-	PUNCT
ejpam-5140	105	9	dtm	dtm	PROPN
ejpam-5140	105	10	assumes	assume	VERB
ejpam-5140	105	11	the	the	DET
ejpam-5140	105	12	following	follow	VERB
ejpam-5140	105	13	solution	solution	NOUN
ejpam-5140	105	14	denoted	denote	VERB
ejpam-5140	105	15	by	by	ADP
ejpam-5140	105	16	x(t	x(t	PROPN
ejpam-5140	105	17	)	)	PUNCT
ejpam-5140	105	18	x(t	x(t	PROPN
ejpam-5140	105	19	)	)	PUNCT
ejpam-5140	105	20	=	=	PUNCT
ejpam-5140	106	1			NUM
ejpam-5140	106	2	x1(t	x1(t	PUNCT
ejpam-5140	106	3	)	)	PUNCT
ejpam-5140	106	4	,	,	PUNCT
ejpam-5140	106	5	t	t	PROPN
ejpam-5140	106	6	∈	∈	PROPN
ejpam-5140	107	1	[	[	X
ejpam-5140	107	2	0	0	NUM
ejpam-5140	107	3	,	,	PUNCT
ejpam-5140	107	4	t1	t1	NOUN
ejpam-5140	107	5	]	]	X
ejpam-5140	107	6	x2(t	x2(t	PROPN
ejpam-5140	107	7	)	)	PUNCT
ejpam-5140	107	8	,	,	PUNCT
ejpam-5140	107	9	t	t	PROPN
ejpam-5140	107	10	∈	∈	PROPN
ejpam-5140	108	1	[	[	X
ejpam-5140	108	2	t1	t1	NOUN
ejpam-5140	108	3	,	,	PUNCT
ejpam-5140	108	4	t2	t2	NOUN
ejpam-5140	108	5	]	]	PUNCT
ejpam-5140	108	6	·	·	PUNCT
ejpam-5140	108	7	·	·	PUNCT
ejpam-5140	108	8	·	·	PUNCT
ejpam-5140	108	9	xm(t	xm(t	PUNCT
ejpam-5140	108	10	)	)	PUNCT
ejpam-5140	108	11	,	,	PUNCT
ejpam-5140	108	12	t	t	PROPN
ejpam-5140	108	13	∈	∈	PROPN
ejpam-5140	109	1	[	[	X
ejpam-5140	109	2	tm−1	tm−1	NOUN
ejpam-5140	109	3	,	,	PUNCT
ejpam-5140	109	4	tm	tm	NOUN
ejpam-5140	109	5	]	]	PUNCT
ejpam-5140	109	6	.	.	PUNCT
ejpam-5140	110	1	(	(	PUNCT
ejpam-5140	110	2	12	12	NUM
ejpam-5140	110	3	)	)	PUNCT
ejpam-5140	110	4	4	4	NUM
ejpam-5140	110	5	.	.	PUNCT
ejpam-5140	110	6	solution	solution	NOUN
ejpam-5140	110	7	of	of	ADP
ejpam-5140	110	8	the	the	DET
ejpam-5140	110	9	system	system	NOUN
ejpam-5140	110	10	via	via	ADP
ejpam-5140	110	11	ms	ms	PROPN
ejpam-5140	110	12	-	-	PUNCT
ejpam-5140	110	13	dtm	dtm	PROPN
ejpam-5140	110	14	in	in	ADP
ejpam-5140	110	15	this	this	DET
ejpam-5140	110	16	section	section	NOUN
ejpam-5140	111	1	,	,	PUNCT
ejpam-5140	111	2	we	we	PRON
ejpam-5140	111	3	apply	apply	VERB
ejpam-5140	111	4	the	the	DET
ejpam-5140	111	5	ms	ms	PROPN
ejpam-5140	111	6	-	-	PUNCT
ejpam-5140	111	7	dtm	dtm	PROPN
ejpam-5140	111	8	to	to	ADP
ejpam-5140	111	9	eqs	eqs	PROPN
ejpam-5140	111	10	.	.	PUNCT
ejpam-5140	112	1	(	(	PUNCT
ejpam-5140	112	2	7)-(8	7)-(8	NOUN
ejpam-5140	112	3	)	)	PUNCT
ejpam-5140	112	4	to	to	PART
ejpam-5140	112	5	demonstrate	demonstrate	VERB
ejpam-5140	112	6	the	the	DET
ejpam-5140	112	7	effectiveness	effectiveness	NOUN
ejpam-5140	112	8	of	of	ADP
ejpam-5140	112	9	ms	ms	PROPN
ejpam-5140	112	10	-	-	PUNCT
ejpam-5140	112	11	dtm	dtm	PROPN
ejpam-5140	112	12	as	as	ADP
ejpam-5140	112	13	an	an	DET
ejpam-5140	112	14	approximate	approximate	ADJ
ejpam-5140	112	15	tool	tool	NOUN
ejpam-5140	112	16	for	for	ADP
ejpam-5140	112	17	solving	solve	VERB
ejpam-5140	112	18	the	the	DET
ejpam-5140	112	19	ode	ode	NOUN
ejpam-5140	112	20	.	.	PUNCT
ejpam-5140	113	1	let	let	VERB
ejpam-5140	113	2	x	x	NOUN
ejpam-5140	113	3	=	=	NOUN
ejpam-5140	113	4	u1	u1	NOUN
ejpam-5140	113	5	,	,	PUNCT
ejpam-5140	113	6	x	x	NOUN
ejpam-5140	113	7	′	′	NOUN
ejpam-5140	113	8	=	=	SYM
ejpam-5140	113	9	u2	u2	PROPN
ejpam-5140	113	10	,	,	PUNCT
ejpam-5140	113	11	y	y	PROPN
ejpam-5140	113	12	=	=	PROPN
ejpam-5140	113	13	u3	u3	PROPN
ejpam-5140	113	14	and	and	CCONJ
ejpam-5140	113	15	y′	y′	NOUN
ejpam-5140	113	16	=	=	SYM
ejpam-5140	113	17	u4	u4	PROPN
ejpam-5140	113	18	.	.	PUNCT
ejpam-5140	114	1	substituting	substitute	VERB
ejpam-5140	114	2	back	back	ADV
ejpam-5140	114	3	into	into	ADP
ejpam-5140	114	4	the	the	DET
ejpam-5140	114	5	ode	ode	NOUN
ejpam-5140	114	6	(	(	PUNCT
ejpam-5140	114	7	keeping	keep	VERB
ejpam-5140	114	8	in	in	ADP
ejpam-5140	114	9	mind	mind	NOUN
ejpam-5140	115	1	that	that	SCONJ
ejpam-5140	115	2	x′′	x′′	PROPN
ejpam-5140	115	3	=	=	SYM
ejpam-5140	115	4	u′2	u′2	PROPN
ejpam-5140	115	5	and	and	CCONJ
ejpam-5140	115	6	y′′	y′′	NOUN
ejpam-5140	115	7	=	=	PUNCT
ejpam-5140	115	8	u′4	u′4	NOUN
ejpam-5140	115	9	)	)	PUNCT
ejpam-5140	116	1	we	we	PRON
ejpam-5140	116	2	get	get	VERB
ejpam-5140	116	3	:	:	PUNCT
ejpam-5140	116	4	u′2	u′2	X
ejpam-5140	116	5	+	+	CCONJ
ejpam-5140	116	6	u2	u2	PROPN
ejpam-5140	116	7	(	(	PUNCT
ejpam-5140	116	8	1.546u21	1.546u21	NUM
ejpam-5140	116	9	+	+	NUM
ejpam-5140	116	10	1.551u23	1.551u23	NUM
ejpam-5140	116	11	−	−	NOUN
ejpam-5140	116	12	1	1	NUM
ejpam-5140	116	13	)	)	PUNCT
ejpam-5140	116	14	+	+	NUM
ejpam-5140	116	15	u1	u1	NOUN
ejpam-5140	116	16	=	=	SYM
ejpam-5140	116	17	0	0	PROPN
ejpam-5140	116	18	.	.	PUNCT
ejpam-5140	117	1	(	(	PUNCT
ejpam-5140	117	2	13	13	NUM
ejpam-5140	117	3	)	)	PUNCT
ejpam-5140	117	4	and	and	CCONJ
ejpam-5140	117	5	u′3	u′3	ADJ
ejpam-5140	117	6	−	−	PROPN
ejpam-5140	117	7	u4	u4	PROPN
ejpam-5140	117	8	(	(	PUNCT
ejpam-5140	117	9	1.546u21	1.546u21	NUM
ejpam-5140	117	10	+	+	NUM
ejpam-5140	117	11	1.551u23	1.551u23	NUM
ejpam-5140	117	12	−	−	NOUN
ejpam-5140	117	13	1	1	NUM
ejpam-5140	117	14	)	)	PUNCT
ejpam-5140	117	15	+	+	NUM
ejpam-5140	117	16	u3	u3	X
ejpam-5140	117	17	=	=	SYM
ejpam-5140	117	18	0	0	PROPN
ejpam-5140	117	19	.	.	PUNCT
ejpam-5140	118	1	(	(	PUNCT
ejpam-5140	118	2	14	14	NUM
ejpam-5140	118	3	)	)	PUNCT
ejpam-5140	118	4	thus	thus	ADV
ejpam-5140	118	5	eqs	eqs	X
ejpam-5140	118	6	.	.	PUNCT
ejpam-5140	118	7	(	(	PUNCT
ejpam-5140	118	8	7)-(8	7)-(8	NOUN
ejpam-5140	118	9	)	)	PUNCT
ejpam-5140	118	10	can	can	AUX
ejpam-5140	118	11	be	be	AUX
ejpam-5140	118	12	expressed	express	VERB
ejpam-5140	118	13	in	in	ADP
ejpam-5140	118	14	the	the	DET
ejpam-5140	118	15	form	form	NOUN
ejpam-5140	118	16	of	of	ADP
ejpam-5140	118	17	four	four	NUM
ejpam-5140	118	18	simultaneous	simultaneous	ADJ
ejpam-5140	118	19	first	first	ADJ
ejpam-5140	118	20	-	-	PUNCT
ejpam-5140	118	21	order	order	NOUN
ejpam-5140	118	22	differential	differential	ADJ
ejpam-5140	118	23	equations	equation	NOUN
ejpam-5140	118	24	in	in	ADP
ejpam-5140	118	25	terms	term	NOUN
ejpam-5140	118	26	of	of	ADP
ejpam-5140	118	27	u1	u1	NOUN
ejpam-5140	118	28	,	,	PUNCT
ejpam-5140	118	29	u2	u2	NOUN
ejpam-5140	118	30	,	,	PUNCT
ejpam-5140	118	31	u3	u3	NOUN
ejpam-5140	118	32	and	and	CCONJ
ejpam-5140	118	33	u4	u4	PROPN
ejpam-5140	118	34	,	,	PUNCT
ejpam-5140	118	35	i.e.	i.e.	X
ejpam-5140	118	36	u′1	u′1	NOUN
ejpam-5140	118	37	=	=	SYM
ejpam-5140	118	38	u2	u2	PROPN
ejpam-5140	118	39	,	,	PUNCT
ejpam-5140	118	40	u′2	u′2	X
ejpam-5140	118	41	=	=	SYM
ejpam-5140	118	42	−u2	−u2	PROPN
ejpam-5140	118	43	(	(	PUNCT
ejpam-5140	118	44	1.546u21	1.546u21	NUM
ejpam-5140	118	45	+	+	NUM
ejpam-5140	118	46	1.551u23	1.551u23	NUM
ejpam-5140	118	47	−	−	NOUN
ejpam-5140	118	48	1	1	NUM
ejpam-5140	118	49	)	)	PUNCT
ejpam-5140	118	50	−	−	PROPN
ejpam-5140	118	51	u1	u1	NOUN
ejpam-5140	118	52	u′3	u′3	NOUN
ejpam-5140	118	53	=	=	SYM
ejpam-5140	118	54	u4	u4	PROPN
ejpam-5140	118	55	u′4	u′4	NOUN
ejpam-5140	118	56	=	=	PROPN
ejpam-5140	118	57	u4	u4	PROPN
ejpam-5140	118	58	(	(	PUNCT
ejpam-5140	118	59	1.546u21	1.546u21	NUM
ejpam-5140	118	60	+	+	NUM
ejpam-5140	118	61	1.551u23	1.551u23	NUM
ejpam-5140	118	62	−	−	NOUN
ejpam-5140	118	63	1	1	NUM
ejpam-5140	118	64	)	)	PUNCT
ejpam-5140	118	65	−	−	PROPN
ejpam-5140	118	66	u3	u3	PROPN
ejpam-5140	118	67	.	.	PUNCT
ejpam-5140	119	1	(	(	PUNCT
ejpam-5140	119	2	15	15	NUM
ejpam-5140	119	3	)	)	PUNCT
ejpam-5140	119	4	j.	j.	PROPN
ejpam-5140	119	5	asad	asad	PROPN
ejpam-5140	119	6	et	et	PROPN
ejpam-5140	119	7	al	al	PROPN
ejpam-5140	119	8	.	.	PUNCT
ejpam-5140	119	9	/	/	SYM
ejpam-5140	119	10	eur	eur	PROPN
ejpam-5140	119	11	.	.	PUNCT
ejpam-5140	120	1	j.	j.	PROPN
ejpam-5140	120	2	pure	pure	PROPN
ejpam-5140	120	3	appl	appl	PROPN
ejpam-5140	120	4	.	.	PROPN
ejpam-5140	120	5	math	math	PROPN
ejpam-5140	120	6	,	,	PUNCT
ejpam-5140	120	7	17	17	NUM
ejpam-5140	120	8	(	(	PUNCT
ejpam-5140	120	9	2	2	NUM
ejpam-5140	120	10	)	)	PUNCT
ejpam-5140	120	11	(	(	PUNCT
ejpam-5140	120	12	2024	2024	NUM
ejpam-5140	120	13	)	)	PUNCT
ejpam-5140	120	14	,	,	PUNCT
ejpam-5140	120	15	1254	1254	NUM
ejpam-5140	120	16	-	-	SYM
ejpam-5140	120	17	1264	1264	NUM
ejpam-5140	120	18	1259	1259	NUM
ejpam-5140	120	19	taking	take	VERB
ejpam-5140	120	20	the	the	DET
ejpam-5140	120	21	dt	dt	NOUN
ejpam-5140	120	22	of	of	ADP
ejpam-5140	120	23	eq	eq	PROPN
ejpam-5140	120	24	.	.	PUNCT
ejpam-5140	121	1	(	(	PUNCT
ejpam-5140	121	2	15	15	NUM
ejpam-5140	121	3	)	)	PUNCT
ejpam-5140	121	4	by	by	ADP
ejpam-5140	121	5	using	use	VERB
ejpam-5140	121	6	the	the	DET
ejpam-5140	121	7	well	well	ADV
ejpam-5140	121	8	-	-	PUNCT
ejpam-5140	121	9	known	know	VERB
ejpam-5140	121	10	differential	differential	NOUN
ejpam-5140	121	11	transform	transform	NOUN
ejpam-5140	121	12	formulas	formula	NOUN
ejpam-5140	121	13	,	,	PUNCT
ejpam-5140	121	14	we	we	PRON
ejpam-5140	121	15	obtain	obtain	VERB
ejpam-5140	121	16	u1(k	u1(k	ADP
ejpam-5140	121	17	+	+	CCONJ
ejpam-5140	121	18	1	1	NUM
ejpam-5140	121	19	)	)	PUNCT
ejpam-5140	121	20	=	=	SYM
ejpam-5140	122	1	1	1	NUM
ejpam-5140	122	2	k	k	X
ejpam-5140	122	3	+	+	PROPN
ejpam-5140	122	4	1	1	NUM
ejpam-5140	122	5	u2(k	u2(k	NOUN
ejpam-5140	122	6	)	)	PUNCT
ejpam-5140	122	7	,	,	PUNCT
ejpam-5140	122	8	u2(k	u2(k	NOUN
ejpam-5140	122	9	+	+	CCONJ
ejpam-5140	122	10	1	1	X
ejpam-5140	122	11	)	)	PUNCT
ejpam-5140	122	12	=	=	SYM
ejpam-5140	123	1	1	1	NUM
ejpam-5140	123	2	k	k	PROPN
ejpam-5140	123	3	+	+	PROPN
ejpam-5140	123	4	1−1.546	1−1.546	NUM
ejpam-5140	123	5	k∑	k∑	NOUN
ejpam-5140	123	6	k2=0	k2=0	PROPN
ejpam-5140	124	1	k2∑	k2∑	PROPN
ejpam-5140	124	2	k1=0	k1=0	PROPN
ejpam-5140	124	3	u2	u2	PROPN
ejpam-5140	124	4	(	(	PUNCT
ejpam-5140	124	5	k1)u1	k1)u1	PROPN
ejpam-5140	124	6	(	(	PUNCT
ejpam-5140	124	7	k2	k2	PROPN
ejpam-5140	124	8	−	−	PROPN
ejpam-5140	124	9	k1)u1	k1)u1	PROPN
ejpam-5140	124	10	(	(	PUNCT
ejpam-5140	124	11	k	k	PROPN
ejpam-5140	124	12	−	−	PROPN
ejpam-5140	124	13	k2	k2	PROPN
ejpam-5140	124	14	)	)	PUNCT
ejpam-5140	124	15	−	−	PROPN
ejpam-5140	124	16	1.551	1.551	NUM
ejpam-5140	124	17	k∑	k∑	NOUN
ejpam-5140	124	18	k2=0	k2=0	PROPN
ejpam-5140	125	1	k2∑	k2∑	PROPN
ejpam-5140	125	2	k1=0	k1=0	PROPN
ejpam-5140	125	3	u2	u2	PROPN
ejpam-5140	125	4	(	(	PUNCT
ejpam-5140	125	5	k1)u3	k1)u3	PROPN
ejpam-5140	125	6	(	(	PUNCT
ejpam-5140	125	7	k2	k2	PROPN
ejpam-5140	125	8	−	−	PROPN
ejpam-5140	125	9	k1)u3	k1)u3	PROPN
ejpam-5140	125	10	(	(	PUNCT
ejpam-5140	125	11	k	k	PROPN
ejpam-5140	125	12	−	−	PROPN
ejpam-5140	125	13	k2	k2	PROPN
ejpam-5140	125	14	)	)	PUNCT
ejpam-5140	126	1	+	+	PUNCT
ejpam-5140	127	1	u2(k	u2(k	NOUN
ejpam-5140	127	2	)	)	PUNCT
ejpam-5140	127	3	−	−	PROPN
ejpam-5140	128	1	u1(k	u1(k	PROPN
ejpam-5140	128	2	)	)	PUNCT
ejpam-5140	128	3			PROPN
ejpam-5140	128	4	u3(k	u3(k	X
ejpam-5140	129	1	+	+	NOUN
ejpam-5140	129	2	1	1	X
ejpam-5140	129	3	)	)	PUNCT
ejpam-5140	129	4	=	=	SYM
ejpam-5140	130	1	1	1	NUM
ejpam-5140	130	2	k	k	X
ejpam-5140	130	3	+	+	PROPN
ejpam-5140	130	4	1	1	NUM
ejpam-5140	130	5	u4(k	u4(k	NOUN
ejpam-5140	130	6	)	)	PUNCT
ejpam-5140	130	7	u4(k	u4(k	PROPN
ejpam-5140	131	1	+	+	CCONJ
ejpam-5140	131	2	1	1	X
ejpam-5140	131	3	)	)	PUNCT
ejpam-5140	131	4	=	=	SYM
ejpam-5140	131	5	1	1	NUM
ejpam-5140	131	6	k	k	NOUN
ejpam-5140	131	7	+	+	NUM
ejpam-5140	131	8	1	1	NUM
ejpam-5140	131	9	,	,	PUNCT
ejpam-5140	131	10	1.546	1.546	NUM
ejpam-5140	131	11	k∑	k∑	VERB
ejpam-5140	132	1	k2=0	k2=0	PROPN
ejpam-5140	132	2	k2∑	k2∑	PROPN
ejpam-5140	133	1	k1=0	k1=0	PROPN
ejpam-5140	133	2	u4	u4	PROPN
ejpam-5140	133	3	(	(	PUNCT
ejpam-5140	133	4	k1)u1	k1)u1	PROPN
ejpam-5140	133	5	(	(	PUNCT
ejpam-5140	133	6	k2	k2	PROPN
ejpam-5140	133	7	−	−	PROPN
ejpam-5140	133	8	k1)u1	k1)u1	PROPN
ejpam-5140	133	9	(	(	PUNCT
ejpam-5140	133	10	k	k	PROPN
ejpam-5140	133	11	−	−	PROPN
ejpam-5140	133	12	k2	k2	PROPN
ejpam-5140	133	13	)	)	PUNCT
ejpam-5140	133	14	+	+	NUM
ejpam-5140	133	15	1.551	1.551	NUM
ejpam-5140	133	16	k∑	k∑	NOUN
ejpam-5140	133	17	k2=0	k2=0	PROPN
ejpam-5140	134	1	k2∑	k2∑	PROPN
ejpam-5140	135	1	k1=0	k1=0	PROPN
ejpam-5140	135	2	u4	u4	PROPN
ejpam-5140	135	3	(	(	PUNCT
ejpam-5140	135	4	k1)u3	k1)u3	PROPN
ejpam-5140	135	5	(	(	PUNCT
ejpam-5140	135	6	k2	k2	PROPN
ejpam-5140	135	7	−	−	PROPN
ejpam-5140	135	8	k1)u3	k1)u3	PROPN
ejpam-5140	135	9	(	(	PUNCT
ejpam-5140	135	10	k	k	PROPN
ejpam-5140	135	11	−	−	PROPN
ejpam-5140	135	12	k2	k2	PROPN
ejpam-5140	135	13	)	)	PUNCT
ejpam-5140	135	14	−	−	PROPN
ejpam-5140	135	15	u4(k	u4(k	PROPN
ejpam-5140	135	16	)	)	PUNCT
ejpam-5140	135	17	−	−	ADP
ejpam-5140	135	18	u3(k	u3(k	X
ejpam-5140	135	19	)	)	PUNCT
ejpam-5140	135	20			PROPN
ejpam-5140	135	21	(	(	PUNCT
ejpam-5140	135	22	16	16	NUM
ejpam-5140	135	23	)	)	PUNCT
ejpam-5140	135	24	where	where	SCONJ
ejpam-5140	135	25	u1(k	u1(k	NOUN
ejpam-5140	135	26	)	)	PUNCT
ejpam-5140	135	27	,	,	PUNCT
ejpam-5140	135	28	u2(k	u2(k	NOUN
ejpam-5140	135	29	)	)	PUNCT
ejpam-5140	135	30	,	,	PUNCT
ejpam-5140	135	31	u3(k	u3(k	NOUN
ejpam-5140	135	32	)	)	PUNCT
ejpam-5140	135	33	and	and	CCONJ
ejpam-5140	135	34	u4(k	u4(k	PROPN
ejpam-5140	135	35	)	)	PUNCT
ejpam-5140	135	36	are	be	AUX
ejpam-5140	135	37	the	the	DET
ejpam-5140	135	38	differential	differential	NOUN
ejpam-5140	135	39	transforms	transform	NOUN
ejpam-5140	135	40	of	of	ADP
ejpam-5140	135	41	u1	u1	NOUN
ejpam-5140	135	42	,	,	PUNCT
ejpam-5140	135	43	u2	u2	NOUN
ejpam-5140	135	44	,	,	PUNCT
ejpam-5140	135	45	u3	u3	NOUN
ejpam-5140	135	46	and	and	CCONJ
ejpam-5140	135	47	u4	u4	PROPN
ejpam-5140	135	48	,	,	PUNCT
ejpam-5140	135	49	respectively	respectively	ADV
ejpam-5140	135	50	.	.	PUNCT
ejpam-5140	136	1	the	the	DET
ejpam-5140	136	2	dt	dt	NOUN
ejpam-5140	136	3	of	of	ADP
ejpam-5140	136	4	the	the	DET
ejpam-5140	136	5	initial	initial	ADJ
ejpam-5140	136	6	conditions	condition	NOUN
ejpam-5140	136	7	are	be	AUX
ejpam-5140	136	8	given	give	VERB
ejpam-5140	136	9	by	by	ADP
ejpam-5140	136	10	u1(0	u1(0	PROPN
ejpam-5140	136	11	)	)	PUNCT
ejpam-5140	136	12	=	=	SYM
ejpam-5140	136	13	1	1	NUM
ejpam-5140	136	14	,	,	PUNCT
ejpam-5140	136	15	u2(0	u2(0	NOUN
ejpam-5140	136	16	)	)	PUNCT
ejpam-5140	136	17	=	=	SYM
ejpam-5140	136	18	0	0	NUM
ejpam-5140	136	19	,	,	PUNCT
ejpam-5140	136	20	u3(0	u3(0	PROPN
ejpam-5140	136	21	)	)	PUNCT
ejpam-5140	136	22	=	=	SYM
ejpam-5140	136	23	1	1	NUM
ejpam-5140	136	24	,	,	PUNCT
ejpam-5140	136	25	and	and	CCONJ
ejpam-5140	136	26	u4(0	u4(0	PROPN
ejpam-5140	136	27	)	)	PUNCT
ejpam-5140	136	28	=	=	NOUN
ejpam-5140	137	1	0	0	X
ejpam-5140	137	2	.	.	PUNCT
ejpam-5140	138	1	in	in	ADP
ejpam-5140	138	2	view	view	NOUN
ejpam-5140	138	3	of	of	ADP
ejpam-5140	138	4	y(t	y(t	NOUN
ejpam-5140	138	5	)	)	PUNCT
ejpam-5140	138	6	=	=	SYM
ejpam-5140	139	1	∑n	∑n	PROPN
ejpam-5140	139	2	k=0	k=0	PROPN
ejpam-5140	139	3	y	y	PROPN
ejpam-5140	139	4	(	(	PUNCT
ejpam-5140	139	5	k	k	NOUN
ejpam-5140	139	6	)	)	PUNCT
ejpam-5140	139	7	(	(	PUNCT
ejpam-5140	139	8	t−	t−	PROPN
ejpam-5140	139	9	t0	t0	PROPN
ejpam-5140	139	10	)	)	PUNCT
ejpam-5140	139	11	n	n	CCONJ
ejpam-5140	139	12	,	,	PUNCT
ejpam-5140	139	13	which	which	PRON
ejpam-5140	139	14	is	be	AUX
ejpam-5140	139	15	called	call	VERB
ejpam-5140	139	16	the	the	DET
ejpam-5140	139	17	differential	differential	ADJ
ejpam-5140	139	18	inverse	inverse	NOUN
ejpam-5140	139	19	transform	transform	NOUN
ejpam-5140	139	20	,	,	PUNCT
ejpam-5140	139	21	dtm	dtm	PROPN
ejpam-5140	139	22	series	series	NOUN
ejpam-5140	139	23	solution	solution	NOUN
ejpam-5140	139	24	for	for	ADP
ejpam-5140	139	25	eqs	eqs	PROPN
ejpam-5140	139	26	.	.	PUNCT
ejpam-5140	140	1	(	(	PUNCT
ejpam-5140	140	2	7)-(8	7)-(8	NOUN
ejpam-5140	140	3	)	)	PUNCT
ejpam-5140	140	4	can	can	AUX
ejpam-5140	140	5	be	be	AUX
ejpam-5140	140	6	obtained	obtain	VERB
ejpam-5140	140	7	as	as	ADP
ejpam-5140	140	8	,	,	PUNCT
ejpam-5140	140	9	u1(t	u1(t	PROPN
ejpam-5140	140	10	)	)	PUNCT
ejpam-5140	140	11	=	=	SYM
ejpam-5140	141	1	n∑	n∑	PROPN
ejpam-5140	141	2	n=0	n=0	X
ejpam-5140	141	3	u1(n)t	u1(n)t	NUM
ejpam-5140	141	4	n	n	NOUN
ejpam-5140	141	5	,	,	PUNCT
ejpam-5140	141	6	u2(t	u2(t	PROPN
ejpam-5140	141	7	)	)	PUNCT
ejpam-5140	141	8	=	=	SYM
ejpam-5140	142	1	n∑	n∑	NOUN
ejpam-5140	142	2	n=0	n=0	NUM
ejpam-5140	142	3	u2(n)t	u2(n)t	NOUN
ejpam-5140	142	4	n	n	CCONJ
ejpam-5140	142	5	,	,	PUNCT
ejpam-5140	142	6	u3(t	u3(t	NUM
ejpam-5140	142	7	)	)	PUNCT
ejpam-5140	142	8	=	=	SYM
ejpam-5140	143	1	n∑	n∑	NOUN
ejpam-5140	143	2	n=0	n=0	X
ejpam-5140	143	3	u3(n)t	u3(n)t	NOUN
ejpam-5140	143	4	n	n	CCONJ
ejpam-5140	143	5	,	,	PUNCT
ejpam-5140	143	6	u4(t	u4(t	ADJ
ejpam-5140	143	7	)	)	PUNCT
ejpam-5140	143	8	=	=	SYM
ejpam-5140	144	1	n∑	n∑	ADJ
ejpam-5140	144	2	n=0	n=0	NUM
ejpam-5140	144	3	u4(n)t	u4(n)t	ADJ
ejpam-5140	144	4	n.	n.	NOUN
ejpam-5140	144	5	(	(	PUNCT
ejpam-5140	144	6	17	17	NUM
ejpam-5140	144	7	)	)	PUNCT
ejpam-5140	144	8	now	now	ADV
ejpam-5140	144	9	,	,	PUNCT
ejpam-5140	144	10	according	accord	VERB
ejpam-5140	144	11	to	to	ADP
ejpam-5140	144	12	the	the	DET
ejpam-5140	144	13	ms	ms	PROPN
ejpam-5140	144	14	-	-	PUNCT
ejpam-5140	144	15	dtm	dtm	PROPN
ejpam-5140	144	16	,	,	PUNCT
ejpam-5140	144	17	taking	take	VERB
ejpam-5140	144	18	n	n	X
ejpam-5140	144	19	=	=	SYM
ejpam-5140	144	20	k.m	k.m	PROPN
ejpam-5140	144	21	,	,	PUNCT
ejpam-5140	144	22	the	the	DET
ejpam-5140	144	23	series	series	NOUN
ejpam-5140	144	24	solution	solution	NOUN
ejpam-5140	144	25	for	for	ADP
ejpam-5140	144	26	eqs	eqs	PROPN
ejpam-5140	144	27	.	.	PUNCT
ejpam-5140	144	28	(	(	PUNCT
ejpam-5140	144	29	7)-(8	7)-(8	NOUN
ejpam-5140	144	30	)	)	PUNCT
ejpam-5140	144	31	is	be	AUX
ejpam-5140	144	32	given	give	VERB
ejpam-5140	144	33	by	by	ADP
ejpam-5140	144	34	,	,	PUNCT
ejpam-5140	144	35	u1(t	u1(t	PROPN
ejpam-5140	144	36	)	)	PUNCT
ejpam-5140	144	37	=	=	SYM
ejpam-5140	144	38			PROPN
ejpam-5140	144	39	∑k	∑k	PROPN
ejpam-5140	144	40	n=0	n=0	NUM
ejpam-5140	144	41	u11(n)t	u11(n)t	NOUN
ejpam-5140	144	42	n	n	CCONJ
ejpam-5140	144	43	,	,	PUNCT
ejpam-5140	144	44	t	t	PROPN
ejpam-5140	144	45	∈	∈	PROPN
ejpam-5140	145	1	[	[	X
ejpam-5140	145	2	0	0	NUM
ejpam-5140	145	3	,	,	PUNCT
ejpam-5140	145	4	t1]∑k	t1]∑k	NOUN
ejpam-5140	145	5	n=0	n=0	ADV
ejpam-5140	145	6	u21(n)t	u21(n)t	PROPN
ejpam-5140	145	7	n	n	NOUN
ejpam-5140	145	8	,	,	PUNCT
ejpam-5140	145	9	t	t	PROPN
ejpam-5140	145	10	∈	∈	PROPN
ejpam-5140	146	1	[	[	X
ejpam-5140	146	2	t1	t1	NOUN
ejpam-5140	146	3	,	,	PUNCT
ejpam-5140	146	4	t2	t2	NOUN
ejpam-5140	146	5	]	]	PUNCT
ejpam-5140	146	6	·	·	PUNCT
ejpam-5140	146	7	·	·	PUNCT
ejpam-5140	146	8	∑k	∑k	PROPN
ejpam-5140	146	9	n=0	n=0	SYM
ejpam-5140	146	10	um1(n)t	um1(n)t	NOUN
ejpam-5140	146	11	n	n	NUM
ejpam-5140	146	12	,	,	PUNCT
ejpam-5140	146	13	t	t	PROPN
ejpam-5140	146	14	∈	∈	PROPN
ejpam-5140	147	1	[	[	X
ejpam-5140	147	2	tm−1	tm−1	NOUN
ejpam-5140	147	3	,	,	PUNCT
ejpam-5140	147	4	tm	tm	NOUN
ejpam-5140	147	5	]	]	X
ejpam-5140	147	6	(	(	PUNCT
ejpam-5140	147	7	18	18	NUM
ejpam-5140	147	8	)	)	PUNCT
ejpam-5140	148	1	j.	j.	PROPN
ejpam-5140	148	2	asad	asad	PROPN
ejpam-5140	148	3	et	et	PROPN
ejpam-5140	148	4	al	al	PROPN
ejpam-5140	148	5	.	.	PUNCT
ejpam-5140	148	6	/	/	SYM
ejpam-5140	148	7	eur	eur	PROPN
ejpam-5140	148	8	.	.	PUNCT
ejpam-5140	149	1	j.	j.	PROPN
ejpam-5140	149	2	pure	pure	PROPN
ejpam-5140	149	3	appl	appl	PROPN
ejpam-5140	149	4	.	.	PROPN
ejpam-5140	149	5	math	math	PROPN
ejpam-5140	149	6	,	,	PUNCT
ejpam-5140	149	7	17	17	NUM
ejpam-5140	149	8	(	(	PUNCT
ejpam-5140	149	9	2	2	NUM
ejpam-5140	149	10	)	)	PUNCT
ejpam-5140	149	11	(	(	PUNCT
ejpam-5140	149	12	2024	2024	NUM
ejpam-5140	149	13	)	)	PUNCT
ejpam-5140	149	14	,	,	PUNCT
ejpam-5140	149	15	1254	1254	NUM
ejpam-5140	149	16	-	-	SYM
ejpam-5140	149	17	1264	1264	NUM
ejpam-5140	149	18	1260	1260	NUM
ejpam-5140	149	19	u2(t	u2(t	NOUN
ejpam-5140	149	20	)	)	PUNCT
ejpam-5140	149	21	=	=	PUNCT
ejpam-5140	150	1			PROPN
ejpam-5140	150	2	∑k	∑k	PROPN
ejpam-5140	150	3	n=0	n=0	NUM
ejpam-5140	150	4	u12(n)t	u12(n)t	PROPN
ejpam-5140	150	5	n	n	NOUN
ejpam-5140	150	6	,	,	PUNCT
ejpam-5140	150	7	t	t	PROPN
ejpam-5140	150	8	∈	∈	PROPN
ejpam-5140	151	1	[	[	X
ejpam-5140	151	2	0	0	NUM
ejpam-5140	151	3	,	,	PUNCT
ejpam-5140	151	4	t1]∑k	t1]∑k	NOUN
ejpam-5140	151	5	n=0	n=0	ADV
ejpam-5140	151	6	u22(n)t	u22(n)t	NUM
ejpam-5140	151	7	n	n	NOUN
ejpam-5140	151	8	,	,	PUNCT
ejpam-5140	151	9	t	t	PROPN
ejpam-5140	151	10	∈	∈	PROPN
ejpam-5140	152	1	[	[	X
ejpam-5140	152	2	t1	t1	NOUN
ejpam-5140	152	3	,	,	PUNCT
ejpam-5140	152	4	t2	t2	NOUN
ejpam-5140	152	5	]	]	PUNCT
ejpam-5140	152	6	·	·	PUNCT
ejpam-5140	152	7	·	·	PUNCT
ejpam-5140	152	8	∑k	∑k	PROPN
ejpam-5140	152	9	n=0	n=0	NUM
ejpam-5140	152	10	um2(n)t	um2(n)t	PROPN
ejpam-5140	152	11	n	n	NUM
ejpam-5140	152	12	,	,	PUNCT
ejpam-5140	152	13	t	t	PROPN
ejpam-5140	152	14	∈	∈	PROPN
ejpam-5140	153	1	[	[	X
ejpam-5140	153	2	tm−1	tm−1	NOUN
ejpam-5140	153	3	,	,	PUNCT
ejpam-5140	153	4	tm	tm	NOUN
ejpam-5140	153	5	]	]	X
ejpam-5140	153	6	(	(	PUNCT
ejpam-5140	153	7	19	19	NUM
ejpam-5140	153	8	)	)	PUNCT
ejpam-5140	153	9	u3(t	u3(t	NUM
ejpam-5140	153	10	)	)	PUNCT
ejpam-5140	153	11	=	=	SYM
ejpam-5140	153	12			PROPN
ejpam-5140	153	13	∑k	∑k	PROPN
ejpam-5140	153	14	n=0	n=0	NUM
ejpam-5140	153	15	u13(n)t	u13(n)t	PROPN
ejpam-5140	153	16	n	n	NOUN
ejpam-5140	153	17	,	,	PUNCT
ejpam-5140	153	18	t	t	PROPN
ejpam-5140	153	19	∈	∈	PROPN
ejpam-5140	154	1	[	[	X
ejpam-5140	154	2	0	0	NUM
ejpam-5140	154	3	,	,	PUNCT
ejpam-5140	154	4	t1]∑k	t1]∑k	NOUN
ejpam-5140	154	5	n=0	n=0	ADV
ejpam-5140	154	6	u23(n)t	u23(n)t	PROPN
ejpam-5140	154	7	n	n	NUM
ejpam-5140	154	8	,	,	PUNCT
ejpam-5140	154	9	t	t	PROPN
ejpam-5140	154	10	∈	∈	PROPN
ejpam-5140	155	1	[	[	X
ejpam-5140	155	2	t1	t1	NOUN
ejpam-5140	155	3	,	,	PUNCT
ejpam-5140	155	4	t2	t2	PROPN
ejpam-5140	155	5	]	]	PUNCT
ejpam-5140	155	6	...	...	PUNCT
ejpam-5140	155	7	·	·	PUNCT
ejpam-5140	155	8	∑k	∑k	PROPN
ejpam-5140	155	9	n=0	n=0	PUNCT
ejpam-5140	155	10	um3(n)t	um3(n)t	PROPN
ejpam-5140	155	11	n	n	CCONJ
ejpam-5140	155	12	,	,	PUNCT
ejpam-5140	155	13	t	t	PROPN
ejpam-5140	155	14	∈	∈	PROPN
ejpam-5140	156	1	[	[	X
ejpam-5140	156	2	tm−1	tm−1	NOUN
ejpam-5140	156	3	,	,	PUNCT
ejpam-5140	156	4	tm	tm	NOUN
ejpam-5140	156	5	]	]	X
ejpam-5140	156	6	(	(	PUNCT
ejpam-5140	156	7	20	20	NUM
ejpam-5140	156	8	)	)	PUNCT
ejpam-5140	156	9	and	and	CCONJ
ejpam-5140	156	10	u4(t	u4(t	X
ejpam-5140	156	11	)	)	PUNCT
ejpam-5140	156	12	=	=	PUNCT
ejpam-5140	156	13			PROPN
ejpam-5140	156	14	∑k	∑k	PROPN
ejpam-5140	156	15	n=0	n=0	NUM
ejpam-5140	156	16	u14(n)t	u14(n)t	PROPN
ejpam-5140	156	17	n	n	NOUN
ejpam-5140	156	18	,	,	PUNCT
ejpam-5140	156	19	t	t	PROPN
ejpam-5140	156	20	∈	∈	PROPN
ejpam-5140	157	1	[	[	X
ejpam-5140	157	2	0	0	NUM
ejpam-5140	157	3	,	,	PUNCT
ejpam-5140	157	4	t1]∑k	t1]∑k	NOUN
ejpam-5140	157	5	n=0	n=0	SYM
ejpam-5140	157	6	u24(n)t	u24(n)t	NOUN
ejpam-5140	157	7	n	n	CCONJ
ejpam-5140	157	8	,	,	PUNCT
ejpam-5140	157	9	t	t	PROPN
ejpam-5140	157	10	∈	∈	PROPN
ejpam-5140	158	1	[	[	X
ejpam-5140	158	2	t1	t1	NOUN
ejpam-5140	158	3	,	,	PUNCT
ejpam-5140	158	4	t2	t2	PROPN
ejpam-5140	158	5	]	]	PUNCT
ejpam-5140	158	6	...	...	PUNCT
ejpam-5140	158	7	·	·	PUNCT
ejpam-5140	158	8	∑k	∑k	PROPN
ejpam-5140	158	9	n=0	n=0	PUNCT
ejpam-5140	158	10	um4(n)t	um4(n)t	PROPN
ejpam-5140	158	11	n	n	CCONJ
ejpam-5140	158	12	,	,	PUNCT
ejpam-5140	158	13	t	t	PROPN
ejpam-5140	158	14	∈	∈	PROPN
ejpam-5140	159	1	[	[	X
ejpam-5140	159	2	tm−1	tm−1	NOUN
ejpam-5140	159	3	,	,	PUNCT
ejpam-5140	159	4	tm	tm	NOUN
ejpam-5140	159	5	]	]	X
ejpam-5140	159	6	(	(	PUNCT
ejpam-5140	159	7	21	21	NUM
ejpam-5140	159	8	)	)	PUNCT
ejpam-5140	159	9	where	where	SCONJ
ejpam-5140	159	10	un1	un1	PROPN
ejpam-5140	159	11	,	,	PUNCT
ejpam-5140	159	12	un2	un2	NOUN
ejpam-5140	159	13	,	,	PUNCT
ejpam-5140	159	14	un3	un3	NOUN
ejpam-5140	159	15	and	and	CCONJ
ejpam-5140	159	16	un4	un4	NOUN
ejpam-5140	159	17	,	,	PUNCT
ejpam-5140	159	18	for	for	ADP
ejpam-5140	159	19	n	n	NOUN
ejpam-5140	159	20	=	=	SYM
ejpam-5140	159	21	1	1	NUM
ejpam-5140	159	22	,	,	PUNCT
ejpam-5140	159	23	2	2	NUM
ejpam-5140	159	24	,	,	PUNCT
ejpam-5140	159	25	.	.	PUNCT
ejpam-5140	159	26	.	.	PUNCT
ejpam-5140	159	27	.	.	PUNCT
ejpam-5140	160	1	,	,	PUNCT
ejpam-5140	160	2	m	m	VERB
ejpam-5140	160	3	,	,	PUNCT
ejpam-5140	160	4	satisfy	satisfy	VERB
ejpam-5140	160	5	the	the	DET
ejpam-5140	160	6	following	follow	VERB
ejpam-5140	160	7	recurrence	recurrence	NOUN
ejpam-5140	160	8	relations	relation	NOUN
ejpam-5140	160	9	,	,	PUNCT
ejpam-5140	160	10	un1(k	un1(k	PROPN
ejpam-5140	160	11	+	+	NOUN
ejpam-5140	160	12	1	1	X
ejpam-5140	160	13	)	)	PUNCT
ejpam-5140	160	14	=	=	SYM
ejpam-5140	161	1	1	1	NUM
ejpam-5140	161	2	k	k	X
ejpam-5140	161	3	+	+	CCONJ
ejpam-5140	161	4	1	1	NUM
ejpam-5140	161	5	un2(k	un2(k	NOUN
ejpam-5140	161	6	)	)	PUNCT
ejpam-5140	161	7	,	,	PUNCT
ejpam-5140	161	8	un2(k	un2(k	PROPN
ejpam-5140	161	9	+	+	NOUN
ejpam-5140	161	10	1	1	NUM
ejpam-5140	161	11	)	)	PUNCT
ejpam-5140	161	12	=	=	SYM
ejpam-5140	162	1	1	1	NUM
ejpam-5140	162	2	k	k	PROPN
ejpam-5140	162	3	+	+	PROPN
ejpam-5140	162	4	1−1.546	1−1.546	NUM
ejpam-5140	162	5	k∑	k∑	NOUN
ejpam-5140	162	6	k2=0	k2=0	PROPN
ejpam-5140	162	7	k2∑	k2∑	PROPN
ejpam-5140	163	1	k1=0	k1=0	PROPN
ejpam-5140	163	2	un2	un2	NOUN
ejpam-5140	163	3	(	(	PUNCT
ejpam-5140	163	4	k1)un1	k1)un1	X
ejpam-5140	163	5	(	(	PUNCT
ejpam-5140	163	6	k2	k2	PROPN
ejpam-5140	163	7	−	−	PROPN
ejpam-5140	163	8	k1)un1	k1)un1	NUM
ejpam-5140	163	9	(	(	PUNCT
ejpam-5140	163	10	k	k	NOUN
ejpam-5140	163	11	−	−	PROPN
ejpam-5140	163	12	k2	k2	PROPN
ejpam-5140	163	13	)	)	PUNCT
ejpam-5140	163	14	−	−	PROPN
ejpam-5140	163	15	1.551	1.551	NUM
ejpam-5140	163	16	k∑	k∑	NOUN
ejpam-5140	163	17	k2=0	k2=0	PROPN
ejpam-5140	164	1	k2∑	k2∑	PROPN
ejpam-5140	164	2	k1=0	k1=0	PROPN
ejpam-5140	164	3	un2	un2	PROPN
ejpam-5140	164	4	(	(	PUNCT
ejpam-5140	164	5	k1)un3	k1)un3	X
ejpam-5140	164	6	(	(	PUNCT
ejpam-5140	164	7	k2	k2	PROPN
ejpam-5140	164	8	−	−	PROPN
ejpam-5140	164	9	k1)un3	k1)un3	PROPN
ejpam-5140	164	10	(	(	PUNCT
ejpam-5140	164	11	k	k	PROPN
ejpam-5140	164	12	−	−	PROPN
ejpam-5140	164	13	k2	k2	PROPN
ejpam-5140	164	14	)	)	PUNCT
ejpam-5140	164	15	+	+	SYM
ejpam-5140	164	16	un2(k	un2(k	PROPN
ejpam-5140	164	17	)	)	PUNCT
ejpam-5140	164	18	−	−	PROPN
ejpam-5140	165	1	un1(k	un1(k	PROPN
ejpam-5140	165	2	)	)	PUNCT
ejpam-5140	165	3			PROPN
ejpam-5140	166	1	un3(k	un3(k	PROPN
ejpam-5140	167	1	+	+	NOUN
ejpam-5140	167	2	1	1	X
ejpam-5140	167	3	)	)	PUNCT
ejpam-5140	167	4	=	=	SYM
ejpam-5140	168	1	1	1	NUM
ejpam-5140	168	2	k	k	X
ejpam-5140	168	3	+	+	CCONJ
ejpam-5140	168	4	1	1	NUM
ejpam-5140	168	5	un4(k	un4(k	NOUN
ejpam-5140	168	6	)	)	PUNCT
ejpam-5140	168	7	,	,	PUNCT
ejpam-5140	168	8	u4(k	u4(k	PROPN
ejpam-5140	169	1	+	+	CCONJ
ejpam-5140	169	2	1	1	X
ejpam-5140	169	3	)	)	PUNCT
ejpam-5140	169	4	=	=	SYM
ejpam-5140	169	5	1	1	NUM
ejpam-5140	169	6	k	k	NOUN
ejpam-5140	169	7	+	+	PROPN
ejpam-5140	169	8	11.546	11.546	PROPN
ejpam-5140	169	9	k∑	k∑	NOUN
ejpam-5140	170	1	k2=0	k2=0	PROPN
ejpam-5140	171	1	k2∑	k2∑	PROPN
ejpam-5140	172	1	k1=0	k1=0	PROPN
ejpam-5140	172	2	un4	un4	NOUN
ejpam-5140	172	3	(	(	PUNCT
ejpam-5140	172	4	k1)un1	k1)un1	PROPN
ejpam-5140	172	5	(	(	PUNCT
ejpam-5140	172	6	k2	k2	PROPN
ejpam-5140	172	7	−	−	PROPN
ejpam-5140	172	8	k1)un1	k1)un1	NUM
ejpam-5140	172	9	(	(	PUNCT
ejpam-5140	172	10	k	k	NOUN
ejpam-5140	172	11	−	−	PROPN
ejpam-5140	172	12	k2	k2	PROPN
ejpam-5140	172	13	)	)	PUNCT
ejpam-5140	172	14	+	+	NUM
ejpam-5140	172	15	1.551	1.551	NUM
ejpam-5140	172	16	k∑	k∑	NOUN
ejpam-5140	172	17	k2=0	k2=0	PROPN
ejpam-5140	173	1	k2∑	k2∑	PROPN
ejpam-5140	173	2	k1=0	k1=0	PROPN
ejpam-5140	173	3	un4	un4	NOUN
ejpam-5140	173	4	(	(	PUNCT
ejpam-5140	173	5	k1)un3	k1)un3	X
ejpam-5140	173	6	(	(	PUNCT
ejpam-5140	173	7	k2	k2	PROPN
ejpam-5140	173	8	−	−	PROPN
ejpam-5140	173	9	k1)un3	k1)un3	PROPN
ejpam-5140	173	10	(	(	PUNCT
ejpam-5140	173	11	k	k	PROPN
ejpam-5140	173	12	−	−	PROPN
ejpam-5140	173	13	k2	k2	PROPN
ejpam-5140	173	14	)	)	PUNCT
ejpam-5140	173	15	−	−	PROPN
ejpam-5140	173	16	un4(k	un4(k	PROPN
ejpam-5140	173	17	)	)	PUNCT
ejpam-5140	173	18	−	−	PROPN
ejpam-5140	174	1	un3(k	un3(k	SYM
ejpam-5140	174	2	)	)	PUNCT
ejpam-5140	174	3			PROPN
ejpam-5140	174	4	(	(	PUNCT
ejpam-5140	174	5	22	22	NUM
ejpam-5140	174	6	)	)	PUNCT
ejpam-5140	174	7	such	such	ADJ
ejpam-5140	174	8	that	that	SCONJ
ejpam-5140	174	9	un1(0	un1(0	NOUN
ejpam-5140	174	10	)	)	PUNCT
ejpam-5140	174	11	=	=	SYM
ejpam-5140	174	12	u(n−1)1(0	u(n−1)1(0	PROPN
ejpam-5140	174	13	)	)	PUNCT
ejpam-5140	174	14	,	,	PUNCT
ejpam-5140	174	15	un2(0	un2(0	NOUN
ejpam-5140	174	16	)	)	PUNCT
ejpam-5140	174	17	=	=	SYM
ejpam-5140	174	18	u(n−1)2(0	u(n−1)2(0	PROPN
ejpam-5140	174	19	)	)	PUNCT
ejpam-5140	174	20	,	,	PUNCT
ejpam-5140	174	21	un3(0	un3(0	X
ejpam-5140	174	22	)	)	PUNCT
ejpam-5140	174	23	=	=	SYM
ejpam-5140	174	24	u(n−1)3(0	u(n−1)3(0	NUM
ejpam-5140	174	25	)	)	PUNCT
ejpam-5140	174	26	and	and	CCONJ
ejpam-5140	174	27	un4(0	un4(0	NOUN
ejpam-5140	174	28	)	)	PUNCT
ejpam-5140	174	29	=	=	SYM
ejpam-5140	174	30	u(n−1)4(0	u(n−1)4(0	PROPN
ejpam-5140	174	31	)	)	PUNCT
ejpam-5140	174	32	.	.	PUNCT
ejpam-5140	175	1	j.	j.	PROPN
ejpam-5140	175	2	asad	asad	PROPN
ejpam-5140	175	3	et	et	PROPN
ejpam-5140	175	4	al	al	PROPN
ejpam-5140	175	5	.	.	PUNCT
ejpam-5140	175	6	/	/	SYM
ejpam-5140	175	7	eur	eur	PROPN
ejpam-5140	175	8	.	.	PUNCT
ejpam-5140	176	1	j.	j.	PROPN
ejpam-5140	176	2	pure	pure	PROPN
ejpam-5140	176	3	appl	appl	PROPN
ejpam-5140	176	4	.	.	PROPN
ejpam-5140	176	5	math	math	PROPN
ejpam-5140	176	6	,	,	PUNCT
ejpam-5140	176	7	17	17	NUM
ejpam-5140	176	8	(	(	PUNCT
ejpam-5140	176	9	2	2	NUM
ejpam-5140	176	10	)	)	PUNCT
ejpam-5140	176	11	(	(	PUNCT
ejpam-5140	176	12	2024	2024	NUM
ejpam-5140	176	13	)	)	PUNCT
ejpam-5140	176	14	,	,	PUNCT
ejpam-5140	176	15	1254	1254	NUM
ejpam-5140	176	16	-	-	SYM
ejpam-5140	176	17	1264	1264	NUM
ejpam-5140	176	18	1261	1261	NUM
ejpam-5140	176	19	finally	finally	ADV
ejpam-5140	176	20	,	,	PUNCT
ejpam-5140	176	21	if	if	SCONJ
ejpam-5140	176	22	we	we	PRON
ejpam-5140	176	23	start	start	VERB
ejpam-5140	176	24	with	with	ADP
ejpam-5140	176	25	u01(0	u01(0	PROPN
ejpam-5140	176	26	)	)	PUNCT
ejpam-5140	176	27	=	=	SYM
ejpam-5140	176	28	1	1	NUM
ejpam-5140	176	29	,	,	PUNCT
ejpam-5140	176	30	u02(0	u02(0	NOUN
ejpam-5140	176	31	)	)	PUNCT
ejpam-5140	176	32	=	=	SYM
ejpam-5140	176	33	0	0	NUM
ejpam-5140	176	34	,	,	PUNCT
ejpam-5140	176	35	u03(0	u03(0	PROPN
ejpam-5140	176	36	)	)	PUNCT
ejpam-5140	176	37	=	=	SYM
ejpam-5140	176	38	1	1	NUM
ejpam-5140	176	39	and	and	CCONJ
ejpam-5140	176	40	u04(0	u04(0	NOUN
ejpam-5140	176	41	)	)	PUNCT
ejpam-5140	176	42	=	=	SYM
ejpam-5140	176	43	0	0	NUM
ejpam-5140	176	44	,	,	PUNCT
ejpam-5140	176	45	using	use	VERB
ejpam-5140	176	46	the	the	DET
ejpam-5140	176	47	recurrence	recurrence	NOUN
ejpam-5140	176	48	relations	relation	NOUN
ejpam-5140	176	49	given	give	VERB
ejpam-5140	176	50	in	in	ADP
ejpam-5140	176	51	eq	eq	ADP
ejpam-5140	176	52	.	.	PUNCT
ejpam-5140	177	1	(	(	PUNCT
ejpam-5140	177	2	11	11	NUM
ejpam-5140	177	3	)	)	PUNCT
ejpam-5140	177	4	,	,	PUNCT
ejpam-5140	177	5	then	then	ADV
ejpam-5140	177	6	we	we	PRON
ejpam-5140	177	7	can	can	AUX
ejpam-5140	177	8	obtain	obtain	VERB
ejpam-5140	177	9	the	the	DET
ejpam-5140	177	10	ms	ms	PROPN
ejpam-5140	177	11	-	-	PUNCT
ejpam-5140	177	12	dtm	dtm	PROPN
ejpam-5140	177	13	solution	solution	NOUN
ejpam-5140	177	14	given	give	VERB
ejpam-5140	177	15	in	in	ADP
ejpam-5140	177	16	eqs	eqs	PROPN
ejpam-5140	177	17	.	.	PUNCT
ejpam-5140	178	1	(	(	PUNCT
ejpam-5140	178	2	7	7	NUM
ejpam-5140	178	3	)	)	PUNCT
ejpam-5140	178	4	,	,	PUNCT
ejpam-5140	178	5	(	(	PUNCT
ejpam-5140	178	6	8)	8)	NUM
ejpam-5140	178	7	,	,	PUNCT
ejpam-5140	178	8	(	(	PUNCT
ejpam-5140	178	9	9	9	NUM
ejpam-5140	178	10	)	)	PUNCT
ejpam-5140	178	11	and	and	CCONJ
ejpam-5140	178	12	(	(	PUNCT
ejpam-5140	178	13	10	10	NUM
ejpam-5140	178	14	)	)	PUNCT
ejpam-5140	178	15	.	.	PUNCT
ejpam-5140	179	1	figure	figure	NOUN
ejpam-5140	179	2	3	3	NUM
ejpam-5140	179	3	shows	show	VERB
ejpam-5140	179	4	the	the	DET
ejpam-5140	179	5	phase	phase	NOUN
ejpam-5140	179	6	-	-	PUNCT
ejpam-5140	179	7	portrait	portrait	NOUN
ejpam-5140	179	8	as	as	SCONJ
ejpam-5140	179	9	obtained	obtain	VERB
ejpam-5140	179	10	from	from	ADP
ejpam-5140	179	11	the	the	DET
ejpam-5140	179	12	approximate	approximate	ADJ
ejpam-5140	179	13	solutions	solution	NOUN
ejpam-5140	179	14	for	for	ADP
ejpam-5140	179	15	eqs	eqs	PROPN
ejpam-5140	179	16	.	.	PUNCT
ejpam-5140	180	1	(	(	PUNCT
ejpam-5140	180	2	7)-(8	7)-(8	NOUN
ejpam-5140	180	3	)	)	PUNCT
ejpam-5140	180	4	obtained	obtain	VERB
ejpam-5140	180	5	using	use	VERB
ejpam-5140	180	6	ms	ms	PROPN
ejpam-5140	180	7	-	-	PUNCT
ejpam-5140	180	8	dtm	dtm	PROPN
ejpam-5140	180	9	.	.	PROPN
ejpam-5140	181	1	from	from	ADP
ejpam-5140	181	2	figure	figure	NOUN
ejpam-5140	181	3	2	2	NUM
ejpam-5140	181	4	(	(	PUNCT
ejpam-5140	181	5	a	a	DET
ejpam-5140	181	6	-	-	PUNCT
ejpam-5140	181	7	b	b	NOUN
ejpam-5140	181	8	)	)	PUNCT
ejpam-5140	181	9	and	and	CCONJ
ejpam-5140	181	10	figure	figure	VERB
ejpam-5140	181	11	3	3	NUM
ejpam-5140	181	12	(	(	PUNCT
ejpam-5140	181	13	a	a	PROPN
ejpam-5140	181	14	-	-	PUNCT
ejpam-5140	181	15	b	b	NOUN
ejpam-5140	181	16	)	)	PUNCT
ejpam-5140	181	17	,	,	PUNCT
ejpam-5140	181	18	we	we	PRON
ejpam-5140	181	19	can	can	AUX
ejpam-5140	181	20	observe	observe	VERB
ejpam-5140	181	21	that	that	SCONJ
ejpam-5140	181	22	the	the	DET
ejpam-5140	181	23	phase	phase	NOUN
ejpam-5140	181	24	-	-	PUNCT
ejpam-5140	181	25	portrait	portrait	NOUN
ejpam-5140	181	26	trajectories	trajectory	NOUN
ejpam-5140	181	27	obtained	obtain	VERB
ejpam-5140	181	28	using	use	VERB
ejpam-5140	181	29	msdtm	msdtm	NOUN
ejpam-5140	181	30	are	be	AUX
ejpam-5140	181	31	in	in	ADP
ejpam-5140	181	32	high	high	ADJ
ejpam-5140	181	33	agreement	agreement	NOUN
ejpam-5140	181	34	with	with	ADP
ejpam-5140	181	35	the	the	DET
ejpam-5140	181	36	phase	phase	NOUN
ejpam-5140	181	37	-	-	PUNCT
ejpam-5140	181	38	portrait	portrait	NOUN
ejpam-5140	181	39	trajectories	trajectory	NOUN
ejpam-5140	181	40	obtained	obtain	VERB
ejpam-5140	181	41	using	use	VERB
ejpam-5140	181	42	fourthorder	fourthorder	NOUN
ejpam-5140	181	43	rungekutta	rungekutta	NOUN
ejpam-5140	181	44	method	method	NOUN
ejpam-5140	181	45	.	.	PUNCT
ejpam-5140	182	1	figure	figure	VERB
ejpam-5140	182	2	3	3	NUM
ejpam-5140	182	3	:	:	PUNCT
ejpam-5140	182	4	phase	phase	NOUN
ejpam-5140	182	5	portrait	portrait	NOUN
ejpam-5140	182	6	of	of	ADP
ejpam-5140	182	7	system	system	NOUN
ejpam-5140	182	8	(	(	PUNCT
ejpam-5140	182	9	7	7	NUM
ejpam-5140	182	10	&	&	CCONJ
ejpam-5140	182	11	8)	8)	NUM
ejpam-5140	182	12	:	:	PUNCT
ejpam-5140	182	13	(	(	PUNCT
ejpam-5140	182	14	a	a	X
ejpam-5140	182	15	)	)	PUNCT
ejpam-5140	182	16	x(t	x(t	PROPN
ejpam-5140	182	17	)	)	PUNCT
ejpam-5140	182	18	vs	vs	ADP
ejpam-5140	182	19	x′(t	x′(t	PROPN
ejpam-5140	182	20	)	)	PUNCT
ejpam-5140	182	21	,	,	PUNCT
ejpam-5140	182	22	and	and	CCONJ
ejpam-5140	182	23	(	(	PUNCT
ejpam-5140	182	24	b	b	NOUN
ejpam-5140	182	25	)	)	PUNCT
ejpam-5140	182	26	y(t	y(t	NUM
ejpam-5140	182	27	)	)	PUNCT
ejpam-5140	182	28	vs	vs	ADP
ejpam-5140	182	29	y′(t	y′(t	NOUN
ejpam-5140	182	30	)	)	PUNCT
ejpam-5140	182	31	using	use	VERB
ejpam-5140	182	32	msdtm	msdtm	NOUN
ejpam-5140	182	33	approach	approach	NOUN
ejpam-5140	182	34	.	.	PUNCT
ejpam-5140	183	1	figure	figure	NOUN
ejpam-5140	183	2	4	4	NUM
ejpam-5140	183	3	(	(	PUNCT
ejpam-5140	183	4	a	a	NOUN
ejpam-5140	183	5	-	-	PUNCT
ejpam-5140	183	6	d	d	NOUN
ejpam-5140	183	7	)	)	PUNCT
ejpam-5140	183	8	below	below	ADP
ejpam-5140	183	9	show	show	VERB
ejpam-5140	183	10	the	the	DET
ejpam-5140	183	11	approximate	approximate	ADJ
ejpam-5140	183	12	solutions	solution	NOUN
ejpam-5140	183	13	for	for	ADP
ejpam-5140	183	14	eqs	eqs	PROPN
ejpam-5140	183	15	.	.	PUNCT
ejpam-5140	184	1	(	(	PUNCT
ejpam-5140	184	2	7)-(8	7)-(8	NOUN
ejpam-5140	184	3	)	)	PUNCT
ejpam-5140	184	4	obtained	obtain	VERB
ejpam-5140	184	5	using	use	VERB
ejpam-5140	184	6	ms	ms	PROPN
ejpam-5140	184	7	-	-	PUNCT
ejpam-5140	184	8	dtm	dtm	PROPN
ejpam-5140	184	9	.	.	PROPN
ejpam-5140	185	1	one	one	PRON
ejpam-5140	185	2	can	can	AUX
ejpam-5140	185	3	see	see	VERB
ejpam-5140	185	4	that	that	SCONJ
ejpam-5140	185	5	there	there	PRON
ejpam-5140	185	6	is	be	VERB
ejpam-5140	185	7	a	a	DET
ejpam-5140	185	8	high	high	ADJ
ejpam-5140	185	9	agreement	agreement	NOUN
ejpam-5140	185	10	with	with	ADP
ejpam-5140	185	11	the	the	DET
ejpam-5140	185	12	time	time	NOUN
ejpam-5140	185	13	-	-	PUNCT
ejpam-5140	185	14	series	series	NOUN
ejpam-5140	185	15	of	of	ADP
ejpam-5140	185	16	the	the	DET
ejpam-5140	185	17	dynamical	dynamical	ADJ
ejpam-5140	185	18	variables	variable	NOUN
ejpam-5140	185	19	obtained	obtain	VERB
ejpam-5140	185	20	using	use	VERB
ejpam-5140	185	21	fourthorder	fourthorder	NOUN
ejpam-5140	185	22	rungekutta	rungekutta	NOUN
ejpam-5140	185	23	method	method	NOUN
ejpam-5140	185	24	shown	show	VERB
ejpam-5140	185	25	in	in	ADP
ejpam-5140	185	26	figure	figure	NOUN
ejpam-5140	185	27	1	1	NUM
ejpam-5140	185	28	(	(	PUNCT
ejpam-5140	185	29	a	a	NOUN
ejpam-5140	185	30	-	-	PUNCT
ejpam-5140	185	31	d	d	NOUN
ejpam-5140	185	32	)	)	PUNCT
ejpam-5140	185	33	.	.	PUNCT
ejpam-5140	186	1	figure	figure	VERB
ejpam-5140	186	2	4	4	NUM
ejpam-5140	186	3	:	:	PUNCT
ejpam-5140	186	4	simulation	simulation	NOUN
ejpam-5140	186	5	of	of	ADP
ejpam-5140	186	6	system	system	NOUN
ejpam-5140	186	7	(	(	PUNCT
ejpam-5140	186	8	7	7	NUM
ejpam-5140	186	9	&	&	CCONJ
ejpam-5140	186	10	8)	8)	NUM
ejpam-5140	186	11	using	use	VERB
ejpam-5140	186	12	ms	ms	PROPN
ejpam-5140	186	13	-	-	PUNCT
ejpam-5140	186	14	dtm	dtm	PROPN
ejpam-5140	186	15	(	(	PUNCT
ejpam-5140	186	16	a	a	NOUN
ejpam-5140	186	17	)	)	PUNCT
ejpam-5140	186	18	x(t	x(t	PROPN
ejpam-5140	186	19	)	)	PUNCT
ejpam-5140	186	20	vs	vs	ADP
ejpam-5140	186	21	time	time	NOUN
ejpam-5140	186	22	,	,	PUNCT
ejpam-5140	186	23	(	(	PUNCT
ejpam-5140	186	24	b	b	X
ejpam-5140	186	25	)	)	PUNCT
ejpam-5140	186	26	y(t	y(t	NUM
ejpam-5140	186	27	)	)	PUNCT
ejpam-5140	186	28	vs	vs	ADP
ejpam-5140	186	29	time	time	NOUN
ejpam-5140	186	30	(	(	PUNCT
ejpam-5140	186	31	c	c	NOUN
ejpam-5140	186	32	)	)	PUNCT
ejpam-5140	186	33	x′(t	x′(t	NOUN
ejpam-5140	186	34	)	)	PUNCT
ejpam-5140	186	35	vs	vs	ADP
ejpam-5140	186	36	time	time	NOUN
ejpam-5140	186	37	,	,	PUNCT
ejpam-5140	186	38	and	and	CCONJ
ejpam-5140	186	39	(	(	PUNCT
ejpam-5140	186	40	d	d	NOUN
ejpam-5140	186	41	)	)	PUNCT
ejpam-5140	186	42	y′(t	y′(t	NOUN
ejpam-5140	186	43	)	)	PUNCT
ejpam-5140	186	44	vs	vs	ADP
ejpam-5140	186	45	time	time	NOUN
ejpam-5140	186	46	references	reference	NOUN
ejpam-5140	186	47	1262	1262	NUM
ejpam-5140	186	48	5	5	NUM
ejpam-5140	186	49	.	.	PUNCT
ejpam-5140	187	1	conclusion	conclusion	NOUN
ejpam-5140	187	2	van	van	PROPN
ejpam-5140	187	3	der	der	PROPN
ejpam-5140	187	4	pol	pol	PROPN
ejpam-5140	187	5	oscillator	oscillator	NOUN
ejpam-5140	187	6	is	be	AUX
ejpam-5140	187	7	one	one	NUM
ejpam-5140	187	8	of	of	ADP
ejpam-5140	187	9	the	the	DET
ejpam-5140	187	10	paradigms	paradigm	NOUN
ejpam-5140	187	11	of	of	ADP
ejpam-5140	187	12	nonlinear	nonlinear	ADJ
ejpam-5140	187	13	dynamics	dynamic	NOUN
ejpam-5140	187	14	and	and	CCONJ
ejpam-5140	187	15	a	a	DET
ejpam-5140	187	16	common	common	ADJ
ejpam-5140	187	17	model	model	NOUN
ejpam-5140	187	18	for	for	ADP
ejpam-5140	187	19	nonlinear	nonlinear	ADJ
ejpam-5140	187	20	phenomena	phenomenon	NOUN
ejpam-5140	187	21	in	in	ADP
ejpam-5140	187	22	science	science	NOUN
ejpam-5140	187	23	and	and	CCONJ
ejpam-5140	187	24	engineering	engineering	NOUN
ejpam-5140	187	25	.	.	PUNCT
ejpam-5140	188	1	in	in	ADP
ejpam-5140	188	2	this	this	DET
ejpam-5140	188	3	study	study	NOUN
ejpam-5140	188	4	,	,	PUNCT
ejpam-5140	188	5	an	an	DET
ejpam-5140	188	6	algorithm	algorithm	NOUN
ejpam-5140	188	7	for	for	ADP
ejpam-5140	188	8	solving	solve	VERB
ejpam-5140	188	9	a	a	DET
ejpam-5140	188	10	two	two	NUM
ejpam-5140	188	11	-	-	PUNCT
ejpam-5140	188	12	dimensional	dimensional	ADJ
ejpam-5140	188	13	coupled	couple	VERB
ejpam-5140	188	14	van	van	PROPN
ejpam-5140	188	15	der	der	PROPN
ejpam-5140	188	16	pol	pol	PROPN
ejpam-5140	188	17	like	like	ADP
ejpam-5140	188	18	oscillator	oscillator	NOUN
ejpam-5140	188	19	was	be	AUX
ejpam-5140	188	20	introduced	introduce	VERB
ejpam-5140	188	21	via	via	ADP
ejpam-5140	188	22	msdtm	msdtm	PROPN
ejpam-5140	188	23	.	.	PUNCT
ejpam-5140	189	1	a	a	DET
ejpam-5140	189	2	reliable	reliable	ADJ
ejpam-5140	189	3	accuracy	accuracy	NOUN
ejpam-5140	189	4	solution	solution	NOUN
ejpam-5140	189	5	was	be	AUX
ejpam-5140	189	6	obtained	obtain	VERB
ejpam-5140	189	7	via	via	ADP
ejpam-5140	189	8	this	this	DET
ejpam-5140	189	9	algorithm	algorithm	NOUN
ejpam-5140	189	10	.	.	PUNCT
ejpam-5140	190	1	the	the	DET
ejpam-5140	190	2	considered	consider	VERB
ejpam-5140	190	3	twodimensional	twodimensional	ADJ
ejpam-5140	190	4	coupled	couple	VERB
ejpam-5140	190	5	asymmetric	asymmetric	ADJ
ejpam-5140	190	6	van	van	PROPN
ejpam-5140	190	7	der	der	PROPN
ejpam-5140	190	8	pol	pol	PROPN
ejpam-5140	190	9	oscillator	oscillator	NOUN
ejpam-5140	190	10	are	be	AUX
ejpam-5140	190	11	discussed	discuss	VERB
ejpam-5140	190	12	and	and	CCONJ
ejpam-5140	190	13	focused	focus	VERB
ejpam-5140	190	14	it	it	PRON
ejpam-5140	190	15	’s	’	VERB
ejpam-5140	190	16	quasi	quasi	ADJ
ejpam-5140	190	17	analytical	analytical	ADJ
ejpam-5140	190	18	solution	solution	NOUN
ejpam-5140	190	19	of	of	ADP
ejpam-5140	190	20	a	a	DET
ejpam-5140	190	21	coupled	couple	VERB
ejpam-5140	190	22	two	two	NUM
ejpam-5140	190	23	-	-	PUNCT
ejpam-5140	190	24	dimensional	dimensional	ADJ
ejpam-5140	190	25	oscillator	oscillator	NOUN
ejpam-5140	190	26	in	in	ADP
ejpam-5140	190	27	strong	strong	ADJ
ejpam-5140	190	28	coupling	coupling	NOUN
ejpam-5140	190	29	regime	regime	NOUN
ejpam-5140	190	30	ω	ω	PROPN
ejpam-5140	190	31	=	=	PROPN
ejpam-5140	190	32	ε	ε	PROPN
ejpam-5140	190	33	=	=	SYM
ejpam-5140	190	34	1	1	NUM
ejpam-5140	190	35	,	,	PUNCT
ejpam-5140	190	36	α	α	PRON
ejpam-5140	190	37	̸=	̸=	PROPN
ejpam-5140	190	38	β	β	NOUN
ejpam-5140	190	39	.	.	PUNCT
ejpam-5140	191	1	for	for	ADP
ejpam-5140	191	2	α	α	NOUN
ejpam-5140	191	3	=	=	SYM
ejpam-5140	191	4	β	β	X
ejpam-5140	191	5	=	=	SYM
ejpam-5140	191	6	1	1	NUM
ejpam-5140	191	7	,	,	PUNCT
ejpam-5140	191	8	solution	solution	NOUN
ejpam-5140	191	9	is	be	AUX
ejpam-5140	191	10	a	a	DET
ejpam-5140	191	11	sinusoidal	sinusoidal	ADJ
ejpam-5140	191	12	nature	nature	NOUN
ejpam-5140	191	13	having	have	VERB
ejpam-5140	191	14	elliptical	elliptical	ADJ
ejpam-5140	191	15	nature	nature	NOUN
ejpam-5140	191	16	phase	phase	NOUN
ejpam-5140	191	17	portrait	portrait	NOUN
ejpam-5140	191	18	.	.	PUNCT
ejpam-5140	192	1	however	however	ADV
ejpam-5140	192	2	,	,	PUNCT
ejpam-5140	192	3	here	here	ADV
ejpam-5140	192	4	α	α	NOUN
ejpam-5140	192	5	̸=	̸=	PROPN
ejpam-5140	192	6	β	β	SYM
ejpam-5140	192	7	̸=	̸=	PROPN
ejpam-5140	192	8	1	1	NUM
ejpam-5140	192	9	we	we	PRON
ejpam-5140	192	10	get	get	VERB
ejpam-5140	192	11	nearly	nearly	ADV
ejpam-5140	192	12	rectangular	rectangular	ADJ
ejpam-5140	192	13	type	type	NOUN
ejpam-5140	192	14	in	in	ADP
ejpam-5140	192	15	both	both	CCONJ
ejpam-5140	192	16	the	the	DET
ejpam-5140	192	17	cases	case	NOUN
ejpam-5140	192	18	,	,	PUNCT
ejpam-5140	192	19	rectangular	rectangular	ADJ
ejpam-5140	192	20	nature	nature	NOUN
ejpam-5140	192	21	is	be	AUX
ejpam-5140	192	22	asymmetric	asymmetric	ADJ
ejpam-5140	192	23	.	.	PUNCT
ejpam-5140	193	1	similarly	similarly	ADV
ejpam-5140	193	2	,	,	PUNCT
ejpam-5140	193	3	we	we	PRON
ejpam-5140	193	4	also	also	ADV
ejpam-5140	193	5	plot	plot	VERB
ejpam-5140	193	6	displacement	displacement	NOUN
ejpam-5140	193	7	vs	vs	ADP
ejpam-5140	193	8	time	time	NOUN
ejpam-5140	193	9	graph	graph	NOUN
ejpam-5140	193	10	(	(	PUNCT
ejpam-5140	193	11	x	x	X
ejpam-5140	193	12	∼	∼	NOUN
ejpam-5140	193	13	t	t	PROPN
ejpam-5140	193	14	,	,	PUNCT
ejpam-5140	193	15	y	y	PROPN
ejpam-5140	193	16	∼	∼	NOUN
ejpam-5140	193	17	t	t	PROPN
ejpam-5140	193	18	)	)	PUNCT
ejpam-5140	193	19	and	and	CCONJ
ejpam-5140	193	20	velocity	velocity	NOUN
ejpam-5140	193	21	vs	vs	ADP
ejpam-5140	193	22	time	time	NOUN
ejpam-5140	193	23	graph	graph	NOUN
ejpam-5140	193	24	(	(	PUNCT
ejpam-5140	193	25	x′	x′	PROPN
ejpam-5140	193	26	∼	∼	NOUN
ejpam-5140	193	27	t	t	PROPN
ejpam-5140	193	28	,	,	PUNCT
ejpam-5140	193	29	y′	y′	NOUN
ejpam-5140	193	30	∼	∼	NOUN
ejpam-5140	193	31	t	t	NOUN
ejpam-5140	193	32	,	,	PUNCT
ejpam-5140	193	33	)	)	PUNCT
ejpam-5140	193	34	we	we	PRON
ejpam-5140	193	35	believe	believe	VERB
ejpam-5140	193	36	present	present	ADJ
ejpam-5140	193	37	twodimensional	twodimensional	ADJ
ejpam-5140	193	38	van	van	PROPN
ejpam-5140	193	39	der	der	PROPN
ejpam-5140	193	40	pol	pol	NOUN
ejpam-5140	193	41	model	model	NOUN
ejpam-5140	193	42	will	will	AUX
ejpam-5140	193	43	generate	generate	VERB
ejpam-5140	193	44	interest	interest	NOUN
ejpam-5140	193	45	among	among	ADP
ejpam-5140	193	46	people	people	NOUN
ejpam-5140	193	47	to	to	PART
ejpam-5140	193	48	look	look	VERB
ejpam-5140	193	49	into	into	ADP
ejpam-5140	193	50	coupling	couple	VERB
ejpam-5140	193	51	regime	regime	NOUN
ejpam-5140	193	52	.	.	PUNCT
ejpam-5140	194	1	the	the	DET
ejpam-5140	194	2	comparison	comparison	NOUN
ejpam-5140	194	3	between	between	ADP
ejpam-5140	194	4	ms	ms	PROPN
ejpam-5140	194	5	-	-	PUNCT
ejpam-5140	194	6	dtm	dtm	PROPN
ejpam-5140	194	7	solution	solution	NOUN
ejpam-5140	194	8	and	and	CCONJ
ejpam-5140	194	9	the	the	DET
ejpam-5140	194	10	fourth	fourth	ADJ
ejpam-5140	194	11	order	order	NOUN
ejpam-5140	194	12	runge	runge	NOUN
ejpam-5140	194	13	-	-	PUNCT
ejpam-5140	194	14	kutta	kutta	NOUN
ejpam-5140	194	15	method	method	NOUN
ejpam-5140	194	16	are	be	AUX
ejpam-5140	194	17	discussed	discuss	VERB
ejpam-5140	194	18	and	and	CCONJ
ejpam-5140	194	19	given	give	VERB
ejpam-5140	194	20	graphically	graphically	ADV
ejpam-5140	194	21	.	.	PUNCT
ejpam-5140	195	1	the	the	DET
ejpam-5140	195	2	solution	solution	NOUN
ejpam-5140	195	3	via	via	ADP
ejpam-5140	195	4	ms	ms	PROPN
ejpam-5140	195	5	-	-	PUNCT
ejpam-5140	195	6	dtm	dtm	PROPN
ejpam-5140	195	7	is	be	AUX
ejpam-5140	195	8	continuous	continuous	ADJ
ejpam-5140	195	9	on	on	ADP
ejpam-5140	195	10	this	this	DET
ejpam-5140	195	11	domain	domain	NOUN
ejpam-5140	195	12	and	and	CCONJ
ejpam-5140	195	13	analytical	analytical	ADJ
ejpam-5140	195	14	at	at	ADP
ejpam-5140	195	15	each	each	DET
ejpam-5140	195	16	subdomain	subdomain	NOUN
ejpam-5140	195	17	.	.	PUNCT
ejpam-5140	196	1	in	in	ADP
ejpam-5140	196	2	this	this	DET
ejpam-5140	196	3	work	work	NOUN
ejpam-5140	196	4	all	all	DET
ejpam-5140	196	5	calculations	calculation	NOUN
ejpam-5140	196	6	are	be	AUX
ejpam-5140	196	7	made	make	VERB
ejpam-5140	196	8	by	by	ADP
ejpam-5140	196	9	mathematica	mathematica	PROPN
ejpam-5140	196	10	software	software	PROPN
ejpam-5140	196	11	.	.	PUNCT
ejpam-5140	197	1	acknowledgements	acknowledgement	NOUN
ejpam-5140	197	2	taqwa	taqwa	VERB
ejpam-5140	197	3	m.	m.	PROPN
ejpam-5140	197	4	al	al	PROPN
ejpam-5140	197	5	-	-	PUNCT
ejpam-5140	197	6	khader	khader	PROPN
ejpam-5140	197	7	,	,	PUNCT
ejpam-5140	197	8	noorhan	noorhan	ADJ
ejpam-5140	197	9	alshaikh	alshaikh	PROPN
ejpam-5140	197	10	and	and	CCONJ
ejpam-5140	197	11	jihad	jihad	PROPN
ejpam-5140	197	12	asad	asad	PROPN
ejpam-5140	197	13	would	would	AUX
ejpam-5140	197	14	like	like	VERB
ejpam-5140	197	15	to	to	PART
ejpam-5140	197	16	thank	thank	VERB
ejpam-5140	197	17	palestine	palestine	PROPN
ejpam-5140	197	18	technical	technical	PROPN
ejpam-5140	197	19	universitykadoorie	universitykadoorie	PROPN
ejpam-5140	197	20	for	for	ADP
ejpam-5140	197	21	funding	fund	VERB
ejpam-5140	197	22	this	this	DET
ejpam-5140	197	23	research	research	NOUN
ejpam-5140	197	24	financially	financially	ADV
ejpam-5140	197	25	.	.	PUNCT
ejpam-5140	198	1	references	reference	NOUN
ejpam-5140	198	2	[	[	X
ejpam-5140	198	3	1	1	X
ejpam-5140	198	4	]	]	PUNCT
ejpam-5140	198	5	ali	ali	PROPN
ejpam-5140	198	6	al	al	PROPN
ejpam-5140	198	7	-	-	PUNCT
ejpam-5140	198	8	qahtani	qahtani	PROPN
ejpam-5140	198	9	,	,	PUNCT
ejpam-5140	198	10	houari	houari	PROPN
ejpam-5140	198	11	b.	b.	PROPN
ejpam-5140	198	12	khenous	khenous	PROPN
ejpam-5140	198	13	,	,	PUNCT
ejpam-5140	198	14	and	and	CCONJ
ejpam-5140	198	15	shaban	shaban	PROPN
ejpam-5140	198	16	aly	aly	PROPN
ejpam-5140	198	17	.	.	PUNCT
ejpam-5140	199	1	synchronization	synchronization	NOUN
ejpam-5140	199	2	of	of	ADP
ejpam-5140	199	3	impulsive	impulsive	ADJ
ejpam-5140	199	4	real	real	ADJ
ejpam-5140	199	5	and	and	CCONJ
ejpam-5140	199	6	complex	complex	ADJ
ejpam-5140	199	7	van	van	PROPN
ejpam-5140	199	8	der	der	ADJ
ejpam-5140	199	9	pol	pol	PROPN
ejpam-5140	199	10	oscillators	oscillator	NOUN
ejpam-5140	199	11	.	.	PUNCT
ejpam-5140	200	1	applied	apply	VERB
ejpam-5140	200	2	mathematics	mathematic	NOUN
ejpam-5140	200	3	,	,	PUNCT
ejpam-5140	200	4	6:6	6:6	NUM
ejpam-5140	200	5	,	,	PUNCT
ejpam-5140	200	6	2015	2015	NUM
ejpam-5140	200	7	.	.	PUNCT
ejpam-5140	201	1	[	[	X
ejpam-5140	201	2	2	2	NUM
ejpam-5140	201	3	]	]	PUNCT
ejpam-5140	201	4	h	h	NOUN
ejpam-5140	201	5	askari	askari	PROPN
ejpam-5140	201	6	,	,	PUNCT
ejpam-5140	201	7	m	m	VERB
ejpam-5140	201	8	k	k	NOUN
ejpam-5140	201	9	yazdi	yazdi	NOUN
ejpam-5140	201	10	,	,	PUNCT
ejpam-5140	201	11	and	and	CCONJ
ejpam-5140	201	12	z	z	PROPN
ejpam-5140	201	13	saadatnia	saadatnia	PROPN
ejpam-5140	201	14	.	.	PUNCT
ejpam-5140	202	1	frequency	frequency	NOUN
ejpam-5140	202	2	analysis	analysis	NOUN
ejpam-5140	202	3	of	of	ADP
ejpam-5140	202	4	nonlinear	nonlinear	ADJ
ejpam-5140	202	5	oscillators	oscillator	NOUN
ejpam-5140	202	6	with	with	ADP
ejpam-5140	202	7	rational	rational	ADJ
ejpam-5140	202	8	restoring	restore	VERB
ejpam-5140	202	9	force	force	NOUN
ejpam-5140	202	10	via	via	ADP
ejpam-5140	203	1	he	he	PRON
ejpam-5140	203	2	’s	’	VERB
ejpam-5140	203	3	energy	energy	NOUN
ejpam-5140	203	4	balance	balance	NOUN
ejpam-5140	203	5	method	method	NOUN
ejpam-5140	204	1	and	and	CCONJ
ejpam-5140	204	2	he	he	PRON
ejpam-5140	204	3	’s	’	VERB
ejpam-5140	204	4	variational	variational	ADJ
ejpam-5140	204	5	approach	approach	NOUN
ejpam-5140	204	6	.	.	PUNCT
ejpam-5140	205	1	nonlinear	nonlinear	ADJ
ejpam-5140	205	2	science	science	PROPN
ejpam-5140	205	3	letters	letter	NOUN
ejpam-5140	205	4	a	a	PRON
ejpam-5140	205	5	,	,	PUNCT
ejpam-5140	205	6	(	(	PUNCT
ejpam-5140	205	7	1):425	1):425	NUM
ejpam-5140	205	8	,	,	PUNCT
ejpam-5140	205	9	2010	2010	NUM
ejpam-5140	205	10	.	.	PUNCT
ejpam-5140	206	1	[	[	X
ejpam-5140	206	2	3	3	X
ejpam-5140	206	3	]	]	X
ejpam-5140	206	4	f	f	PROPN
ejpam-5140	206	5	m	m	PROPN
ejpam-5140	206	6	atay	atay	NOUN
ejpam-5140	206	7	.	.	PUNCT
ejpam-5140	207	1	van	van	PROPN
ejpam-5140	207	2	der	der	PROPN
ejpam-5140	207	3	pol	pol	PROPN
ejpam-5140	207	4	’s	’s	PART
ejpam-5140	207	5	oscillator	oscillator	NOUN
ejpam-5140	207	6	under	under	ADP
ejpam-5140	207	7	delayed	delay	VERB
ejpam-5140	207	8	feedback	feedback	NOUN
ejpam-5140	207	9	.	.	PUNCT
ejpam-5140	208	1	journal	journal	NOUN
ejpam-5140	208	2	of	of	ADP
ejpam-5140	208	3	sound	sound	NOUN
ejpam-5140	208	4	and	and	CCONJ
ejpam-5140	208	5	vibration	vibration	NOUN
ejpam-5140	208	6	,	,	PUNCT
ejpam-5140	208	7	218(2):333	218(2):333	NOUN
ejpam-5140	208	8	,	,	PUNCT
ejpam-5140	208	9	1998	1998	NUM
ejpam-5140	208	10	.	.	PUNCT
ejpam-5140	209	1	[	[	X
ejpam-5140	209	2	4	4	X
ejpam-5140	209	3	]	]	PUNCT
ejpam-5140	209	4	m.	m.	NOUN
ejpam-5140	209	5	l.	l.	PROPN
ejpam-5140	209	6	cartwright	cartwright	PROPN
ejpam-5140	209	7	.	.	PUNCT
ejpam-5140	210	1	balthazar	balthazar	PROPN
ejpam-5140	210	2	van	van	PROPN
ejpam-5140	210	3	der	der	PROPN
ejpam-5140	210	4	pol	pol	PROPN
ejpam-5140	210	5	.	.	PUNCT
ejpam-5140	211	1	j.london	j.london	ADJ
ejpam-5140	211	2	mathematical	mathematical	ADJ
ejpam-5140	211	3	society	society	NOUN
ejpam-5140	211	4	,	,	PUNCT
ejpam-5140	211	5	35:367–376	35:367–376	NUM
ejpam-5140	211	6	,	,	PUNCT
ejpam-5140	211	7	1960	1960	NUM
ejpam-5140	211	8	.	.	PUNCT
ejpam-5140	212	1	[	[	X
ejpam-5140	212	2	5	5	NUM
ejpam-5140	212	3	]	]	PUNCT
ejpam-5140	212	4	a	a	DET
ejpam-5140	212	5	g	g	NOUN
ejpam-5140	212	6	davodi	davodi	NOUN
ejpam-5140	212	7	,	,	PUNCT
ejpam-5140	212	8	d	d	PROPN
ejpam-5140	212	9	d	d	X
ejpam-5140	212	10	gangi	gangi	PROPN
ejpam-5140	212	11	,	,	PUNCT
ejpam-5140	212	12	r	r	NOUN
ejpam-5140	212	13	azami	azami	NOUN
ejpam-5140	212	14	,	,	PUNCT
ejpam-5140	212	15	and	and	CCONJ
ejpam-5140	212	16	h	h	NOUN
ejpam-5140	212	17	babazadeh	babazadeh	PROPN
ejpam-5140	212	18	.	.	PUNCT
ejpam-5140	213	1	application	application	NOUN
ejpam-5140	213	2	of	of	ADP
ejpam-5140	213	3	improved	improved	ADJ
ejpam-5140	213	4	amplitude	amplitude	NOUN
ejpam-5140	213	5	-	-	PUNCT
ejpam-5140	213	6	frequency	frequency	NOUN
ejpam-5140	213	7	formulation	formulation	NOUN
ejpam-5140	213	8	to	to	ADP
ejpam-5140	213	9	nonlinear	nonlinear	ADJ
ejpam-5140	213	10	differential	differential	ADJ
ejpam-5140	213	11	equation	equation	NOUN
ejpam-5140	213	12	of	of	ADP
ejpam-5140	213	13	motion	motion	NOUN
ejpam-5140	213	14	equations	equation	NOUN
ejpam-5140	213	15	.	.	PUNCT
ejpam-5140	214	1	modern	modern	ADJ
ejpam-5140	214	2	physics	physics	PROPN
ejpam-5140	214	3	letters	letters	PROPN
ejpam-5140	214	4	b	b	PROPN
ejpam-5140	214	5	,	,	PUNCT
ejpam-5140	214	6	23:3427–3436	23:3427–3436	NUM
ejpam-5140	214	7	,	,	PUNCT
ejpam-5140	214	8	2009	2009	NUM
ejpam-5140	214	9	.	.	PUNCT
ejpam-5140	215	1	[	[	X
ejpam-5140	215	2	6	6	NUM
ejpam-5140	215	3	]	]	PUNCT
ejpam-5140	215	4	serge	serge	NOUN
ejpam-5140	215	5	d’alessio	d’alessio	PROPN
ejpam-5140	215	6	.	.	PUNCT
ejpam-5140	216	1	solutions	solution	NOUN
ejpam-5140	216	2	of	of	ADP
ejpam-5140	216	3	the	the	DET
ejpam-5140	216	4	van	van	PROPN
ejpam-5140	216	5	der	der	ADJ
ejpam-5140	216	6	pol	pol	NOUN
ejpam-5140	216	7	equation	equation	NOUN
ejpam-5140	216	8	.	.	PUNCT
ejpam-5140	217	1	the	the	DET
ejpam-5140	217	2	college	college	NOUN
ejpam-5140	217	3	mathematics	mathematics	PROPN
ejpam-5140	217	4	journal	journal	NOUN
ejpam-5140	217	5	,	,	PUNCT
ejpam-5140	217	6	24(2):90	24(2):90	NOUN
ejpam-5140	217	7	,	,	PUNCT
ejpam-5140	217	8	2023	2023	NUM
ejpam-5140	217	9	.	.	PUNCT
ejpam-5140	218	1	references	reference	NOUN
ejpam-5140	218	2	1263	1263	NUM
ejpam-5140	218	3	[	[	X
ejpam-5140	218	4	7	7	NUM
ejpam-5140	218	5	]	]	X
ejpam-5140	218	6	d	d	X
ejpam-5140	218	7	d	d	X
ejpam-5140	218	8	ganji	ganji	X
ejpam-5140	218	9	.	.	PUNCT
ejpam-5140	219	1	the	the	DET
ejpam-5140	219	2	application	application	NOUN
ejpam-5140	219	3	of	of	ADP
ejpam-5140	219	4	he	he	PRON
ejpam-5140	219	5	’s	’s	NOUN
ejpam-5140	219	6	homotopy	homotopy	PROPN
ejpam-5140	219	7	perturbation	perturbation	NOUN
ejpam-5140	219	8	method	method	NOUN
ejpam-5140	219	9	to	to	ADP
ejpam-5140	219	10	nonlinear	nonlinear	ADJ
ejpam-5140	219	11	equations	equation	NOUN
ejpam-5140	219	12	arising	arise	VERB
ejpam-5140	219	13	in	in	ADP
ejpam-5140	219	14	heat	heat	NOUN
ejpam-5140	219	15	transfer	transfer	NOUN
ejpam-5140	219	16	.	.	PUNCT
ejpam-5140	220	1	physics	physics	NOUN
ejpam-5140	220	2	letters	letter	NOUN
ejpam-5140	220	3	a	a	DET
ejpam-5140	220	4	,	,	PUNCT
ejpam-5140	220	5	355:337	355:337	NUM
ejpam-5140	220	6	,	,	PUNCT
ejpam-5140	220	7	2006	2006	NUM
ejpam-5140	220	8	.	.	PUNCT
ejpam-5140	221	1	[	[	X
ejpam-5140	221	2	8	8	NUM
ejpam-5140	221	3	]	]	X
ejpam-5140	221	4	j	j	PROPN
ejpam-5140	221	5	h	h	NOUN
ejpam-5140	221	6	he	he	PRON
ejpam-5140	221	7	.	.	PUNCT
ejpam-5140	222	1	a	a	DET
ejpam-5140	222	2	coupling	coupling	NOUN
ejpam-5140	222	3	method	method	NOUN
ejpam-5140	222	4	of	of	ADP
ejpam-5140	222	5	a	a	DET
ejpam-5140	222	6	homotopy	homotopy	NOUN
ejpam-5140	222	7	technique	technique	NOUN
ejpam-5140	222	8	and	and	CCONJ
ejpam-5140	222	9	a	a	DET
ejpam-5140	222	10	perturbation	perturbation	NOUN
ejpam-5140	222	11	technique	technique	NOUN
ejpam-5140	222	12	for	for	ADP
ejpam-5140	222	13	non	non	ADJ
ejpam-5140	222	14	-	-	ADJ
ejpam-5140	222	15	linear	linear	ADJ
ejpam-5140	222	16	problems	problem	NOUN
ejpam-5140	222	17	.	.	PUNCT
ejpam-5140	223	1	international	international	ADJ
ejpam-5140	223	2	journal	journal	PROPN
ejpam-5140	223	3	of	of	ADP
ejpam-5140	223	4	non	non	ADJ
ejpam-5140	223	5	-	-	ADJ
ejpam-5140	223	6	linear	linear	ADJ
ejpam-5140	223	7	mechanics	mechanic	NOUN
ejpam-5140	223	8	,	,	PUNCT
ejpam-5140	223	9	35(1):37	35(1):37	NUM
ejpam-5140	223	10	,	,	PUNCT
ejpam-5140	223	11	2000	2000	NUM
ejpam-5140	223	12	.	.	PUNCT
ejpam-5140	224	1	[	[	X
ejpam-5140	224	2	9	9	NUM
ejpam-5140	224	3	]	]	X
ejpam-5140	224	4	j	j	PROPN
ejpam-5140	224	5	h	h	NOUN
ejpam-5140	224	6	he	he	PRON
ejpam-5140	224	7	.	.	PUNCT
ejpam-5140	225	1	application	application	NOUN
ejpam-5140	225	2	of	of	ADP
ejpam-5140	225	3	homotopy	homotopy	NOUN
ejpam-5140	225	4	perturbation	perturbation	NOUN
ejpam-5140	225	5	method	method	NOUN
ejpam-5140	225	6	to	to	ADP
ejpam-5140	225	7	nonlinear	nonlinear	ADJ
ejpam-5140	225	8	wave	wave	NOUN
ejpam-5140	225	9	equations	equation	NOUN
ejpam-5140	225	10	.	.	PUNCT
ejpam-5140	226	1	chaos	chaos	NOUN
ejpam-5140	226	2	solitons	soliton	NOUN
ejpam-5140	226	3	and	and	CCONJ
ejpam-5140	226	4	fractals	fractal	NOUN
ejpam-5140	226	5	,	,	PUNCT
ejpam-5140	226	6	26:695	26:695	NUM
ejpam-5140	226	7	,	,	PUNCT
ejpam-5140	226	8	2005	2005	NUM
ejpam-5140	226	9	.	.	PUNCT
ejpam-5140	227	1	[	[	X
ejpam-5140	227	2	10	10	NUM
ejpam-5140	227	3	]	]	X
ejpam-5140	227	4	j	j	PROPN
ejpam-5140	227	5	h	h	NOUN
ejpam-5140	227	6	he	he	PRON
ejpam-5140	227	7	.	.	PUNCT
ejpam-5140	228	1	new	new	ADJ
ejpam-5140	228	2	interpretation	interpretation	NOUN
ejpam-5140	228	3	of	of	ADP
ejpam-5140	228	4	homotopy	homotopy	NOUN
ejpam-5140	228	5	perturbation	perturbation	NOUN
ejpam-5140	228	6	method	method	NOUN
ejpam-5140	228	7	.	.	PUNCT
ejpam-5140	229	1	international	international	ADJ
ejpam-5140	229	2	journal	journal	NOUN
ejpam-5140	229	3	of	of	ADP
ejpam-5140	229	4	modern	modern	ADJ
ejpam-5140	229	5	physics	physics	PROPN
ejpam-5140	229	6	b	b	PROPN
ejpam-5140	229	7	,	,	PUNCT
ejpam-5140	229	8	20:2561	20:2561	NUM
ejpam-5140	229	9	,	,	PUNCT
ejpam-5140	229	10	2006	2006	NUM
ejpam-5140	229	11	.	.	PUNCT
ejpam-5140	230	1	[	[	X
ejpam-5140	230	2	11	11	NUM
ejpam-5140	230	3	]	]	X
ejpam-5140	230	4	j	j	PROPN
ejpam-5140	230	5	h	h	NOUN
ejpam-5140	230	6	he	he	PRON
ejpam-5140	230	7	.	.	PUNCT
ejpam-5140	231	1	some	some	DET
ejpam-5140	231	2	asymptotic	asymptotic	ADJ
ejpam-5140	231	3	methods	method	NOUN
ejpam-5140	231	4	for	for	ADP
ejpam-5140	231	5	strongly	strongly	ADV
ejpam-5140	231	6	nonlinear	nonlinear	ADJ
ejpam-5140	231	7	equations	equation	NOUN
ejpam-5140	231	8	.	.	PUNCT
ejpam-5140	232	1	international	international	ADJ
ejpam-5140	232	2	journal	journal	NOUN
ejpam-5140	232	3	of	of	ADP
ejpam-5140	232	4	modern	modern	ADJ
ejpam-5140	232	5	physics	physics	PROPN
ejpam-5140	232	6	b	b	PROPN
ejpam-5140	232	7	,	,	PUNCT
ejpam-5140	232	8	20:1141	20:1141	NUM
ejpam-5140	232	9	,	,	PUNCT
ejpam-5140	232	10	2006	2006	NUM
ejpam-5140	232	11	.	.	PUNCT
ejpam-5140	233	1	[	[	X
ejpam-5140	233	2	12	12	NUM
ejpam-5140	233	3	]	]	X
ejpam-5140	233	4	j	j	PROPN
ejpam-5140	233	5	h	h	NOUN
ejpam-5140	233	6	he	he	PRON
ejpam-5140	233	7	.	.	PUNCT
ejpam-5140	234	1	comment	comment	NOUN
ejpam-5140	234	2	on	on	ADP
ejpam-5140	234	3	’	'	PUNCT
ejpam-5140	234	4	he	he	PRON
ejpam-5140	234	5	’s	’	VERB
ejpam-5140	234	6	frequency	frequency	NOUN
ejpam-5140	234	7	formulation	formulation	NOUN
ejpam-5140	234	8	for	for	ADP
ejpam-5140	234	9	nonlinear	nonlinear	ADJ
ejpam-5140	234	10	oscillators	oscillator	NOUN
ejpam-5140	234	11	.	.	PUNCT
ejpam-5140	235	1	european	european	ADJ
ejpam-5140	235	2	journal	journal	PROPN
ejpam-5140	235	3	of	of	ADP
ejpam-5140	235	4	physics	physics	PROPN
ejpam-5140	235	5	,	,	PUNCT
ejpam-5140	235	6	29:19	29:19	NUM
ejpam-5140	235	7	,	,	PUNCT
ejpam-5140	235	8	2008	2008	NUM
ejpam-5140	235	9	.	.	PUNCT
ejpam-5140	236	1	[	[	X
ejpam-5140	236	2	13	13	NUM
ejpam-5140	236	3	]	]	X
ejpam-5140	236	4	j	j	PROPN
ejpam-5140	236	5	h	h	NOUN
ejpam-5140	236	6	he	he	PRON
ejpam-5140	236	7	.	.	PUNCT
ejpam-5140	237	1	max	max	PROPN
ejpam-5140	237	2	-	-	PUNCT
ejpam-5140	237	3	min	min	PROPN
ejpam-5140	237	4	approach	approach	NOUN
ejpam-5140	237	5	to	to	ADP
ejpam-5140	237	6	nonlinear	nonlinear	ADJ
ejpam-5140	237	7	oscillators	oscillator	NOUN
ejpam-5140	237	8	.	.	PUNCT
ejpam-5140	238	1	international	international	ADJ
ejpam-5140	238	2	journal	journal	PROPN
ejpam-5140	238	3	of	of	ADP
ejpam-5140	238	4	nonlinear	nonlinear	PROPN
ejpam-5140	238	5	science	science	PROPN
ejpam-5140	238	6	and	and	CCONJ
ejpam-5140	238	7	numerical	numerical	PROPN
ejpam-5140	238	8	simulation	simulation	PROPN
ejpam-5140	238	9	,	,	PUNCT
ejpam-5140	238	10	9:211	9:211	NUM
ejpam-5140	238	11	,	,	PUNCT
ejpam-5140	238	12	2008	2008	NUM
ejpam-5140	238	13	.	.	PUNCT
ejpam-5140	239	1	[	[	X
ejpam-5140	239	2	14	14	NUM
ejpam-5140	239	3	]	]	X
ejpam-5140	239	4	j	j	PROPN
ejpam-5140	239	5	h	h	NOUN
ejpam-5140	239	6	he	he	PRON
ejpam-5140	239	7	,	,	PUNCT
ejpam-5140	239	8	g	g	PROPN
ejpam-5140	239	9	c	c	PROPN
ejpam-5140	239	10	wu	wu	PROPN
ejpam-5140	239	11	,	,	PUNCT
ejpam-5140	239	12	and	and	CCONJ
ejpam-5140	239	13	f	f	PROPN
ejpam-5140	239	14	austin	austin	PROPN
ejpam-5140	239	15	.	.	PUNCT
ejpam-5140	240	1	the	the	DET
ejpam-5140	240	2	variational	variational	ADJ
ejpam-5140	240	3	iteration	iteration	NOUN
ejpam-5140	240	4	method	method	NOUN
ejpam-5140	240	5	which	which	PRON
ejpam-5140	240	6	should	should	AUX
ejpam-5140	240	7	be	be	AUX
ejpam-5140	240	8	followed	follow	VERB
ejpam-5140	240	9	.	.	PUNCT
ejpam-5140	241	1	nonlinear	nonlinear	ADJ
ejpam-5140	241	2	science	science	PROPN
ejpam-5140	241	3	letters	letter	NOUN
ejpam-5140	241	4	a	a	DET
ejpam-5140	241	5	,	,	PUNCT
ejpam-5140	241	6	1:1	1:1	NUM
ejpam-5140	241	7	,	,	PUNCT
ejpam-5140	241	8	2010	2010	NUM
ejpam-5140	241	9	.	.	PUNCT
ejpam-5140	242	1	[	[	X
ejpam-5140	242	2	15	15	NUM
ejpam-5140	242	3	]	]	PUNCT
ejpam-5140	242	4	n	n	NUM
ejpam-5140	242	5	herisanu	herisanu	NOUN
ejpam-5140	242	6	and	and	CCONJ
ejpam-5140	242	7	v	v	NOUN
ejpam-5140	242	8	marinca	marinca	NOUN
ejpam-5140	242	9	.	.	PUNCT
ejpam-5140	243	1	a	a	DET
ejpam-5140	243	2	modified	modify	VERB
ejpam-5140	243	3	variational	variational	ADJ
ejpam-5140	243	4	iteration	iteration	NOUN
ejpam-5140	243	5	method	method	NOUN
ejpam-5140	243	6	for	for	ADP
ejpam-5140	243	7	strongly	strongly	ADV
ejpam-5140	243	8	nonlinear	nonlinear	ADJ
ejpam-5140	243	9	problems	problem	NOUN
ejpam-5140	243	10	.	.	PUNCT
ejpam-5140	244	1	nonlinear	nonlinear	ADJ
ejpam-5140	244	2	science	science	PROPN
ejpam-5140	244	3	letters	letter	NOUN
ejpam-5140	244	4	a	a	PRON
ejpam-5140	244	5	,	,	PUNCT
ejpam-5140	244	6	1:183	1:183	NUM
ejpam-5140	244	7	,	,	PUNCT
ejpam-5140	244	8	2010	2010	NUM
ejpam-5140	244	9	.	.	PUNCT
ejpam-5140	245	1	[	[	X
ejpam-5140	245	2	16	16	NUM
ejpam-5140	245	3	]	]	X
ejpam-5140	245	4	i	i	PRON
ejpam-5140	245	5	mehdipour	mehdipour	VERB
ejpam-5140	245	6	,	,	PUNCT
ejpam-5140	245	7	d	d	X
ejpam-5140	245	8	d	d	X
ejpam-5140	245	9	ganji	ganji	X
ejpam-5140	245	10	,	,	PUNCT
ejpam-5140	245	11	and	and	CCONJ
ejpam-5140	245	12	m	m	PROPN
ejpam-5140	245	13	mozaffari	mozaffari	ADJ
ejpam-5140	245	14	.	.	PUNCT
ejpam-5140	246	1	application	application	NOUN
ejpam-5140	246	2	of	of	ADP
ejpam-5140	246	3	the	the	DET
ejpam-5140	246	4	energy	energy	NOUN
ejpam-5140	246	5	balance	balance	NOUN
ejpam-5140	246	6	method	method	NOUN
ejpam-5140	246	7	to	to	PART
ejpam-5140	246	8	nonlinear	nonlinear	ADJ
ejpam-5140	246	9	vibrating	vibrating	NOUN
ejpam-5140	246	10	equations	equation	NOUN
ejpam-5140	246	11	.	.	PUNCT
ejpam-5140	247	1	current	current	ADJ
ejpam-5140	247	2	applied	applied	ADJ
ejpam-5140	247	3	physics	physic	NOUN
ejpam-5140	247	4	,	,	PUNCT
ejpam-5140	247	5	10:104	10:104	PROPN
ejpam-5140	247	6	,	,	PUNCT
ejpam-5140	247	7	2010	2010	NUM
ejpam-5140	247	8	.	.	PUNCT
ejpam-5140	248	1	[	[	X
ejpam-5140	248	2	17	17	NUM
ejpam-5140	248	3	]	]	X
ejpam-5140	248	4	s	s	PART
ejpam-5140	248	5	s.	s.	PROPN
ejpam-5140	248	6	motsa	motsa	PROPN
ejpam-5140	248	7	and	and	CCONJ
ejpam-5140	248	8	p	p	PRON
ejpam-5140	248	9	sibanda	sibanda	NOUN
ejpam-5140	248	10	.	.	PUNCT
ejpam-5140	249	1	a	a	DET
ejpam-5140	249	2	note	note	NOUN
ejpam-5140	249	3	on	on	ADP
ejpam-5140	249	4	the	the	DET
ejpam-5140	249	5	solutions	solution	NOUN
ejpam-5140	249	6	of	of	ADP
ejpam-5140	249	7	the	the	DET
ejpam-5140	249	8	van	van	PROPN
ejpam-5140	249	9	der	der	ADJ
ejpam-5140	249	10	pol	pol	NOUN
ejpam-5140	249	11	and	and	CCONJ
ejpam-5140	249	12	duffing	duffe	VERB
ejpam-5140	249	13	equations	equation	NOUN
ejpam-5140	249	14	using	use	VERB
ejpam-5140	249	15	a	a	DET
ejpam-5140	249	16	linearisation	linearisation	NOUN
ejpam-5140	249	17	method	method	NOUN
ejpam-5140	249	18	.	.	PUNCT
ejpam-5140	250	1	mathematical	mathematical	ADJ
ejpam-5140	250	2	problems	problem	NOUN
ejpam-5140	250	3	in	in	ADP
ejpam-5140	250	4	engineering	engineering	NOUN
ejpam-5140	250	5	,	,	PUNCT
ejpam-5140	250	6	2012:693453	2012:693453	NUM
ejpam-5140	250	7	,	,	PUNCT
ejpam-5140	250	8	2012	2012	NUM
ejpam-5140	250	9	.	.	PUNCT
ejpam-5140	251	1	[	[	X
ejpam-5140	251	2	18	18	NUM
ejpam-5140	251	3	]	]	PUNCT
ejpam-5140	251	4	attia	attia	PROPN
ejpam-5140	251	5	n.	n.	PROPN
ejpam-5140	251	6	,	,	PUNCT
ejpam-5140	251	7	seba	seba	PROPN
ejpam-5140	251	8	d.	d.	PROPN
ejpam-5140	251	9	,	,	PUNCT
ejpam-5140	251	10	akgul	akgul	PROPN
ejpam-5140	251	11	a.	a.	PROPN
ejpam-5140	251	12	,	,	PUNCT
ejpam-5140	251	13	and	and	CCONJ
ejpam-5140	251	14	noura	noura	NOUN
ejpam-5140	251	15	.	.	PUNCT
ejpam-5140	252	1	solving	solve	VERB
ejpam-5140	252	2	duffing	duffing	NOUN
ejpam-5140	252	3	-	-	PUNCT
ejpam-5140	252	4	van	van	PROPN
ejpam-5140	252	5	der	der	ADJ
ejpam-5140	252	6	pol	pol	PROPN
ejpam-5140	252	7	oscillator	oscillator	NOUN
ejpam-5140	252	8	equations	equation	NOUN
ejpam-5140	252	9	of	of	ADP
ejpam-5140	252	10	fractional	fractional	ADJ
ejpam-5140	252	11	order	order	NOUN
ejpam-5140	252	12	by	by	ADP
ejpam-5140	252	13	an	an	DET
ejpam-5140	252	14	accurate	accurate	ADJ
ejpam-5140	252	15	technique	technique	NOUN
ejpam-5140	252	16	.	.	PUNCT
ejpam-5140	253	1	journal	journal	NOUN
ejpam-5140	253	2	of	of	ADP
ejpam-5140	253	3	applied	applied	ADJ
ejpam-5140	253	4	and	and	CCONJ
ejpam-5140	253	5	computational	computational	ADJ
ejpam-5140	253	6	mechanics	mechanic	NOUN
ejpam-5140	253	7	,	,	PUNCT
ejpam-5140	253	8	7(3):1480–1487	7(3):1480–1487	PROPN
ejpam-5140	253	9	,	,	PUNCT
ejpam-5140	253	10	2021	2021	NUM
ejpam-5140	253	11	.	.	PUNCT
ejpam-5140	254	1	[	[	X
ejpam-5140	254	2	19	19	NUM
ejpam-5140	254	3	]	]	X
ejpam-5140	254	4	p	p	X
ejpam-5140	254	5	v	v	X
ejpam-5140	254	6	ramana	ramana	NOUN
ejpam-5140	254	7	and	and	CCONJ
ejpam-5140	254	8	p	p	PROPN
ejpam-5140	254	9	b	b	PROPN
ejpam-5140	254	10	k	k	PROPN
ejpam-5140	254	11	raghu	raghu	PROPN
ejpam-5140	254	12	.	.	PUNCT
ejpam-5140	255	1	modified	modify	VERB
ejpam-5140	255	2	adomian	adomian	NOUN
ejpam-5140	255	3	decomposition	decomposition	NOUN
ejpam-5140	255	4	method	method	NOUN
ejpam-5140	255	5	for	for	ADP
ejpam-5140	255	6	van	van	PROPN
ejpam-5140	255	7	der	der	ADJ
ejpam-5140	255	8	pol	pol	PROPN
ejpam-5140	255	9	equations	equation	NOUN
ejpam-5140	255	10	.	.	PUNCT
ejpam-5140	256	1	international	international	ADJ
ejpam-5140	256	2	journal	journal	PROPN
ejpam-5140	256	3	of	of	ADP
ejpam-5140	256	4	non	non	PROPN
ejpam-5140	256	5	linear	linear	PROPN
ejpam-5140	256	6	mechanics	mechanic	NOUN
ejpam-5140	256	7	,	,	PUNCT
ejpam-5140	256	8	65:121	65:121	NOUN
ejpam-5140	256	9	,	,	PUNCT
ejpam-5140	256	10	2014	2014	NUM
ejpam-5140	256	11	.	.	PUNCT
ejpam-5140	257	1	[	[	X
ejpam-5140	257	2	20	20	NUM
ejpam-5140	257	3	]	]	PUNCT
ejpam-5140	257	4	a	a	DET
ejpam-5140	257	5	s	s	NOUN
ejpam-5140	257	6	soomro	soomro	NOUN
ejpam-5140	257	7	,	,	PUNCT
ejpam-5140	257	8	g	g	PROPN
ejpam-5140	257	9	a	a	DET
ejpam-5140	257	10	tularam	tularam	NOUN
ejpam-5140	257	11	,	,	PUNCT
ejpam-5140	257	12	and	and	CCONJ
ejpam-5140	257	13	m	m	NOUN
ejpam-5140	257	14	m	m	NOUN
ejpam-5140	257	15	s	s	NOUN
ejpam-5140	257	16	shaikh	shaikh	ADJ
ejpam-5140	257	17	.	.	PUNCT
ejpam-5140	258	1	a	a	DET
ejpam-5140	258	2	comparison	comparison	NOUN
ejpam-5140	258	3	of	of	ADP
ejpam-5140	258	4	numerical	numerical	ADJ
ejpam-5140	258	5	methods	method	NOUN
ejpam-5140	258	6	for	for	ADP
ejpam-5140	258	7	solving	solve	VERB
ejpam-5140	258	8	the	the	DET
ejpam-5140	258	9	unforced	unforced	ADJ
ejpam-5140	258	10	van	van	PROPN
ejpam-5140	258	11	der	der	PROPN
ejpam-5140	258	12	pol	pol	PROPN
ejpam-5140	258	13	’s	’s	PART
ejpam-5140	258	14	equation	equation	NOUN
ejpam-5140	258	15	.	.	PUNCT
ejpam-5140	259	1	mathematical	mathematical	ADJ
ejpam-5140	259	2	theory	theory	NOUN
ejpam-5140	259	3	and	and	CCONJ
ejpam-5140	259	4	modeling	modeling	NOUN
ejpam-5140	259	5	,	,	PUNCT
ejpam-5140	259	6	3(2):66	3(2):66	NUM
ejpam-5140	259	7	,	,	PUNCT
ejpam-5140	259	8	2013	2013	NUM
ejpam-5140	259	9	.	.	PUNCT
ejpam-5140	260	1	[	[	X
ejpam-5140	260	2	21	21	NUM
ejpam-5140	260	3	]	]	X
ejpam-5140	260	4	b.	b.	PROPN
ejpam-5140	260	5	van	van	PROPN
ejpam-5140	260	6	der	der	PROPN
ejpam-5140	260	7	pol	pol	PROPN
ejpam-5140	260	8	.	.	PUNCT
ejpam-5140	261	1	a	a	DET
ejpam-5140	261	2	theory	theory	NOUN
ejpam-5140	261	3	of	of	ADP
ejpam-5140	261	4	the	the	DET
ejpam-5140	261	5	amplitude	amplitude	NOUN
ejpam-5140	261	6	of	of	ADP
ejpam-5140	261	7	free	free	ADJ
ejpam-5140	261	8	and	and	CCONJ
ejpam-5140	261	9	forced	forced	ADJ
ejpam-5140	261	10	vibrations	vibration	NOUN
ejpam-5140	261	11	.	.	PUNCT
ejpam-5140	262	1	radio	radio	NOUN
ejpam-5140	262	2	review	review	NOUN
ejpam-5140	262	3	,	,	PUNCT
ejpam-5140	262	4	1:701–710	1:701–710	NUM
ejpam-5140	262	5	,	,	PUNCT
ejpam-5140	262	6	754–762	754–762	NUM
ejpam-5140	262	7	,	,	PUNCT
ejpam-5140	262	8	1920	1920	NUM
ejpam-5140	262	9	.	.	PUNCT
ejpam-5140	263	1	references	reference	NOUN
ejpam-5140	263	2	1264	1264	NUM
ejpam-5140	263	3	[	[	X
ejpam-5140	263	4	22	22	NUM
ejpam-5140	263	5	]	]	PUNCT
ejpam-5140	263	6	b.	b.	PROPN
ejpam-5140	263	7	van	van	PROPN
ejpam-5140	263	8	der	der	PROPN
ejpam-5140	263	9	pol	pol	PROPN
ejpam-5140	263	10	.	.	PUNCT
ejpam-5140	264	1	on	on	ADP
ejpam-5140	264	2	“	"	PUNCT
ejpam-5140	264	3	relaxation	relaxation	NOUN
ejpam-5140	264	4	-	-	PUNCT
ejpam-5140	264	5	oscillations	oscillation	NOUN
ejpam-5140	264	6	”	"	PUNCT
ejpam-5140	264	7	.	.	PUNCT
ejpam-5140	265	1	phil	phil	PROPN
ejpam-5140	265	2	.mag	.mag	PROPN
ejpam-5140	265	3	.	.	PROPN
ejpam-5140	265	4	,	,	PUNCT
ejpam-5140	265	5	2:978–992	2:978–992	NUM
ejpam-5140	265	6	,	,	PUNCT
ejpam-5140	265	7	1926	1926	NUM
ejpam-5140	265	8	.	.	PUNCT
ejpam-5140	266	1	[	[	X
ejpam-5140	266	2	23	23	NUM
ejpam-5140	266	3	]	]	PUNCT
ejpam-5140	266	4	b.	b.	PROPN
ejpam-5140	266	5	van	van	PROPN
ejpam-5140	266	6	der	der	PROPN
ejpam-5140	266	7	pol	pol	PROPN
ejpam-5140	266	8	.	.	PUNCT
ejpam-5140	267	1	the	the	DET
ejpam-5140	267	2	nonlinear	nonlinear	ADJ
ejpam-5140	267	3	theory	theory	NOUN
ejpam-5140	267	4	of	of	ADP
ejpam-5140	267	5	electric	electric	ADJ
ejpam-5140	267	6	oscillations	oscillation	NOUN
ejpam-5140	267	7	.	.	PUNCT
ejpam-5140	268	1	proc.ire	proc.ire	NOUN
ejpam-5140	268	2	,	,	PUNCT
ejpam-5140	268	3	22:1051–1086	22:1051–1086	NUM
ejpam-5140	268	4	,	,	PUNCT
ejpam-5140	268	5	1934	1934	NUM
ejpam-5140	268	6	.	.	PUNCT
ejpam-5140	269	1	[	[	X
ejpam-5140	269	2	24	24	NUM
ejpam-5140	269	3	]	]	PUNCT
ejpam-5140	269	4	b.	b.	PROPN
ejpam-5140	269	5	van	van	PROPN
ejpam-5140	269	6	der	der	PROPN
ejpam-5140	269	7	pol	pol	PROPN
ejpam-5140	269	8	and	and	CCONJ
ejpam-5140	269	9	j.	j.	PROPN
ejpam-5140	269	10	van	van	PROPN
ejpam-5140	269	11	der	der	PROPN
ejpam-5140	269	12	mark	mark	PROPN
ejpam-5140	269	13	.	.	PUNCT
ejpam-5140	270	1	frequency	frequency	NOUN
ejpam-5140	270	2	demultiplication	demultiplication	NOUN
ejpam-5140	270	3	.	.	PUNCT
ejpam-5140	271	1	nature	nature	NOUN
ejpam-5140	271	2	,	,	PUNCT
ejpam-5140	271	3	120:363–364	120:363–364	NUM
ejpam-5140	271	4	,	,	PUNCT
ejpam-5140	271	5	1927	1927	NUM
ejpam-5140	271	6	.	.	PUNCT
ejpam-5140	272	1	[	[	X
ejpam-5140	272	2	25	25	NUM
ejpam-5140	272	3	]	]	PUNCT
ejpam-5140	272	4	l	l	NOUN
ejpam-5140	272	5	xu	xu	PROPN
ejpam-5140	272	6	.	.	PUNCT
ejpam-5140	273	1	determination	determination	NOUN
ejpam-5140	273	2	of	of	ADP
ejpam-5140	273	3	limit	limit	NOUN
ejpam-5140	273	4	cycle	cycle	NOUN
ejpam-5140	273	5	by	by	ADP
ejpam-5140	273	6	he	he	PRON
ejpam-5140	273	7	’s	’	VERB
ejpam-5140	273	8	parameter	parameter	NOUN
ejpam-5140	273	9	-	-	PUNCT
ejpam-5140	273	10	expanding	expand	VERB
ejpam-5140	273	11	method	method	NOUN
ejpam-5140	273	12	for	for	ADP
ejpam-5140	273	13	strongly	strongly	ADV
ejpam-5140	273	14	nonlinear	nonlinear	ADJ
ejpam-5140	273	15	oscillators	oscillator	NOUN
ejpam-5140	273	16	.	.	PUNCT
ejpam-5140	274	1	journal	journal	NOUN
ejpam-5140	274	2	of	of	ADP
ejpam-5140	274	3	sound	sound	NOUN
ejpam-5140	274	4	and	and	CCONJ
ejpam-5140	274	5	vibration	vibration	NOUN
ejpam-5140	274	6	,	,	PUNCT
ejpam-5140	274	7	302:178	302:178	NUM
ejpam-5140	274	8	,	,	PUNCT
ejpam-5140	274	9	2007	2007	NUM
ejpam-5140	274	10	.	.	PUNCT
ejpam-5140	275	1	[	[	X
ejpam-5140	275	2	26	26	NUM
ejpam-5140	275	3	]	]	PUNCT
ejpam-5140	275	4	l	l	NOUN
ejpam-5140	276	1	xu	xu	PROPN
ejpam-5140	276	2	.	.	PUNCT
ejpam-5140	277	1	variational	variational	ADJ
ejpam-5140	277	2	iteration	iteration	NOUN
ejpam-5140	277	3	method	method	NOUN
ejpam-5140	277	4	-	-	PUNCT
ejpam-5140	277	5	reality	reality	NOUN
ejpam-5140	277	6	,	,	PUNCT
ejpam-5140	277	7	potential	potential	NOUN
ejpam-5140	277	8	,	,	PUNCT
ejpam-5140	277	9	and	and	CCONJ
ejpam-5140	277	10	challenges	challenge	NOUN
ejpam-5140	277	11	.	.	PUNCT
ejpam-5140	278	1	jownal	jownal	ADJ
ejpam-5140	278	2	of	of	ADP
ejpam-5140	278	3	computational	computational	ADJ
ejpam-5140	278	4	and	and	CCONJ
ejpam-5140	278	5	applied	applied	ADJ
ejpam-5140	278	6	mathematics	mathematic	NOUN
ejpam-5140	278	7	,	,	PUNCT
ejpam-5140	278	8	207:148	207:148	NUM
ejpam-5140	278	9	,	,	PUNCT
ejpam-5140	278	10	2007	2007	NUM
ejpam-5140	278	11	.	.	PUNCT
ejpam-5140	279	1	[	[	X
ejpam-5140	279	2	27	27	NUM
ejpam-5140	279	3	]	]	X
ejpam-5140	279	4	d	d	X
ejpam-5140	279	5	younesian	younesian	NOUN
ejpam-5140	279	6	,	,	PUNCT
ejpam-5140	279	7	h	h	NOUN
ejpam-5140	279	8	askari	askari	PROPN
ejpam-5140	279	9	,	,	PUNCT
ejpam-5140	279	10	z	z	PROPN
ejpam-5140	279	11	saadatnia	saadatnia	PROPN
ejpam-5140	279	12	,	,	PUNCT
ejpam-5140	279	13	and	and	CCONJ
ejpam-5140	279	14	m	m	PROPN
ejpam-5140	279	15	kalami	kalami	PROPN
ejpam-5140	279	16	yazdi	yazdi	PROPN
ejpam-5140	279	17	.	.	PUNCT
ejpam-5140	280	1	frequency	frequency	NOUN
ejpam-5140	280	2	analysis	analysis	NOUN
ejpam-5140	280	3	of	of	ADP
ejpam-5140	280	4	strongly	strongly	ADV
ejpam-5140	280	5	nonlinear	nonlinear	ADJ
ejpam-5140	280	6	generalized	generalized	ADJ
ejpam-5140	280	7	duffing	duffing	NOUN
ejpam-5140	280	8	oscillators	oscillator	NOUN
ejpam-5140	280	9	using	use	VERB
ejpam-5140	280	10	he	he	PRON
ejpam-5140	280	11	’s	’s	PART
ejpam-5140	280	12	frequency	frequency	NOUN
ejpam-5140	280	13	–	–	PUNCT
ejpam-5140	280	14	amplitude	amplitude	NOUN
ejpam-5140	280	15	formulation	formulation	NOUN
ejpam-5140	280	16	and	and	CCONJ
ejpam-5140	280	17	he	he	PRON
ejpam-5140	280	18	’s	’	VERB
ejpam-5140	280	19	energy	energy	NOUN
ejpam-5140	280	20	balance	balance	NOUN
ejpam-5140	280	21	method	method	NOUN
ejpam-5140	280	22	.	.	PUNCT
ejpam-5140	281	1	computers	computer	NOUN
ejpam-5140	281	2	and	and	CCONJ
ejpam-5140	281	3	mathematics	mathematic	NOUN
ejpam-5140	281	4	with	with	ADP
ejpam-5140	281	5	applications	application	NOUN
ejpam-5140	281	6	,	,	PUNCT
ejpam-5140	281	7	59:3222	59:3222	NUM
ejpam-5140	281	8	,	,	PUNCT
ejpam-5140	281	9	2010	2010	NUM
ejpam-5140	281	10	.	.	PUNCT