id	sid	tid	token	lemma	pos
iajs-805	1	1	ibn	ibn	PROPN
iajs-805	1	2	alhaitham	alhaitham	NOUN
iajs-805	1	3	j.	j.	PROPN
iajs-805	1	4	for	for	ADP
iajs-805	1	5	pure	pure	ADJ
iajs-805	1	6	&	&	CCONJ
iajs-805	1	7	appl	appl	PROPN
iajs-805	1	8	.	.	PUNCT
iajs-805	2	1	sci	sci	PROPN
iajs-805	2	2	.	.	PUNCT
iajs-805	2	3	vol.24	vol.24	NOUN
iajs-805	2	4	(	(	PUNCT
iajs-805	2	5	3	3	NUM
iajs-805	2	6	)	)	PUNCT
iajs-805	2	7	2011	2011	NUM
iajs-805	2	8	extend	extend	VERB
iajs-805	2	9	differential	differential	ADJ
iajs-805	2	10	transform	transform	NOUN
iajs-805	2	11	methods	method	NOUN
iajs-805	2	12	for	for	ADP
iajs-805	2	13	solving	solve	VERB
iajs-805	2	14	differential	differential	ADJ
iajs-805	2	15	equations	equation	NOUN
iajs-805	2	16	with	with	ADP
iajs-805	2	17	multiple	multiple	ADJ
iajs-805	2	18	delay	delay	NOUN
iajs-805	2	19	gh	gh	PROPN
iajs-805	2	20	.	.	PUNCT
iajs-805	3	1	j.	j.	PROPN
iajs-805	3	2	mohammed	mohammed	PROPN
iajs-805	3	3	,	,	PUNCT
iajs-805	3	4	f.s	f.s	PROPN
iajs-805	3	5	.	.	PROPN
iajs-805	3	6	fadhel	fadhel	PROPN
iajs-805	3	7	department	department	PROPN
iajs-805	3	8	of	of	ADP
iajs-805	3	9	mathematics	mathematics	PROPN
iajs-805	3	10	,	,	PUNCT
iajs-805	3	11	college	college	NOUN
iajs-805	3	12	of	of	ADP
iajs-805	3	13	education	education	NOUN
iajs-805	3	14	(	(	PUNCT
iajs-805	3	15	ibn	ibn	PROPN
iajs-805	3	16	al	al	PROPN
iajs-805	3	17	-	-	PUNCT
iajs-805	3	18	haitham	haitham	PROPN
iajs-805	3	19	)	)	PUNCT
iajs-805	3	20	,	,	PUNCT
iajs-805	3	21	university	university	NOUN
iajs-805	3	22	of	of	ADP
iajs-805	3	23	baghdad	baghdad	PROPN
iajs-805	3	24	department	department	PROPN
iajs-805	3	25	of	of	ADP
iajs-805	3	26	mathematics	mathematics	PROPN
iajs-805	3	27	and	and	CCONJ
iajs-805	3	28	computer	computer	NOUN
iajs-805	3	29	applications	application	NOUN
iajs-805	3	30	,	,	PUNCT
iajs-805	3	31	college	college	NOUN
iajs-805	3	32	of	of	ADP
iajs-805	3	33	science	science	PROPN
iajs-805	3	34	,	,	PUNCT
iajs-805	3	35	al	al	PROPN
iajs-805	3	36	-	-	PUNCT
iajs-805	3	37	nahrain	nahrain	PROPN
iajs-805	3	38	university	university	NOUN
iajs-805	3	39	received	receive	VERB
iajs-805	3	40	in	in	ADP
iajs-805	3	41	:	:	PUNCT
iajs-805	3	42	29	29	NUM
iajs-805	3	43	november	november	NOUN
iajs-805	3	44	2010	2010	NUM
iajs-805	3	45	accepted	accept	VERB
iajs-805	3	46	in	in	ADP
iajs-805	3	47	:	:	PUNCT
iajs-805	3	48	20	20	NUM
iajs-805	3	49	september	september	PROPN
iajs-805	3	50	2011	2011	NUM
iajs-805	3	51	abstract	abstract	NOUN
iajs-805	3	52	in	in	ADP
iajs-805	3	53	this	this	DET
iajs-805	3	54	paper	paper	NOUN
iajs-805	3	55	,	,	PUNCT
iajs-805	3	56	we	we	PRON
iajs-805	3	57	present	present	VERB
iajs-805	3	58	an	an	DET
iajs-805	3	59	approximate	approximate	ADJ
iajs-805	3	60	analytical	analytical	ADJ
iajs-805	3	61	and	and	CCONJ
iajs-805	3	62	numerical	numerical	ADJ
iajs-805	3	63	solutions	solution	NOUN
iajs-805	3	64	for	for	ADP
iajs-805	3	65	the	the	DET
iajs-805	3	66	differential	differential	ADJ
iajs-805	3	67	equations	equation	NOUN
iajs-805	3	68	with	with	ADP
iajs-805	3	69	multiple	multiple	ADJ
iajs-805	3	70	delay	delay	NOUN
iajs-805	3	71	using	use	VERB
iajs-805	3	72	the	the	DET
iajs-805	3	73	extend	extend	NOUN
iajs-805	3	74	differential	differential	ADJ
iajs-805	3	75	transform	transform	NOUN
iajs-805	3	76	method	method	NOUN
iajs-805	3	77	(	(	PUNCT
iajs-805	3	78	dtm	dtm	PROPN
iajs-805	3	79	)	)	PUNCT
iajs-805	3	80	.	.	PUNCT
iajs-805	4	1	this	this	DET
iajs-805	4	2	method	method	NOUN
iajs-805	4	3	is	be	AUX
iajs-805	4	4	used	use	VERB
iajs-805	4	5	to	to	PART
iajs-805	4	6	solve	solve	VERB
iajs-805	4	7	many	many	ADJ
iajs-805	4	8	linear	linear	ADJ
iajs-805	4	9	and	and	CCONJ
iajs-805	4	10	non	non	ADJ
iajs-805	4	11	linear	linear	PROPN
iajs-805	4	12	problems	problem	NOUN
iajs-805	4	13	.	.	PUNCT
iajs-805	5	1	key	key	ADJ
iajs-805	5	2	words	word	NOUN
iajs-805	5	3	:	:	PUNCT
iajs-805	5	4	(	(	PUNCT
iajs-805	5	5	differential	differential	ADJ
iajs-805	5	6	transform	transform	NOUN
iajs-805	5	7	method	method	NOUN
iajs-805	5	8	,	,	PUNCT
iajs-805	5	9	solving	solve	VERB
iajs-805	5	10	differential	differential	ADJ
iajs-805	5	11	equation	equation	NOUN
iajs-805	5	12	,	,	PUNCT
iajs-805	5	13	multiple	multiple	ADJ
iajs-805	5	14	delay	delay	NOUN
iajs-805	5	15	)	)	PUNCT
iajs-805	5	16	.	.	PUNCT
iajs-805	6	1	introduction	introduction	NOUN
iajs-805	6	2	in	in	ADP
iajs-805	6	3	this	this	DET
iajs-805	6	4	paper	paper	NOUN
iajs-805	6	5	,	,	PUNCT
iajs-805	6	6	we	we	PRON
iajs-805	6	7	extend	extend	VERB
iajs-805	6	8	the	the	DET
iajs-805	6	9	differential	differential	ADJ
iajs-805	6	10	transform	transform	NOUN
iajs-805	6	11	method	method	NOUN
iajs-805	6	12	(	(	PUNCT
iajs-805	6	13	dtm	dtm	PROPN
iajs-805	6	14	)	)	PUNCT
iajs-805	6	15	to	to	PART
iajs-805	6	16	solve	solve	VERB
iajs-805	6	17	the	the	DET
iajs-805	6	18	nth	nth	NOUN
iajs-805	6	19	order	order	NOUN
iajs-805	6	20	differential	differential	ADJ
iajs-805	6	21	equations	equation	NOUN
iajs-805	6	22	with	with	ADP
iajs-805	6	23	multiple	multiple	ADJ
iajs-805	6	24	delay	delay	NOUN
iajs-805	6	25	of	of	ADP
iajs-805	6	26	the	the	DET
iajs-805	6	27	form	form	NOUN
iajs-805	6	28	:	:	PUNCT
iajs-805	6	29	y(n)(x	y(n)(x	NUM
iajs-805	6	30	)	)	PUNCT
iajs-805	6	31	=	=	SYM
iajs-805	6	32	f(x	f(x	PROPN
iajs-805	6	33	,	,	PUNCT
iajs-805	6	34	y(x),y(x	y(x),y(x	NUM
iajs-805	6	35	–	–	PUNCT
iajs-805	6	36	r1	r1	PROPN
iajs-805	6	37	)	)	PUNCT
iajs-805	6	38	,	,	PUNCT
iajs-805	6	39	y(x	y(x	PROPN
iajs-805	6	40	–	–	PUNCT
iajs-805	6	41	r2	r2	PROPN
iajs-805	6	42	)	)	PUNCT
iajs-805	6	43	,	,	PUNCT
iajs-805	6	44	…	…	PUNCT
iajs-805	6	45	,	,	PUNCT
iajs-805	6	46	y(x	y(x	PROPN
iajs-805	6	47	–	–	PUNCT
iajs-805	6	48	rm	rm	PROPN
iajs-805	6	49	)	)	PUNCT
iajs-805	6	50	)	)	PUNCT
iajs-805	6	51	,	,	PUNCT
iajs-805	6	52	mℕ	mℕ	NOUN
iajs-805	6	53	…	…	PUNCT
iajs-805	6	54	(	(	PUNCT
iajs-805	6	55	1	1	NUM
iajs-805	6	56	)	)	PUNCT
iajs-805	6	57	where	where	SCONJ
iajs-805	6	58	y	y	NOUN
iajs-805	6	59	:	:	PUNCT
iajs-805	7	1	i	i	PRON
iajs-805	7	2			X
iajs-805	7	3	ℝ	ℝ	PROPN
iajs-805	7	4	,	,	PUNCT
iajs-805	7	5	f	f	X
iajs-805	7	6	:	:	PUNCT
iajs-805	7	7	i	i	PROPN
iajs-805	7	8	ℝ2	ℝ2	PROPN
iajs-805	7	9			PROPN
iajs-805	7	10	ℝ	ℝ	PROPN
iajs-805	7	11	,	,	PUNCT
iajs-805	7	12	i	i	PRON
iajs-805	7	13			PROPN
iajs-805	7	14	ℝ	ℝ	PROPN
iajs-805	7	15	,	,	PUNCT
iajs-805	8	1	r	r	VERB
iajs-805	8	2	i	i	X
iajs-805	8	3	>	>	X
iajs-805	8	4	0	0	NUM
iajs-805	8	5	,	,	PUNCT
iajs-805	8	6	i	i	PRON
iajs-805	8	7	=	=	NOUN
iajs-805	8	8	1,2	1,2	NUM
iajs-805	8	9	,	,	PUNCT
iajs-805	8	10	…	…	PUNCT
iajs-805	8	11	,	,	PUNCT
iajs-805	8	12	m	m	AUX
iajs-805	8	13	the	the	DET
iajs-805	8	14	differential	differential	ADJ
iajs-805	8	15	transform	transform	NOUN
iajs-805	8	16	method	method	NOUN
iajs-805	8	17	was	be	AUX
iajs-805	8	18	first	first	ADV
iajs-805	8	19	applied	apply	VERB
iajs-805	8	20	in	in	ADP
iajs-805	8	21	the	the	DET
iajs-805	8	22	engineering	engineering	NOUN
iajs-805	8	23	domain	domain	NOUN
iajs-805	8	24	in	in	ADP
iajs-805	8	25	[	[	X
iajs-805	8	26	1	1	NUM
iajs-805	8	27	]	]	PUNCT
iajs-805	8	28	.	.	PUNCT
iajs-805	9	1	in	in	ADP
iajs-805	9	2	general	general	ADJ
iajs-805	9	3	,	,	PUNCT
iajs-805	9	4	the	the	DET
iajs-805	9	5	dtm	dtm	PROPN
iajs-805	9	6	is	be	AUX
iajs-805	9	7	applied	apply	VERB
iajs-805	9	8	to	to	PART
iajs-805	9	9	find	find	VERB
iajs-805	9	10	the	the	DET
iajs-805	9	11	solution	solution	NOUN
iajs-805	9	12	of	of	ADP
iajs-805	9	13	electric	electric	ADJ
iajs-805	9	14	circuit	circuit	NOUN
iajs-805	9	15	problems	problem	NOUN
iajs-805	9	16	[	[	X
iajs-805	9	17	2	2	NUM
iajs-805	9	18	]	]	PUNCT
iajs-805	9	19	.	.	PUNCT
iajs-805	10	1	the	the	DET
iajs-805	10	2	dtm	dtm	PROPN
iajs-805	10	3	is	be	AUX
iajs-805	10	4	numerical	numerical	ADJ
iajs-805	10	5	method	method	NOUN
iajs-805	10	6	based	base	VERB
iajs-805	10	7	on	on	ADP
iajs-805	10	8	taylor	taylor	PROPN
iajs-805	10	9	series	series	PROPN
iajs-805	10	10	expansion	expansion	PROPN
iajs-805	10	11	,	,	PUNCT
iajs-805	10	12	which	which	PRON
iajs-805	10	13	is	be	AUX
iajs-805	10	14	constructed	construct	VERB
iajs-805	10	15	as	as	ADP
iajs-805	10	16	an	an	DET
iajs-805	10	17	analytical	analytical	ADJ
iajs-805	10	18	solution	solution	NOUN
iajs-805	10	19	in	in	ADP
iajs-805	10	20	the	the	DET
iajs-805	10	21	form	form	NOUN
iajs-805	10	22	of	of	ADP
iajs-805	10	23	a	a	DET
iajs-805	10	24	polynomial	polynomial	NOUN
iajs-805	10	25	.	.	PUNCT
iajs-805	11	1	the	the	DET
iajs-805	11	2	traditional	traditional	ADJ
iajs-805	11	3	high	high	ADJ
iajs-805	11	4	order	order	NOUN
iajs-805	11	5	taylor	taylor	PROPN
iajs-805	11	6	series	series	PROPN
iajs-805	11	7	method	method	PROPN
iajs-805	11	8	requires	require	VERB
iajs-805	11	9	symbolic	symbolic	ADJ
iajs-805	11	10	computation	computation	NOUN
iajs-805	11	11	.	.	PUNCT
iajs-805	12	1	however	however	ADV
iajs-805	12	2	,	,	PUNCT
iajs-805	12	3	the	the	DET
iajs-805	12	4	dtm	dtm	PROPN
iajs-805	12	5	obtains	obtain	VERB
iajs-805	12	6	a	a	DET
iajs-805	12	7	polynomial	polynomial	ADJ
iajs-805	12	8	series	series	NOUN
iajs-805	12	9	solution	solution	NOUN
iajs-805	12	10	by	by	ADP
iajs-805	12	11	means	mean	NOUN
iajs-805	12	12	of	of	ADP
iajs-805	12	13	an	an	DET
iajs-805	12	14	iterative	iterative	NOUN
iajs-805	12	15	procedure	procedure	NOUN
iajs-805	12	16	[	[	X
iajs-805	12	17	3	3	NUM
iajs-805	12	18	]	]	PUNCT
iajs-805	12	19	.	.	PUNCT
iajs-805	13	1	recently	recently	ADV
iajs-805	13	2	the	the	DET
iajs-805	13	3	application	application	NOUN
iajs-805	13	4	of	of	ADP
iajs-805	13	5	differential	differential	ADJ
iajs-805	13	6	transform	transform	NOUN
iajs-805	13	7	method	method	NOUN
iajs-805	13	8	is	be	AUX
iajs-805	13	9	successfully	successfully	ADV
iajs-805	13	10	extended	extend	VERB
iajs-805	13	11	to	to	PART
iajs-805	13	12	obtain	obtain	VERB
iajs-805	13	13	approximate	approximate	ADJ
iajs-805	13	14	solutions	solution	NOUN
iajs-805	13	15	to	to	PART
iajs-805	13	16	linear	linear	VERB
iajs-805	13	17	and	and	CCONJ
iajs-805	13	18	nonlinear	nonlinear	ADJ
iajs-805	13	19	functional	functional	ADJ
iajs-805	13	20	equations	equation	NOUN
iajs-805	13	21	.	.	PUNCT
iajs-805	14	1	delay	delay	NOUN
iajs-805	14	2	differential	differential	ADJ
iajs-805	14	3	equations	equation	NOUN
iajs-805	14	4	are	be	AUX
iajs-805	14	5	observed	observe	VERB
iajs-805	14	6	in	in	ADP
iajs-805	14	7	many	many	ADJ
iajs-805	14	8	fields	field	NOUN
iajs-805	14	9	of	of	ADP
iajs-805	14	10	science	science	NOUN
iajs-805	14	11	and	and	CCONJ
iajs-805	14	12	technology	technology	NOUN
iajs-805	14	13	,	,	PUNCT
iajs-805	14	14	such	such	ADJ
iajs-805	14	15	as	as	ADP
iajs-805	14	16	biology	biology	NOUN
iajs-805	14	17	engineering	engineering	NOUN
iajs-805	14	18	and	and	CCONJ
iajs-805	14	19	physics	physics	NOUN
iajs-805	14	20	.	.	PUNCT
iajs-805	15	1	many	many	ADJ
iajs-805	15	2	dynamic	dynamic	ADJ
iajs-805	15	3	population	population	NOUN
iajs-805	15	4	first	first	ADV
iajs-805	15	5	order	order	VERB
iajs-805	15	6	nonlinear	nonlinear	ADJ
iajs-805	15	7	scalar	scalar	ADJ
iajs-805	15	8	equation	equation	NOUN
iajs-805	15	9	of	of	ADP
iajs-805	15	10	the	the	DET
iajs-805	15	11	form	form	NOUN
iajs-805	15	12	y'(x	y'(x	NOUN
iajs-805	15	13	)	)	PUNCT
iajs-805	15	14	=	=	PUNCT
iajs-805	15	15	g(y(x	g(y(x	NOUN
iajs-805	15	16	)	)	PUNCT
iajs-805	15	17	)	)	PUNCT
iajs-805	15	18	–	–	PUNCT
iajs-805	15	19	g(y(x	g(y(x	NOUN
iajs-805	15	20	–	–	PUNCT
iajs-805	15	21	l	l	NOUN
iajs-805	15	22	)	)	PUNCT
iajs-805	15	23	)	)	PUNCT
iajs-805	15	24	…	…	PUNCT
iajs-805	15	25	(	(	PUNCT
iajs-805	15	26	2	2	NUM
iajs-805	15	27	)	)	PUNCT
iajs-805	15	28	may	may	AUX
iajs-805	15	29	be	be	AUX
iajs-805	15	30	used	use	VERB
iajs-805	15	31	as	as	ADP
iajs-805	15	32	a	a	DET
iajs-805	15	33	model	model	NOUN
iajs-805	15	34	for	for	ADP
iajs-805	15	35	certain	certain	ADJ
iajs-805	15	36	population	population	NOUN
iajs-805	15	37	growth	growth	NOUN
iajs-805	15	38	if	if	SCONJ
iajs-805	15	39	individuals	individual	NOUN
iajs-805	15	40	have	have	VERB
iajs-805	15	41	a	a	DET
iajs-805	15	42	constant	constant	ADJ
iajs-805	15	43	life	life	NOUN
iajs-805	15	44	span	span	NOUN
iajs-805	15	45	l	l	NOUN
iajs-805	15	46	,	,	PUNCT
iajs-805	15	47	where	where	SCONJ
iajs-805	15	48	y(x	y(x	NOUN
iajs-805	15	49	)	)	PUNCT
iajs-805	15	50	is	be	AUX
iajs-805	15	51	the	the	DET
iajs-805	15	52	population	population	NOUN
iajs-805	15	53	size	size	NOUN
iajs-805	15	54	at	at	ADP
iajs-805	15	55	time	time	NOUN
iajs-805	15	56	t	t	PROPN
iajs-805	15	57	and	and	CCONJ
iajs-805	15	58	g(y	g(y	PROPN
iajs-805	15	59	)	)	PUNCT
iajs-805	15	60	is	be	AUX
iajs-805	15	61	the	the	DET
iajs-805	15	62	birth	birth	NOUN
iajs-805	15	63	rate	rate	NOUN
iajs-805	15	64	.	.	PUNCT
iajs-805	16	1	recently	recently	ADV
iajs-805	16	2	,	,	PUNCT
iajs-805	16	3	various	various	ADJ
iajs-805	16	4	methods	method	NOUN
iajs-805	16	5	such	such	ADJ
iajs-805	16	6	as	as	ADP
iajs-805	16	7	,	,	PUNCT
iajs-805	16	8	monotone	monotone	ADJ
iajs-805	16	9	iterative	iterative	NOUN
iajs-805	16	10	technique	technique	NOUN
iajs-805	16	11	,	,	PUNCT
iajs-805	16	12	a	a	DET
iajs-805	16	13	domain	domain	NOUN
iajs-805	16	14	decomposition	decomposition	NOUN
iajs-805	16	15	method	method	NOUN
iajs-805	16	16	and	and	CCONJ
iajs-805	16	17	the	the	DET
iajs-805	16	18	spline	spline	NOUN
iajs-805	16	19	functions	function	NOUN
iajs-805	16	20	method	method	NOUN
iajs-805	16	21	have	have	AUX
iajs-805	16	22	been	be	AUX
iajs-805	16	23	considered	consider	VERB
iajs-805	16	24	for	for	ADP
iajs-805	16	25	approximate	approximate	ADJ
iajs-805	16	26	solutions	solution	NOUN
iajs-805	16	27	of	of	ADP
iajs-805	16	28	dde	dde	PROPN
iajs-805	16	29	[	[	X
iajs-805	16	30	4	4	NUM
iajs-805	16	31	]	]	PUNCT
iajs-805	16	32	.	.	PUNCT
iajs-805	17	1	ibn	ibn	PROPN
iajs-805	17	2	alhaitham	alhaitham	PROPN
iajs-805	17	3	j.	j.	PROPN
iajs-805	17	4	for	for	ADP
iajs-805	17	5	pure	pure	ADJ
iajs-805	17	6	&	&	CCONJ
iajs-805	17	7	appl	appl	PROPN
iajs-805	17	8	.	.	PUNCT
iajs-805	18	1	sci	sci	PROPN
iajs-805	18	2	.	.	PUNCT
iajs-805	18	3	vol.24	vol.24	NOUN
iajs-805	18	4	(	(	PUNCT
iajs-805	18	5	3	3	NUM
iajs-805	18	6	)	)	PUNCT
iajs-805	18	7	2011	2011	NUM
iajs-805	18	8	hence	hence	ADV
iajs-805	18	9	,	,	PUNCT
iajs-805	18	10	due	due	ADP
iajs-805	18	11	to	to	ADP
iajs-805	18	12	practical	practical	ADJ
iajs-805	18	13	reasons	reason	NOUN
iajs-805	18	14	and	and	CCONJ
iajs-805	18	15	the	the	DET
iajs-805	18	16	papers	paper	NOUN
iajs-805	18	17	mentioned	mention	VERB
iajs-805	18	18	above	above	ADV
iajs-805	18	19	,	,	PUNCT
iajs-805	18	20	we	we	PRON
iajs-805	18	21	have	have	AUX
iajs-805	18	22	been	be	AUX
iajs-805	18	23	motivated	motivate	VERB
iajs-805	18	24	to	to	PART
iajs-805	18	25	deal	deal	VERB
iajs-805	18	26	with	with	ADP
iajs-805	18	27	dde	dde	PROPN
iajs-805	18	28	and	and	CCONJ
iajs-805	18	29	develop	develop	VERB
iajs-805	18	30	dtm	dtm	PROPN
iajs-805	18	31	for	for	ADP
iajs-805	18	32	both	both	CCONJ
iajs-805	18	33	linear	linear	ADJ
iajs-805	18	34	and	and	CCONJ
iajs-805	18	35	nonlinear	nonlinear	ADJ
iajs-805	18	36	delay	delay	NOUN
iajs-805	18	37	differential	differential	PROPN
iajs-805	18	38	equations	equation	NOUN
iajs-805	18	39	.	.	PUNCT
iajs-805	19	1	according	accord	VERB
iajs-805	19	2	to	to	ADP
iajs-805	19	3	the	the	DET
iajs-805	19	4	best	good	ADJ
iajs-805	19	5	of	of	ADP
iajs-805	19	6	our	our	PRON
iajs-805	19	7	knowledge	knowledge	NOUN
iajs-805	19	8	,	,	PUNCT
iajs-805	19	9	dtm	dtm	PROPN
iajs-805	19	10	has	have	AUX
iajs-805	19	11	not	not	PART
iajs-805	19	12	been	be	AUX
iajs-805	19	13	studied	study	VERB
iajs-805	19	14	for	for	ADP
iajs-805	19	15	dde	dde	PROPN
iajs-805	19	16	till	till	SCONJ
iajs-805	19	17	now	now	ADV
iajs-805	19	18	.	.	PUNCT
iajs-805	20	1	with	with	ADP
iajs-805	20	2	this	this	DET
iajs-805	20	3	technique	technique	NOUN
iajs-805	20	4	,	,	PUNCT
iajs-805	20	5	it	it	PRON
iajs-805	20	6	is	be	AUX
iajs-805	20	7	possible	possible	ADJ
iajs-805	20	8	to	to	PART
iajs-805	20	9	obtain	obtain	VERB
iajs-805	20	10	highly	highly	ADV
iajs-805	20	11	accurate	accurate	ADJ
iajs-805	20	12	numerical	numerical	ADJ
iajs-805	20	13	solution	solution	NOUN
iajs-805	20	14	,	,	PUNCT
iajs-805	20	15	analytical	analytical	ADJ
iajs-805	20	16	solution	solution	NOUN
iajs-805	20	17	and	and	CCONJ
iajs-805	20	18	as	as	ADV
iajs-805	20	19	well	well	ADV
iajs-805	20	20	as	as	ADP
iajs-805	20	21	exact	exact	ADJ
iajs-805	20	22	solutions	solution	NOUN
iajs-805	20	23	.	.	PUNCT
iajs-805	21	1	the	the	DET
iajs-805	21	2	aim	aim	NOUN
iajs-805	21	3	this	this	DET
iajs-805	21	4	paper	paper	NOUN
iajs-805	21	5	is	be	AUX
iajs-805	21	6	to	to	PART
iajs-805	21	7	extend	extend	VERB
iajs-805	21	8	the	the	DET
iajs-805	21	9	method	method	NOUN
iajs-805	21	10	of	of	ADP
iajs-805	21	11	differential	differential	ADJ
iajs-805	21	12	transformation	transformation	NOUN
iajs-805	21	13	for	for	ADP
iajs-805	21	14	solving	solve	VERB
iajs-805	21	15	differential	differential	ADJ
iajs-805	21	16	equations	equation	NOUN
iajs-805	21	17	with	with	ADP
iajs-805	21	18	multiple	multiple	ADJ
iajs-805	21	19	delay	delay	NOUN
iajs-805	21	20	of	of	ADP
iajs-805	21	21	difference	difference	NOUN
iajs-805	21	22	types	type	NOUN
iajs-805	21	23	as	as	ADP
iajs-805	21	24	in	in	ADP
iajs-805	21	25	equation	equation	NOUN
iajs-805	21	26	(	(	PUNCT
iajs-805	21	27	1	1	NUM
iajs-805	21	28	)	)	PUNCT
iajs-805	21	29	.	.	PUNCT
iajs-805	22	1	differential	differential	ADJ
iajs-805	22	2	transform	transform	NOUN
iajs-805	22	3	method	method	VERB
iajs-805	22	4	the	the	DET
iajs-805	22	5	differential	differential	ADJ
iajs-805	22	6	transform	transform	NOUN
iajs-805	22	7	of	of	ADP
iajs-805	22	8	a	a	DET
iajs-805	22	9	function	function	NOUN
iajs-805	22	10	y(x	y(x	NOUN
iajs-805	22	11	)	)	PUNCT
iajs-805	22	12	is	be	AUX
iajs-805	22	13	defined	define	VERB
iajs-805	22	14	as	as	ADP
iajs-805	22	15	,	,	PUNCT
iajs-805	22	16	[	[	X
iajs-805	22	17	2	2	NUM
iajs-805	22	18	]	]	PUNCT
iajs-805	22	19	:	:	PUNCT
iajs-805	22	20	0	0	NUM
iajs-805	23	1	k	k	X
iajs-805	23	2	x	x	SYM
iajs-805	23	3	xk	xk	PROPN
iajs-805	23	4	1	1	NUM
iajs-805	23	5	d	d	PROPN
iajs-805	23	6	y(k	y(k	PROPN
iajs-805	23	7	)	)	PUNCT
iajs-805	23	8	[	[	PUNCT
iajs-805	23	9	y(x	y(x	PROPN
iajs-805	23	10	)	)	PUNCT
iajs-805	23	11	]	]	PUNCT
iajs-805	23	12	,	,	PUNCT
iajs-805	23	13	k	k	PROPN
iajs-805	23	14	k	k	X
iajs-805	23	15	!	!	PROPN
iajs-805	23	16	dx	dx	PROPN
iajs-805	23	17			NUM
iajs-805	23	18			PROPN
iajs-805	23	19	�	�	PROPN
iajs-805	23	20	…	…	PUNCT
iajs-805	23	21	(	(	PUNCT
iajs-805	23	22	3	3	NUM
iajs-805	23	23	)	)	PUNCT
iajs-805	23	24	where	where	SCONJ
iajs-805	23	25	y(k	y(k	PROPN
iajs-805	23	26	)	)	PUNCT
iajs-805	23	27	refers	refer	VERB
iajs-805	23	28	to	to	ADP
iajs-805	23	29	the	the	DET
iajs-805	23	30	differential	differential	ADJ
iajs-805	23	31	transform	transform	NOUN
iajs-805	23	32	of	of	ADP
iajs-805	23	33	a	a	DET
iajs-805	23	34	given	give	VERB
iajs-805	23	35	function	function	NOUN
iajs-805	23	36	y(x	y(x	NOUN
iajs-805	23	37	)	)	PUNCT
iajs-805	23	38	,	,	PUNCT
iajs-805	23	39	and	and	CCONJ
iajs-805	23	40	0x	0x	NOUN
iajs-805	23	41	is	be	AUX
iajs-805	23	42	the	the	DET
iajs-805	23	43	initial	initial	ADJ
iajs-805	23	44	state	state	NOUN
iajs-805	23	45	.	.	PUNCT
iajs-805	24	1	throughout	throughout	ADP
iajs-805	24	2	this	this	DET
iajs-805	24	3	paper	paper	NOUN
iajs-805	24	4	,	,	PUNCT
iajs-805	24	5	we	we	PRON
iajs-805	24	6	use	use	VERB
iajs-805	24	7	the	the	DET
iajs-805	24	8	small	small	ADJ
iajs-805	24	9	and	and	CCONJ
iajs-805	24	10	capital	capital	NOUN
iajs-805	24	11	letters	letter	NOUN
iajs-805	24	12	to	to	PART
iajs-805	24	13	represent	represent	VERB
iajs-805	24	14	the	the	DET
iajs-805	24	15	original	original	ADJ
iajs-805	24	16	and	and	CCONJ
iajs-805	24	17	transformed	transform	VERB
iajs-805	24	18	functions	function	NOUN
iajs-805	24	19	,	,	PUNCT
iajs-805	24	20	respectively	respectively	ADV
iajs-805	24	21	.	.	PUNCT
iajs-805	25	1	the	the	DET
iajs-805	25	2	inverse	inverse	NOUN
iajs-805	25	3	of	of	ADP
iajs-805	25	4	the	the	DET
iajs-805	25	5	differential	differential	ADJ
iajs-805	25	6	transform	transform	NOUN
iajs-805	25	7	y(k	y(k	PROPN
iajs-805	25	8	)	)	PUNCT
iajs-805	25	9	is	be	AUX
iajs-805	25	10	defined	define	VERB
iajs-805	25	11	by	by	ADP
iajs-805	25	12	k	k	PROPN
iajs-805	25	13	0	0	PROPN
iajs-805	25	14	k	k	NOUN
iajs-805	25	15	0	0	NUM
iajs-805	25	16	y(x	y(x	PROPN
iajs-805	25	17	)	)	PUNCT
iajs-805	25	18	y(k)(x	y(k)(x	NOUN
iajs-805	25	19	x	x	SYM
iajs-805	25	20	)	)	PUNCT
iajs-805	25	21			VERB
iajs-805	25	22			NUM
iajs-805	25	23			NUM
iajs-805	26	1			NOUN
iajs-805	26	2	…	…	PUNCT
iajs-805	26	3	(	(	PUNCT
iajs-805	26	4	4	4	NUM
iajs-805	26	5	)	)	PUNCT
iajs-805	26	6	the	the	DET
iajs-805	26	7	automatic	automatic	ADJ
iajs-805	26	8	computation	computation	NOUN
iajs-805	26	9	of	of	ADP
iajs-805	26	10	dtm	dtm	PROPN
iajs-805	26	11	might	might	AUX
iajs-805	26	12	be	be	AUX
iajs-805	26	13	done	do	VERB
iajs-805	26	14	.	.	PUNCT
iajs-805	27	1	in	in	ADP
iajs-805	27	2	this	this	DET
iajs-805	27	3	case	case	NOUN
iajs-805	27	4	,	,	PUNCT
iajs-805	27	5	the	the	DET
iajs-805	27	6	following	follow	VERB
iajs-805	27	7	steps	step	NOUN
iajs-805	27	8	should	should	AUX
iajs-805	27	9	be	be	AUX
iajs-805	27	10	taken	take	VERB
iajs-805	27	11	into	into	ADP
iajs-805	27	12	consideration	consideration	NOUN
iajs-805	27	13	successively	successively	ADV
iajs-805	27	14	:	:	PUNCT
iajs-805	27	15	i	i	X
iajs-805	27	16	)	)	PUNCT
iajs-805	27	17	the	the	DET
iajs-805	27	18	differential	differential	ADJ
iajs-805	27	19	transform	transform	NOUN
iajs-805	27	20	of	of	ADP
iajs-805	27	21	each	each	DET
iajs-805	27	22	term	term	NOUN
iajs-805	27	23	in	in	ADP
iajs-805	27	24	the	the	DET
iajs-805	27	25	dde	dde	PROPN
iajs-805	27	26	is	be	AUX
iajs-805	27	27	computed	compute	VERB
iajs-805	27	28	;	;	PUNCT
iajs-805	27	29	ii	ii	X
iajs-805	27	30	)	)	PUNCT
iajs-805	27	31	the	the	DET
iajs-805	27	32	recurrence	recurrence	NOUN
iajs-805	27	33	equation	equation	NOUN
iajs-805	27	34	is	be	AUX
iajs-805	27	35	obtained	obtain	VERB
iajs-805	27	36	;	;	PUNCT
iajs-805	27	37	iii)y(0	iii)y(0	PROPN
iajs-805	27	38	)	)	PUNCT
iajs-805	27	39	,	,	PUNCT
iajs-805	27	40	y(1	y(1	PROPN
iajs-805	27	41	)	)	PUNCT
iajs-805	27	42	,	,	PUNCT
iajs-805	27	43	y(2	y(2	PROPN
iajs-805	27	44	)	)	PUNCT
iajs-805	27	45	,	,	PUNCT
iajs-805	27	46	y(3	y(3	PROPN
iajs-805	27	47	)	)	PUNCT
iajs-805	27	48	,	,	PUNCT
iajs-805	27	49	…	…	PUNCT
iajs-805	27	50	are	be	AUX
iajs-805	27	51	calculated	calculate	VERB
iajs-805	27	52	by	by	ADP
iajs-805	27	53	the	the	DET
iajs-805	27	54	recurrence	recurrence	NOUN
iajs-805	27	55	equation	equation	NOUN
iajs-805	27	56	and	and	CCONJ
iajs-805	27	57	given	give	VERB
iajs-805	27	58	initial	initial	ADJ
iajs-805	27	59	condition	condition	NOUN
iajs-805	27	60	;	;	PUNCT
iajs-805	27	61	iv)finally	iv)finally	ADV
iajs-805	27	62	,	,	PUNCT
iajs-805	27	63	these	these	DET
iajs-805	27	64	values	value	NOUN
iajs-805	27	65	are	be	AUX
iajs-805	27	66	substituted	substitute	VERB
iajs-805	27	67	back	back	ADV
iajs-805	27	68	into	into	ADP
iajs-805	27	69	eq	eq	NOUN
iajs-805	27	70	.	.	PUNCT
iajs-805	28	1	(	(	PUNCT
iajs-805	28	2	4	4	NUM
iajs-805	28	3	)	)	PUNCT
iajs-805	28	4	.	.	PUNCT
iajs-805	29	1	preliminaries	preliminary	NOUN
iajs-805	29	2	of	of	ADP
iajs-805	29	3	the	the	DET
iajs-805	29	4	dtm	dtm	NOUN
iajs-805	29	5	the	the	DET
iajs-805	29	6	following	follow	VERB
iajs-805	29	7	theorems	theorem	NOUN
iajs-805	29	8	give	give	VERB
iajs-805	29	9	the	the	DET
iajs-805	29	10	properties	property	NOUN
iajs-805	29	11	of	of	ADP
iajs-805	29	12	the	the	DET
iajs-805	29	13	dtm	dtm	NOUN
iajs-805	29	14	which	which	PRON
iajs-805	29	15	can	can	AUX
iajs-805	29	16	be	be	AUX
iajs-805	29	17	easily	easily	ADV
iajs-805	29	18	derived	derive	VERB
iajs-805	29	19	from	from	ADP
iajs-805	29	20	equations	equation	NOUN
iajs-805	29	21	(	(	PUNCT
iajs-805	29	22	3	3	NUM
iajs-805	29	23	)	)	PUNCT
iajs-805	29	24	and	and	CCONJ
iajs-805	29	25	(	(	PUNCT
iajs-805	29	26	4	4	NUM
iajs-805	29	27	)	)	PUNCT
iajs-805	29	28	,	,	PUNCT
iajs-805	29	29	for	for	ADP
iajs-805	29	30	their	their	PRON
iajs-805	29	31	proofs	proof	NOUN
iajs-805	29	32	and	and	CCONJ
iajs-805	29	33	more	more	ADJ
iajs-805	29	34	details	detail	NOUN
iajs-805	29	35	(	(	PUNCT
iajs-805	29	36	see	see	VERB
iajs-805	29	37	[	[	X
iajs-805	29	38	5	5	NUM
iajs-805	29	39	]	]	PUNCT
iajs-805	29	40	,	,	PUNCT
iajs-805	29	41	[	[	X
iajs-805	29	42	6	6	NUM
iajs-805	29	43	]	]	NUM
iajs-805	29	44	)	)	PUNCT
iajs-805	29	45	.	.	PUNCT
iajs-805	30	1	theorem	theorem	NOUN
iajs-805	30	2	(	(	PUNCT
iajs-805	30	3	1):if	1):if	NUM
iajs-805	30	4	y(x	y(x	NOUN
iajs-805	30	5	)	)	PUNCT
iajs-805	30	6	=	=	SYM
iajs-805	30	7	f(x	f(x	PROPN
iajs-805	30	8	)	)	PUNCT
iajs-805	31	1			PROPN
iajs-805	31	2	g(x	g(x	PROPN
iajs-805	31	3	)	)	PUNCT
iajs-805	31	4	,	,	PUNCT
iajs-805	31	5	then	then	ADV
iajs-805	31	6	y(k	y(k	PROPN
iajs-805	31	7	)	)	PUNCT
iajs-805	31	8	=	=	SYM
iajs-805	31	9	f(x	f(x	PROPN
iajs-805	31	10	)	)	PUNCT
iajs-805	32	1			PROPN
iajs-805	32	2	g(x	g(x	PROPN
iajs-805	32	3	)	)	PUNCT
iajs-805	32	4	.	.	PUNCT
iajs-805	33	1	theorem	theorem	NOUN
iajs-805	33	2	(	(	PUNCT
iajs-805	33	3	2):if	2):if	NUM
iajs-805	33	4	y(x	y(x	NOUN
iajs-805	33	5	)	)	PUNCT
iajs-805	33	6	=	=	SYM
iajs-805	33	7	c	c	PROPN
iajs-805	33	8	f(x	f(x	PROPN
iajs-805	33	9	)	)	PUNCT
iajs-805	33	10	,	,	PUNCT
iajs-805	33	11	then	then	ADV
iajs-805	33	12	y(k	y(k	PROPN
iajs-805	33	13	)	)	PUNCT
iajs-805	33	14	=	=	SYM
iajs-805	33	15	c	c	PROPN
iajs-805	33	16	f(x	f(x	PROPN
iajs-805	33	17	)	)	PUNCT
iajs-805	33	18	theorem	theorem	NOUN
iajs-805	33	19	(	(	PUNCT
iajs-805	33	20	3):if	3):if	NUM
iajs-805	33	21	n	n	CCONJ
iajs-805	33	22	n	n	PROPN
iajs-805	33	23	d	d	X
iajs-805	33	24	f	f	X
iajs-805	33	25	(	(	PUNCT
iajs-805	33	26	x	x	X
iajs-805	33	27	)	)	PUNCT
iajs-805	33	28	(	(	PUNCT
iajs-805	33	29	k	k	NOUN
iajs-805	33	30	n	n	CCONJ
iajs-805	33	31	)	)	PUNCT
iajs-805	33	32	!	!	PUNCT
iajs-805	34	1	y(x	y(x	PROPN
iajs-805	34	2	)	)	PUNCT
iajs-805	34	3	,	,	PUNCT
iajs-805	34	4	then	then	ADV
iajs-805	34	5	y(k	y(k	PROPN
iajs-805	34	6	)	)	PUNCT
iajs-805	34	7	[	[	PUNCT
iajs-805	34	8	]	]	X
iajs-805	34	9	f(k	f(k	ADJ
iajs-805	34	10	n	n	CCONJ
iajs-805	34	11	)	)	PUNCT
iajs-805	34	12	k!dx	k!dx	PROPN
iajs-805	34	13			X
iajs-805	34	14			PROPN
iajs-805	34	15			PROPN
iajs-805	34	16			ADV
iajs-805	34	17	,	,	PUNCT
iajs-805	34	18	k	k	PROPN
iajs-805	34	19	ℕ.	ℕ.	PRON
iajs-805	34	20	theorem	theorem	NOUN
iajs-805	34	21	(	(	PUNCT
iajs-805	34	22	4):if	4):if	NUM
iajs-805	34	23	1	1	NUM
iajs-805	34	24	k	k	NOUN
iajs-805	34	25	1	1	NUM
iajs-805	34	26	1	1	NUM
iajs-805	34	27	k	k	NOUN
iajs-805	34	28	0	0	NUM
iajs-805	34	29	y(x	y(x	PROPN
iajs-805	34	30	)	)	PUNCT
iajs-805	34	31	f	f	PROPN
iajs-805	34	32	(	(	PUNCT
iajs-805	34	33	x).g(x	x).g(x	NUM
iajs-805	34	34	)	)	PUNCT
iajs-805	34	35	,	,	PUNCT
iajs-805	34	36	theny(k	theny(k	NOUN
iajs-805	34	37	)	)	PUNCT
iajs-805	34	38	f(k	f(k	PUNCT
iajs-805	34	39	)	)	PUNCT
iajs-805	34	40	g(k	g(k	NOUN
iajs-805	34	41	k	k	NOUN
iajs-805	34	42	)	)	PUNCT
iajs-805	35	1			NUM
iajs-805	36	1			NUM
iajs-805	36	2			NUM
iajs-805	37	1			NOUN
iajs-805	37	2	,	,	PUNCT
iajs-805	37	3	k	k	PROPN
iajs-805	37	4	ℕ.	ℕ.	ADV
iajs-805	37	5	moreover	moreover	ADV
iajs-805	37	6	,	,	PUNCT
iajs-805	37	7	we	we	PRON
iajs-805	37	8	need	need	VERB
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iajs-805	63	17			PUNCT
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iajs-805	63	22			PROPN
iajs-805	63	23			PROPN
iajs-805	63	24			PUNCT
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iajs-805	65	7	)	)	PUNCT
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iajs-805	65	17			VERB
iajs-805	65	18			PROPN
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iajs-805	65	20			NUM
iajs-805	65	21			NUM
iajs-805	65	22			PROPN
iajs-805	65	23			PROPN
iajs-805	65	24			VERB
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iajs-805	67	3	)	)	PUNCT
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iajs-805	67	13	1	1	NUM
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iajs-805	68	6	)	)	PUNCT
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iajs-805	68	8	1	1	X
iajs-805	68	9	)	)	PUNCT
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iajs-805	68	15			ADJ
iajs-805	68	16			NOUN
iajs-805	68	17			NOUN
iajs-805	68	18			DET
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iajs-805	68	20	(	(	PUNCT
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iajs-805	68	25	y(x	y(x	NOUN
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iajs-805	68	33	)	)	PUNCT
iajs-805	68	34	,	,	PUNCT
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iajs-805	68	39	0	0	PUNCT
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iajs-805	68	43	0	0	NUM
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iajs-805	68	46	1	1	NUM
iajs-805	68	47	1	1	NUM
iajs-805	68	48	2	2	NUM
iajs-805	68	49	1	1	NUM
iajs-805	68	50	2	2	NUM
iajs-805	68	51	1	1	NUM
iajs-805	68	52	2	2	NUM
iajs-805	68	53	1	1	NUM
iajs-805	68	54	1	1	NUM
iajs-805	68	55	11	11	NUM
iajs-805	68	56	1	1	NUM
iajs-805	68	57	2	2	NUM
iajs-805	68	58	1	1	NUM
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iajs-805	70	3	h	h	NOUN
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iajs-805	72	2	h	h	PROPN
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iajs-805	73	5	1	1	NUM
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iajs-805	73	7	2	2	NUM
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iajs-805	74	2	k	k	PROPN
iajs-805	74	3	k	k	PROPN
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iajs-805	75	2	k	k	PROPN
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iajs-805	75	19			PUNCT
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iajs-805	75	21			PROPN
iajs-805	75	22			PROPN
iajs-805	75	23			VERB
iajs-805	75	24			ADJ
iajs-805	75	25			PROPN
iajs-805	75	26			NOUN
iajs-805	75	27			PROPN
iajs-805	75	28			PROPN
iajs-805	76	1			PROPN
iajs-805	76	2			NOUN
iajs-805	76	3			PRON
iajs-805	77	1			X
iajs-805	77	2			PROPN
iajs-805	77	3			X
iajs-805	77	4			X
iajs-805	78	1			PROPN
iajs-805	78	2			PROPN
iajs-805	78	3			NOUN
iajs-805	78	4			NOUN
iajs-805	78	5			NOUN
iajs-805	78	6	n	n	ADJ
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iajs-805	78	8	:	:	PUNCT
iajs-805	78	9	let	let	VERB
iajs-805	78	10	the	the	DET
iajs-805	78	11	differential	differential	NOUN
iajs-805	78	12	transforms	transform	VERB
iajs-805	78	13	of	of	ADP
iajs-805	78	14	f1(x	f1(x	PROPN
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iajs-805	78	16	r1	r1	PROPN
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iajs-805	78	19	f2(x	f2(x	PROPN
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iajs-805	78	21	r2	r2	PROPN
iajs-805	78	22	)	)	PUNCT
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iajs-805	78	24	x	x	X
iajs-805	78	25	=	=	SYM
iajs-805	78	26	x0	x0	PROPN
iajs-805	78	27	be	be	AUX
iajs-805	78	28	g1(k	g1(k	NOUN
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iajs-805	78	30	and	and	CCONJ
iajs-805	78	31	g2(k	g2(k	NOUN
iajs-805	78	32	)	)	PUNCT
iajs-805	78	33	,	,	PUNCT
iajs-805	78	34	respectively	respectively	ADV
iajs-805	78	35	.	.	PUNCT
iajs-805	79	1	using	use	VERB
iajs-805	79	2	theorem	theorem	NOUN
iajs-805	79	3	(	(	PUNCT
iajs-805	79	4	4	4	NUM
iajs-805	79	5	)	)	PUNCT
iajs-805	79	6	,	,	PUNCT
iajs-805	79	7	we	we	PRON
iajs-805	79	8	have	have	VERB
iajs-805	79	9	the	the	DET
iajs-805	79	10	differential	differential	ADJ
iajs-805	79	11	transform	transform	NOUN
iajs-805	79	12	of	of	ADP
iajs-805	79	13	y(x	y(x	NOUN
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iajs-805	80	2	.	.	PUNCT
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iajs-805	80	4	(	(	PUNCT
iajs-805	80	5	3	3	NUM
iajs-805	80	6	)	)	PUNCT
iajs-805	80	7	2011	2011	NUM
iajs-805	80	8	1	1	NUM
iajs-805	80	9	k	k	NOUN
iajs-805	80	10	1	1	NUM
iajs-805	80	11	2	2	NUM
iajs-805	80	12	1	1	NUM
iajs-805	80	13	k	k	NOUN
iajs-805	80	14	0	0	NUM
iajs-805	80	15	y(x	y(x	PROPN
iajs-805	80	16	)	)	PUNCT
iajs-805	80	17	g(k)g	g(k)g	PROPN
iajs-805	80	18	(	(	PUNCT
iajs-805	80	19	k	k	PROPN
iajs-805	80	20	k	k	PROPN
iajs-805	80	21	)	)	PUNCT
iajs-805	80	22	...	...	PUNCT
iajs-805	80	23	(	(	PUNCT
iajs-805	80	24	6	6	X
iajs-805	80	25	)	)	PUNCT
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iajs-805	80	27			NUM
iajs-805	81	1			PROPN
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iajs-805	81	3	theorem	theorem	NOUN
iajs-805	81	4	(	(	PUNCT
iajs-805	81	5	6	6	NUM
iajs-805	81	6	)	)	PUNCT
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iajs-805	81	8	we	we	PRON
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iajs-805	81	10	:	:	PUNCT
iajs-805	81	11	1	1	NUM
iajs-805	81	12	1	1	NUM
iajs-805	81	13	1	1	NUM
iajs-805	81	14	1	1	NUM
iajs-805	81	15	11	11	NUM
iajs-805	81	16	1	1	NUM
iajs-805	81	17	hn	hn	NOUN
iajs-805	81	18	h	h	NOUN
iajs-805	82	1	k	k	PROPN
iajs-805	82	2	h	h	PROPN
iajs-805	83	1	k	k	PROPN
iajs-805	83	2	h1	h1	PROPN
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iajs-805	83	4	k	k	PROPN
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iajs-805	83	6	(	(	PUNCT
iajs-805	83	7	k	k	NOUN
iajs-805	83	8	)	)	PUNCT
iajs-805	83	9	(	(	PUNCT
iajs-805	83	10	1	1	X
iajs-805	83	11	)	)	PUNCT
iajs-805	83	12	r	r	NOUN
iajs-805	83	13	f	f	X
iajs-805	83	14	(	(	PUNCT
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iajs-805	83	17	forn	forn	PROPN
iajs-805	84	1			PROPN
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iajs-805	84	13	2	2	NUM
iajs-805	84	14	2	2	NUM
iajs-805	84	15	1	1	NUM
iajs-805	84	16	2	2	NUM
iajs-805	84	17	1	1	NUM
iajs-805	84	18	2	2	NUM
iajs-805	84	19	11	11	NUM
iajs-805	84	20	1	1	NUM
iajs-805	84	21	hn	hn	NOUN
iajs-805	84	22	h	h	NOUN
iajs-805	85	1	k	k	PROPN
iajs-805	85	2	k	k	PROPN
iajs-805	85	3	h	h	PROPN
iajs-805	86	1	k	k	PROPN
iajs-805	86	2	k	k	PROPN
iajs-805	86	3	h2	h2	PROPN
iajs-805	86	4	1	1	NUM
iajs-805	87	1	k	k	PROPN
iajs-805	87	2	kh	kh	PROPN
iajs-805	87	3	k	k	PROPN
iajs-805	88	1	k	k	PROPN
iajs-805	88	2	g	g	PROPN
iajs-805	88	3	(	(	PUNCT
iajs-805	88	4	k	k	PROPN
iajs-805	88	5	k	k	PROPN
iajs-805	88	6	)	)	PUNCT
iajs-805	88	7	(	(	PUNCT
iajs-805	88	8	1	1	X
iajs-805	88	9	)	)	PUNCT
iajs-805	88	10	r	r	NOUN
iajs-805	88	11	f	f	X
iajs-805	88	12	(	(	PUNCT
iajs-805	88	13	)	)	PUNCT
iajs-805	88	14	,	,	PUNCT
iajs-805	88	15	forn	forn	PROPN
iajs-805	88	16			PROPN
iajs-805	88	17			PROPN
iajs-805	88	18			VERB
iajs-805	88	19			ADJ
iajs-805	88	20			PROPN
iajs-805	88	21			NOUN
iajs-805	88	22			PROPN
iajs-805	88	23			VERB
iajs-805	88	24			PRON
iajs-805	88	25			PROPN
iajs-805	88	26			ADV
iajs-805	88	27			PROPN
iajs-805	88	28			PROPN
iajs-805	88	29			ADJ
iajs-805	88	30			NOUN
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iajs-805	88	32	these	these	DET
iajs-805	88	33	values	value	NOUN
iajs-805	88	34	in	in	ADP
iajs-805	88	35	to	to	ADP
iajs-805	88	36	equation	equation	NOUN
iajs-805	88	37	(	(	PUNCT
iajs-805	88	38	6	6	NUM
iajs-805	88	39	)	)	PUNCT
iajs-805	88	40	,	,	PUNCT
iajs-805	88	41	we	we	PRON
iajs-805	88	42	obtain	obtain	VERB
iajs-805	88	43	:	:	PUNCT
iajs-805	88	44	1	1	NUM
iajs-805	88	45	2	2	NUM
iajs-805	88	46	1	1	NUM
iajs-805	88	47	2	2	NUM
iajs-805	88	48	1	1	NUM
iajs-805	88	49	2	2	NUM
iajs-805	88	50	1	1	NUM
iajs-805	88	51	1	1	NUM
iajs-805	88	52	11	11	NUM
iajs-805	88	53	1	1	NUM
iajs-805	88	54	2	2	NUM
iajs-805	88	55	1	1	NUM
iajs-805	88	56	h	h	NOUN
iajs-805	88	57	hk	hk	PROPN
iajs-805	88	58	n	n	PROPN
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iajs-805	88	60	h	h	NOUN
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iajs-805	90	1	k	k	PROPN
iajs-805	90	2	h	h	PROPN
iajs-805	91	1	k	k	PROPN
iajs-805	91	2	k	k	PROPN
iajs-805	91	3	1	1	NUM
iajs-805	91	4	1	1	NUM
iajs-805	91	5	2	2	NUM
iajs-805	91	6	2	2	NUM
iajs-805	91	7	k	k	NOUN
iajs-805	91	8	k	k	PROPN
iajs-805	91	9	kk	kk	PROPN
iajs-805	92	1	h	h	NOUN
iajs-805	92	2	h	h	NOUN
iajs-805	93	1	k	k	PROPN
iajs-805	93	2	k	k	PROPN
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iajs-805	93	8	)	)	PUNCT
iajs-805	93	9	(	(	PUNCT
iajs-805	93	10	)	)	PUNCT
iajs-805	93	11	r	r	NOUN
iajs-805	93	12	r	r	NOUN
iajs-805	93	13	f	f	X
iajs-805	93	14	(	(	PUNCT
iajs-805	93	15	h	h	NOUN
iajs-805	93	16	)	)	PUNCT
iajs-805	93	17	f	f	PROPN
iajs-805	93	18	(	(	PUNCT
iajs-805	93	19	h	h	NOUN
iajs-805	93	20	)	)	PUNCT
iajs-805	93	21	,	,	PUNCT
iajs-805	93	22	n	n	CCONJ
iajs-805	93	23	k	k	X
iajs-805	93	24			PROPN
iajs-805	93	25			PUNCT
iajs-805	93	26			PROPN
iajs-805	93	27			PROPN
iajs-805	93	28			PROPN
iajs-805	93	29			VERB
iajs-805	93	30			ADJ
iajs-805	93	31			PROPN
iajs-805	93	32			NOUN
iajs-805	93	33			PROPN
iajs-805	93	34			PROPN
iajs-805	93	35			PROPN
iajs-805	93	36			PROPN
iajs-805	93	37			PRON
iajs-805	93	38			VERB
iajs-805	93	39			X
iajs-805	94	1			PROPN
iajs-805	94	2			NOUN
iajs-805	94	3			PROPN
iajs-805	95	1			ADJ
iajs-805	95	2			NOUN
iajs-805	95	3			NOUN
iajs-805	95	4	the	the	DET
iajs-805	95	5	next	next	ADJ
iajs-805	95	6	remark	remark	NOUN
iajs-805	95	7	shows	show	VERB
iajs-805	95	8	that	that	SCONJ
iajs-805	95	9	the	the	DET
iajs-805	95	10	dtm	dtm	PROPN
iajs-805	95	11	in	in	ADP
iajs-805	95	12	ddes	ddes	PROPN
iajs-805	95	13	is	be	AUX
iajs-805	95	14	generalization	generalization	NOUN
iajs-805	95	15	to	to	ADP
iajs-805	95	16	the	the	DET
iajs-805	95	17	dtm	dtm	PROPN
iajs-805	95	18	in	in	ADP
iajs-805	95	19	odes	ode	NOUN
iajs-805	95	20	.	.	PUNCT
iajs-805	96	1	remark	remark	NOUN
iajs-805	96	2	:	:	PUNCT
iajs-805	96	3	if	if	SCONJ
iajs-805	96	4	r1	r1	PROPN
iajs-805	96	5	=	=	SYM
iajs-805	96	6	0	0	NUM
iajs-805	96	7	and	and	CCONJ
iajs-805	96	8	r2	r2	PROPN
iajs-805	96	9	=	=	SYM
iajs-805	96	10	0	0	NUM
iajs-805	96	11	,	,	PUNCT
iajs-805	96	12	then	then	ADV
iajs-805	96	13	theorem	theorem	ADJ
iajs-805	96	14	(	(	PUNCT
iajs-805	96	15	7	7	NUM
iajs-805	96	16	)	)	PUNCT
iajs-805	96	17	reduces	reduce	VERB
iajs-805	96	18	to	to	PART
iajs-805	96	19	theorem	theorem	VERB
iajs-805	96	20	(	(	PUNCT
iajs-805	96	21	4	4	NUM
iajs-805	96	22	)	)	PUNCT
iajs-805	96	23	.	.	PUNCT
iajs-805	97	1	similarly	similarly	ADV
iajs-805	97	2	,	,	PUNCT
iajs-805	97	3	as	as	ADP
iajs-805	97	4	in	in	ADP
iajs-805	97	5	theorem	theorem	NOUN
iajs-805	97	6	(	(	PUNCT
iajs-805	97	7	7	7	X
iajs-805	97	8	)	)	PUNCT
iajs-805	97	9	we	we	PRON
iajs-805	97	10	may	may	AUX
iajs-805	97	11	generalize	generalize	VERB
iajs-805	97	12	the	the	DET
iajs-805	97	13	result	result	NOUN
iajs-805	97	14	for	for	ADP
iajs-805	97	15	the	the	DET
iajs-805	97	16	n	n	NOUN
iajs-805	97	17	-	-	PUNCT
iajs-805	97	18	delays	delay	NOUN
iajs-805	97	19	as	as	ADP
iajs-805	97	20	in	in	ADP
iajs-805	97	21	the	the	DET
iajs-805	97	22	next	next	ADJ
iajs-805	97	23	theorem	theorem	NOUN
iajs-805	97	24	:	:	PUNCT
iajs-805	97	25	theorem	theorem	NOUN
iajs-805	97	26	(	(	PUNCT
iajs-805	97	27	8):the	8):the	DET
iajs-805	97	28	differential	differential	ADJ
iajs-805	97	29	transform	transform	NOUN
iajs-805	97	30	of	of	ADP
iajs-805	97	31	y(x	y(x	NOUN
iajs-805	97	32	)	)	PUNCT
iajs-805	97	33	=	=	SYM
iajs-805	97	34	f1(x	f1(x	PROPN
iajs-805	97	35	–	–	PUNCT
iajs-805	97	36	r1)f2(x	r1)f2(x	NOUN
iajs-805	97	37	–	–	PUNCT
iajs-805	97	38	r2)	r2)	NOUN
iajs-805	97	39	…	…	PUNCT
iajs-805	97	40			NUM
iajs-805	97	41	fn(x	fn(x	NUM
iajs-805	97	42	–	–	PUNCT
iajs-805	97	43	rn	rn	NOUN
iajs-805	97	44	)	)	PUNCT
iajs-805	97	45	,	,	PUNCT
iajs-805	97	46	provided	provide	VERB
iajs-805	97	47	that	that	SCONJ
iajs-805	97	48	ri	ri	PROPN
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iajs-805	97	50	,	,	PUNCT
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iajs-805	97	52	=	=	NOUN
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iajs-805	97	54	,	,	PUNCT
iajs-805	97	55	2	2	NUM
iajs-805	97	56	,	,	PUNCT
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iajs-805	97	58	,	,	PUNCT
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iajs-805	97	62	h	h	PROPN
iajs-805	97	63	h	h	NOUN
iajs-805	98	1	hk	hk	PROPN
iajs-805	98	2	kk	kk	INTJ
iajs-805	98	3	k	k	PROPN
iajs-805	99	1	n	n	CCONJ
iajs-805	99	2	n	n	CCONJ
iajs-805	99	3	n	n	CCONJ
iajs-805	99	4	n	n	ADV
iajs-805	99	5	1	1	NUM
iajs-805	99	6	2	2	NUM
iajs-805	99	7	n	n	NOUN
iajs-805	99	8	13n	13n	NUM
iajs-805	99	9	1	1	NUM
iajs-805	99	10	2	2	NUM
iajs-805	99	11	h	h	NOUN
iajs-805	99	12	h	h	NOUN
iajs-805	99	13	...	...	PUNCT
iajs-805	100	1	h	h	PROPN
iajs-805	100	2	k1	k1	PROPN
iajs-805	100	3	2	2	NUM
iajs-805	100	4	ny(k	ny(k	NUM
iajs-805	100	5	)	)	PUNCT
iajs-805	100	6	.....	.....	PUNCT
iajs-805	101	1	.....	.....	PUNCT
iajs-805	101	2	(	(	PUNCT
iajs-805	101	3	1	1	X
iajs-805	101	4	)	)	PUNCT
iajs-805	101	5	..	..	PUNCT
iajs-805	102	1	k	k	X
iajs-805	103	1	k	k	PROPN
iajs-805	103	2	k	k	PROPN
iajs-805	103	3	k	k	PROPN
iajs-805	103	4	kk	kk	PROPN
iajs-805	104	1	0h	0h	X
iajs-805	104	2	0	0	PUNCT
iajs-805	105	1	k	k	PROPN
iajs-805	105	2	0k	0k	NOUN
iajs-805	105	3	0h	0h	PROPN
iajs-805	106	1	k	k	PROPN
iajs-805	106	2	h	h	PROPN
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iajs-805	108	1	k	k	PROPN
iajs-805	109	1	h	h	NOUN
iajs-805	110	1	k	k	PROPN
iajs-805	111	1	k	k	PROPN
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iajs-805	113	1	k	k	PROPN
iajs-805	113	2	k	k	PROPN
iajs-805	113	3	1	1	NUM
iajs-805	113	4	2	2	NUM
iajs-805	113	5	1	1	NUM
iajs-805	113	6	n	n	NUM
iajs-805	113	7	1	1	NUM
iajs-805	113	8	n	n	NUM
iajs-805	113	9	2n	2n	NUM
iajs-805	113	10	1	1	NUM
iajs-805	113	11	n	n	NUM
iajs-805	113	12	2	2	NUM
iajs-805	113	13	2	2	NUM
iajs-805	113	14	1	1	NUM
iajs-805	113	15	1	1	NUM
iajs-805	113	16	1	1	NUM
iajs-805	113	17	2	2	NUM
iajs-805	113	18	2	2	NUM
iajs-805	113	19	1	1	NUM
iajs-805	113	20	n	n	NUM
iajs-805	113	21	1	1	NUM
iajs-805	113	22	n	n	NUM
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iajs-805	113	26	n	n	NUM
iajs-805	113	27	n	n	NOUN
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iajs-805	114	2	h	h	PROPN
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iajs-805	115	6	r	r	NOUN
iajs-805	115	7	....	....	PUNCT
iajs-805	115	8	r1	r1	NOUN
iajs-805	115	9	2	2	NUM
iajs-805	115	10	n	n	NUM
iajs-805	115	11	1	1	NUM
iajs-805	115	12	k	k	NOUN
iajs-805	115	13	kn	kn	PROPN
iajs-805	115	14	1	1	NUM
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iajs-805	115	17			PROPN
iajs-805	115	18			PROPN
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iajs-805	115	20			PUNCT
iajs-805	115	21			PUNCT
iajs-805	115	22			PUNCT
iajs-805	115	23			PROPN
iajs-805	115	24			PROPN
iajs-805	115	25			NOUN
iajs-805	116	1			PROPN
iajs-805	117	1			PROPN
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iajs-805	118	1			X
iajs-805	118	2			X
iajs-805	118	3			X
iajs-805	118	4			X
iajs-805	118	5			X
iajs-805	118	6			X
iajs-805	118	7			X
iajs-805	119	1			PROPN
iajs-805	119	2			NOUN
iajs-805	120	1			PROPN
iajs-805	120	2			PROPN
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iajs-805	120	4			PROPN
iajs-805	120	5			PROPN
iajs-805	121	1			NUM
iajs-805	121	2			NUM
iajs-805	122	1			NUM
iajs-805	122	2			PROPN
iajs-805	122	3			PROPN
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iajs-805	122	15			PROPN
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iajs-805	122	17			PROPN
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iajs-805	122	22			PROPN
iajs-805	122	23			PROPN
iajs-805	122	24			PROPN
iajs-805	122	25			PROPN
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iajs-805	123	18	)	)	PUNCT
iajs-805	123	19	...	...	PUNCT
iajs-805	124	1	f	f	X
iajs-805	124	2	(	(	PUNCT
iajs-805	124	3	h	h	NOUN
iajs-805	124	4	)	)	PUNCT
iajs-805	124	5	f	f	PROPN
iajs-805	124	6	(	(	PUNCT
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iajs-805	124	8	)	)	PUNCT
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iajs-805	124	12	1	1	NUM
iajs-805	124	13	1	1	NUM
iajs-805	124	14	2	2	NUM
iajs-805	124	15	2	2	NUM
iajs-805	124	16	n	n	NUM
iajs-805	124	17	1	1	NUM
iajs-805	124	18	n	n	NUM
iajs-805	124	19	1	1	NUM
iajs-805	124	20	n	n	CCONJ
iajs-805	124	21	n	n	PRON
iajs-805	124	22			NOUN
iajs-805	124	23			PUNCT
iajs-805	124	24			PROPN
iajs-805	124	25			PROPN
iajs-805	124	26			PROPN
iajs-805	124	27			PROPN
iajs-805	124	28			PART
iajs-805	124	29			PUNCT
iajs-805	124	30			VERB
iajs-805	124	31			NOUN
iajs-805	124	32	…	…	PUNCT
iajs-805	124	33	(	(	PUNCT
iajs-805	124	34	7	7	X
iajs-805	124	35	)	)	PUNCT
iajs-805	124	36	illustrative	illustrative	ADJ
iajs-805	124	37	examples	example	NOUN
iajs-805	124	38	in	in	ADP
iajs-805	124	39	this	this	DET
iajs-805	124	40	section	section	NOUN
iajs-805	124	41	,	,	PUNCT
iajs-805	124	42	some	some	DET
iajs-805	124	43	liner	liner	NOUN
iajs-805	124	44	and	and	CCONJ
iajs-805	124	45	nonlinear	nonlinear	ADJ
iajs-805	124	46	differential	differential	ADJ
iajs-805	124	47	equations	equation	NOUN
iajs-805	124	48	with	with	ADP
iajs-805	124	49	multiple	multiple	ADJ
iajs-805	124	50	delay	delay	NOUN
iajs-805	124	51	are	be	AUX
iajs-805	124	52	considered	consider	VERB
iajs-805	124	53	.by	.by	PUNCT
iajs-805	124	54	using	use	VERB
iajs-805	124	55	dtm	dtm	PROPN
iajs-805	124	56	,	,	PUNCT
iajs-805	124	57	we	we	PRON
iajs-805	124	58	obtain	obtain	VERB
iajs-805	124	59	an	an	DET
iajs-805	124	60	approximate	approximate	ADJ
iajs-805	124	61	and	and	CCONJ
iajs-805	124	62	exact	exact	ADJ
iajs-805	124	63	solutions	solution	NOUN
iajs-805	124	64	when	when	SCONJ
iajs-805	124	65	the	the	DET
iajs-805	124	66	original	original	ADJ
iajs-805	124	67	problem	problem	NOUN
iajs-805	124	68	has	have	VERB
iajs-805	124	69	an	an	DET
iajs-805	124	70	exact	exact	ADJ
iajs-805	124	71	solution	solution	NOUN
iajs-805	124	72	in	in	ADP
iajs-805	124	73	polynomial	polynomial	ADJ
iajs-805	124	74	form	form	NOUN
iajs-805	124	75	.	.	PUNCT
iajs-805	125	1	example	example	NOUN
iajs-805	125	2	1	1	NUM
iajs-805	125	3	:	:	PUNCT
iajs-805	125	4	let	let	VERB
iajs-805	125	5	us	we	PRON
iajs-805	125	6	consider	consider	VERB
iajs-805	125	7	the	the	DET
iajs-805	125	8	following	follow	VERB
iajs-805	125	9	initial	initial	ADJ
iajs-805	125	10	value	value	NOUN
iajs-805	125	11	problem	problem	NOUN
iajs-805	125	12	:	:	PUNCT
iajs-805	125	13	dy	dy	NOUN
iajs-805	125	14	y(x	y(x	PROPN
iajs-805	125	15	1	1	NUM
iajs-805	125	16	)	)	PUNCT
iajs-805	125	17	y(x	y(x	PROPN
iajs-805	125	18	2	2	NUM
iajs-805	125	19	)	)	PUNCT
iajs-805	125	20	2x	2x	NUM
iajs-805	125	21	2,0	2,0	NUM
iajs-805	125	22	x	x	SYM
iajs-805	125	23	1	1	NUM
iajs-805	125	24	...	...	PUNCT
iajs-805	125	25	(	(	PUNCT
iajs-805	125	26	8)	8)	NUM
iajs-805	125	27	dx	dx	PROPN
iajs-805	125	28			ADV
iajs-805	125	29			PROPN
iajs-805	125	30			VERB
iajs-805	125	31			PROPN
iajs-805	125	32			PROPN
iajs-805	125	33			PROPN
iajs-805	125	34			NOUN
iajs-805	125	35			NOUN
iajs-805	125	36	ibn	ibn	PROPN
iajs-805	125	37	alhaitham	alhaitham	NOUN
iajs-805	125	38	j.	j.	PROPN
iajs-805	125	39	for	for	ADP
iajs-805	125	40	pure	pure	ADJ
iajs-805	125	41	&	&	CCONJ
iajs-805	125	42	appl	appl	PROPN
iajs-805	125	43	.	.	PUNCT
iajs-805	126	1	sci	sci	PROPN
iajs-805	126	2	.	.	PUNCT
iajs-805	126	3	vol.24	vol.24	NOUN
iajs-805	126	4	(	(	PUNCT
iajs-805	126	5	3	3	NUM
iajs-805	126	6	)	)	PUNCT
iajs-805	126	7	2011	2011	NUM
iajs-805	126	8	with	with	ADP
iajs-805	126	9	the	the	DET
iajs-805	126	10	initial	initial	ADJ
iajs-805	126	11	condition	condition	NOUN
iajs-805	126	12	y(0	y(0	PROPN
iajs-805	126	13	)	)	PUNCT
iajs-805	126	14	=	=	NOUN
iajs-805	126	15	0	0	NUM
iajs-805	126	16	…	…	PUNCT
iajs-805	126	17	(	(	PUNCT
iajs-805	126	18	9	9	NUM
iajs-805	126	19	)	)	PUNCT
iajs-805	126	20	by	by	ADP
iajs-805	126	21	applying	apply	VERB
iajs-805	126	22	the	the	DET
iajs-805	126	23	dtm	dtm	NOUN
iajs-805	126	24	,	,	PUNCT
iajs-805	126	25	we	we	PRON
iajs-805	126	26	can	can	AUX
iajs-805	126	27	get	get	VERB
iajs-805	126	28	the	the	DET
iajs-805	126	29	exact	exact	ADJ
iajs-805	126	30	solution	solution	NOUN
iajs-805	126	31	for	for	ADP
iajs-805	126	32	eq	eq	PROPN
iajs-805	126	33	.	.	PUNCT
iajs-805	127	1	(	(	PUNCT
iajs-805	127	2	8)	8)	NUM
iajs-805	127	3	and	and	CCONJ
iajs-805	127	4	eq	eq	NOUN
iajs-805	127	5	.	.	PUNCT
iajs-805	128	1	(	(	PUNCT
iajs-805	128	2	9	9	NUM
iajs-805	128	3	)	)	PUNCT
iajs-805	128	4	.	.	PUNCT
iajs-805	129	1	indeed	indeed	ADV
iajs-805	129	2	,	,	PUNCT
iajs-805	129	3	using	use	VERB
iajs-805	129	4	theorems	theorem	NOUN
iajs-805	129	5	(	(	PUNCT
iajs-805	129	6	2	2	NUM
iajs-805	129	7	)	)	PUNCT
iajs-805	129	8	,	,	PUNCT
iajs-805	129	9	(	(	PUNCT
iajs-805	129	10	3	3	X
iajs-805	129	11	)	)	PUNCT
iajs-805	129	12	and	and	CCONJ
iajs-805	129	13	(	(	PUNCT
iajs-805	129	14	6	6	X
iajs-805	129	15	)	)	PUNCT
iajs-805	129	16	the	the	DET
iajs-805	129	17	differential	differential	ADJ
iajs-805	129	18	transform	transform	NOUN
iajs-805	129	19	for	for	ADP
iajs-805	129	20	equation	equation	NOUN
iajs-805	129	21	(	(	PUNCT
iajs-805	129	22	8)	8)	NUM
iajs-805	129	23	is	be	AUX
iajs-805	129	24	found	find	VERB
iajs-805	129	25	as	as	ADP
iajs-805	129	26	h	h	NOUN
iajs-805	129	27	hn	hn	PROPN
iajs-805	129	28	n1	n1	PROPN
iajs-805	129	29	2h	2h	NUM
iajs-805	130	1	k	k	NOUN
iajs-805	130	2	h	h	PROPN
iajs-805	131	1	kh	kh	PROPN
iajs-805	131	2	k	k	PROPN
iajs-805	131	3	h	h	PROPN
iajs-805	131	4	k1	k1	PROPN
iajs-805	131	5	21	21	NUM
iajs-805	131	6	2(k	2(k	NUM
iajs-805	131	7	1)y(k	1)y(k	NUM
iajs-805	131	8	1	1	NUM
iajs-805	131	9	)	)	PUNCT
iajs-805	131	10	(	(	PUNCT
iajs-805	131	11	1	1	NUM
iajs-805	131	12	)	)	SYM
iajs-805	131	13	1	1	NUM
iajs-805	131	14	y(h	y(h	NOUN
iajs-805	131	15	)	)	PUNCT
iajs-805	131	16	(	(	PUNCT
iajs-805	131	17	1	1	X
iajs-805	131	18	)	)	SYM
iajs-805	131	19	2	2	NUM
iajs-805	131	20	y(h	y(h	NOUN
iajs-805	131	21	)	)	PUNCT
iajs-805	131	22	2	2	NUM
iajs-805	131	23	(	(	PUNCT
iajs-805	131	24	k	k	NOUN
iajs-805	131	25	1	1	NUM
iajs-805	131	26	)	)	PUNCT
iajs-805	131	27	2	2	NUM
iajs-805	131	28	(	(	PUNCT
iajs-805	131	29	k)1	k)1	NOUN
iajs-805	131	30	2	2	NUM
iajs-805	131	31	k	k	PROPN
iajs-805	131	32	kh	kh	PROPN
iajs-805	131	33	k	k	PROPN
iajs-805	131	34	h	h	PROPN
iajs-805	131	35	k1	k1	PROPN
iajs-805	131	36	11	11	NUM
iajs-805	131	37	1	1	NUM
iajs-805	131	38	2	2	NUM
iajs-805	131	39			NOUN
iajs-805	131	40			NOUN
iajs-805	131	41			NOUN
iajs-805	131	42			NOUN
iajs-805	131	43			PUNCT
iajs-805	132	1			PROPN
iajs-805	132	2			PROPN
iajs-805	133	1			PROPN
iajs-805	133	2			PRON
iajs-805	134	1			PROPN
iajs-805	134	2			PUNCT
iajs-805	134	3			PUNCT
iajs-805	134	4			PROPN
iajs-805	134	5			VERB
iajs-805	134	6			VERB
iajs-805	134	7			PROPN
iajs-805	134	8			NUM
iajs-805	134	9			PROPN
iajs-805	134	10			PROPN
iajs-805	134	11			PROPN
iajs-805	134	12			PROPN
iajs-805	135	1			PROPN
iajs-805	136	1			PROPN
iajs-805	136	2			NOUN
iajs-805	137	1			PROPN
iajs-805	137	2			NOUN
iajs-805	137	3			PROPN
iajs-805	137	4			NOUN
iajs-805	137	5	…	…	PUNCT
iajs-805	137	6	(	(	PUNCT
iajs-805	137	7	10	10	NUM
iajs-805	137	8	)	)	PUNCT
iajs-805	137	9	where	where	SCONJ
iajs-805	137	10	(k	(k	PROPN
iajs-805	137	11	–	–	PUNCT
iajs-805	137	12	n	n	CCONJ
iajs-805	137	13	)	)	PUNCT
iajs-805	137	14	is	be	AUX
iajs-805	137	15	the	the	DET
iajs-805	137	16	differential	differential	ADJ
iajs-805	137	17	transform	transform	NOUN
iajs-805	137	18	of	of	ADP
iajs-805	137	19	xn	xn	PROPN
iajs-805	137	20	at	at	ADP
iajs-805	137	21	x0	x0	PROPN
iajs-805	138	1	=	=	SYM
iajs-805	138	2	0	0	PUNCT
iajs-805	139	1	and	and	CCONJ
iajs-805	139	2	it	it	PRON
iajs-805	139	3	is	be	AUX
iajs-805	139	4	easily	easily	ADV
iajs-805	139	5	show	show	VERB
iajs-805	139	6	that	that	SCONJ
iajs-805	139	7	:	:	PUNCT
iajs-805	139	8	1,k	1,k	PROPN
iajs-805	139	9	n	n	CCONJ
iajs-805	139	10	(	(	PUNCT
iajs-805	139	11	k	k	PROPN
iajs-805	139	12	n	n	CCONJ
iajs-805	139	13	)	)	PUNCT
iajs-805	139	14	...	...	PUNCT
iajs-805	140	1	(	(	PUNCT
iajs-805	140	2	11	11	NUM
iajs-805	140	3	)	)	PUNCT
iajs-805	140	4	0,k	0,k	NUM
iajs-805	140	5	n	n	CCONJ
iajs-805	140	6	,	,	PUNCT
iajs-805	140	7	n	n	CCONJ
iajs-805	140	8	0,2	0,2	NUM
iajs-805	140	9			PROPN
iajs-805	140	10			PROPN
iajs-805	140	11			PROPN
iajs-805	140	12			NUM
iajs-805	140	13			NOUN
iajs-805	140	14			NOUN
iajs-805	140	15	considering	considering	NOUN
iajs-805	140	16	,	,	PUNCT
iajs-805	140	17	the	the	DET
iajs-805	140	18	differential	differential	ADJ
iajs-805	140	19	transform	transform	NOUN
iajs-805	140	20	of	of	ADP
iajs-805	140	21	y(x	y(x	NOUN
iajs-805	140	22	)	)	PUNCT
iajs-805	140	23	at	at	ADP
iajs-805	140	24	x0	x0	PROPN
iajs-805	140	25	=	=	SYM
iajs-805	140	26	0	0	PROPN
iajs-805	140	27	,	,	PUNCT
iajs-805	140	28	the	the	DET
iajs-805	140	29	initial	initial	ADJ
iajs-805	140	30	conditions	condition	NOUN
iajs-805	140	31	in	in	ADP
iajs-805	140	32	equation	equation	NOUN
iajs-805	140	33	(	(	PUNCT
iajs-805	140	34	9	9	NUM
iajs-805	140	35	)	)	PUNCT
iajs-805	140	36	are	be	AUX
iajs-805	140	37	transformed	transform	VERB
iajs-805	140	38	into	into	ADP
iajs-805	140	39	y(0	y(0	PROPN
iajs-805	140	40	)	)	PUNCT
iajs-805	140	41	=	=	SYM
iajs-805	140	42	0	0	NUM
iajs-805	140	43	,	,	PUNCT
iajs-805	140	44	respectively	respectively	ADV
iajs-805	140	45	.	.	PUNCT
iajs-805	141	1	form	form	PROPN
iajs-805	141	2	equation(10	equation(10	PROPN
iajs-805	141	3	)	)	PUNCT
iajs-805	141	4	,	,	PUNCT
iajs-805	141	5	we	we	PRON
iajs-805	141	6	obtain	obtain	VERB
iajs-805	141	7	:	:	PUNCT
iajs-805	141	8	y(1	y(1	PROPN
iajs-805	141	9	)	)	PUNCT
iajs-805	141	10	=	=	SYM
iajs-805	142	1	1	1	NUM
iajs-805	142	2	,	,	PUNCT
iajs-805	142	3	y(k	y(k	PROPN
iajs-805	142	4	)	)	PUNCT
iajs-805	142	5	=	=	SYM
iajs-805	143	1	0	0	NUM
iajs-805	143	2	,	,	PUNCT
iajs-805	143	3	for	for	ADP
iajs-805	143	4	k	k	PROPN
iajs-805	143	5			NUM
iajs-805	143	6	2	2	NUM
iajs-805	143	7	then	then	ADV
iajs-805	143	8	,	,	PUNCT
iajs-805	143	9	by	by	ADP
iajs-805	143	10	using	use	VERB
iajs-805	143	11	the	the	DET
iajs-805	143	12	inverse	inverse	NOUN
iajs-805	143	13	transform	transform	NOUN
iajs-805	143	14	defined	define	VERB
iajs-805	143	15	by	by	ADP
iajs-805	143	16	equation	equation	NOUN
iajs-805	143	17	(	(	PUNCT
iajs-805	143	18	4	4	NUM
iajs-805	143	19	)	)	PUNCT
iajs-805	143	20	,	,	PUNCT
iajs-805	143	21	we	we	PRON
iajs-805	143	22	obtain	obtain	VERB
iajs-805	143	23	the	the	DET
iajs-805	143	24	exact	exact	ADJ
iajs-805	143	25	solution	solution	NOUN
iajs-805	143	26	y(x	y(x	NOUN
iajs-805	143	27	)	)	PUNCT
iajs-805	144	1	=	=	PUNCT
iajs-805	144	2	x.	x.	NOUN
iajs-805	144	3	example	example	NOUN
iajs-805	144	4	2	2	NUM
iajs-805	144	5	:	:	PUNCT
iajs-805	144	6	in	in	ADP
iajs-805	144	7	this	this	DET
iajs-805	144	8	example	example	NOUN
iajs-805	144	9	,	,	PUNCT
iajs-805	144	10	we	we	PRON
iajs-805	144	11	consider	consider	VERB
iajs-805	144	12	the	the	DET
iajs-805	144	13	second	second	ADJ
iajs-805	144	14	order	order	NOUN
iajs-805	144	15	linear	linear	NOUN
iajs-805	144	16	differential	differential	ADJ
iajs-805	144	17	equation	equation	NOUN
iajs-805	144	18	with	with	ADP
iajs-805	144	19	multiple	multiple	ADJ
iajs-805	144	20	delay	delay	NOUN
iajs-805	144	21	:	:	PUNCT
iajs-805	144	22	2	2	NUM
iajs-805	144	23	2	2	NUM
iajs-805	144	24	2	2	NUM
iajs-805	144	25	d	d	NOUN
iajs-805	144	26	y	y	PROPN
iajs-805	144	27	y(x	y(x	PROPN
iajs-805	144	28	1	1	NUM
iajs-805	144	29	)	)	PUNCT
iajs-805	144	30	y(x	y(x	PROPN
iajs-805	144	31	2	2	NUM
iajs-805	144	32	)	)	PUNCT
iajs-805	144	33	2x	2x	NOUN
iajs-805	144	34	6x	6x	NUM
iajs-805	144	35	7,0	7,0	NUM
iajs-805	144	36	x	x	SYM
iajs-805	144	37	1	1	NUM
iajs-805	144	38	...	...	PUNCT
iajs-805	144	39	(	(	PUNCT
iajs-805	144	40	12	12	NUM
iajs-805	144	41	)	)	PUNCT
iajs-805	144	42	dx	dx	PROPN
iajs-805	144	43			PROPN
iajs-805	144	44			PROPN
iajs-805	144	45			VERB
iajs-805	144	46			PROPN
iajs-805	144	47			PROPN
iajs-805	144	48			PROPN
iajs-805	144	49			PART
iajs-805	144	50			NOUN
iajs-805	144	51			NOUN
iajs-805	144	52	and	and	CCONJ
iajs-805	144	53	the	the	DET
iajs-805	144	54	following	follow	VERB
iajs-805	144	55	initial	initial	ADJ
iajs-805	144	56	condition	condition	NOUN
iajs-805	144	57	:	:	PUNCT
iajs-805	144	58	y(0	y(0	NOUN
iajs-805	144	59	)	)	PUNCT
iajs-805	144	60	=	=	SYM
iajs-805	144	61	0	0	NUM
iajs-805	144	62	,	,	PUNCT
iajs-805	144	63	y'(0	y'(0	PROPN
iajs-805	144	64	)	)	PUNCT
iajs-805	144	65	=	=	SYM
iajs-805	144	66	0	0	NUM
iajs-805	144	67	…	…	PUNCT
iajs-805	144	68	(	(	PUNCT
iajs-805	144	69	13	13	NUM
iajs-805	144	70	)	)	PUNCT
iajs-805	144	71	using	use	VERB
iajs-805	144	72	theorem	theorem	NOUN
iajs-805	144	73	(	(	PUNCT
iajs-805	144	74	3	3	NUM
iajs-805	144	75	)	)	PUNCT
iajs-805	144	76	and	and	CCONJ
iajs-805	144	77	(	(	PUNCT
iajs-805	144	78	6	6	NUM
iajs-805	144	79	)	)	PUNCT
iajs-805	144	80	,	,	PUNCT
iajs-805	144	81	the	the	DET
iajs-805	144	82	differential	differential	ADJ
iajs-805	144	83	transform	transform	NOUN
iajs-805	144	84	for	for	ADP
iajs-805	144	85	eq	eq	NOUN
iajs-805	144	86	.	.	PUNCT
iajs-805	145	1	(	(	PUNCT
iajs-805	145	2	12	12	NUM
iajs-805	145	3	)	)	PUNCT
iajs-805	145	4	is	be	AUX
iajs-805	145	5	found	find	VERB
iajs-805	145	6	as	as	ADP
iajs-805	145	7	:	:	PUNCT
iajs-805	145	8	h	h	PROPN
iajs-805	145	9	hn	hn	PROPN
iajs-805	145	10	n1	n1	PROPN
iajs-805	145	11	2h	2h	NUM
iajs-805	146	1	k	k	NOUN
iajs-805	146	2	h	h	PROPN
iajs-805	147	1	kh	kh	PROPN
iajs-805	147	2	k	k	PROPN
iajs-805	147	3	h	h	PROPN
iajs-805	147	4	k1	k1	PROPN
iajs-805	147	5	21	21	NUM
iajs-805	147	6	2(k	2(k	NUM
iajs-805	147	7	1)(k	1)(k	NUM
iajs-805	147	8	2)y(k	2)y(k	NUM
iajs-805	147	9	2	2	NUM
iajs-805	147	10	)	)	PUNCT
iajs-805	147	11	(	(	PUNCT
iajs-805	147	12	1	1	NUM
iajs-805	147	13	)	)	SYM
iajs-805	147	14	1	1	NUM
iajs-805	147	15	y(h	y(h	NOUN
iajs-805	147	16	)	)	PUNCT
iajs-805	147	17	(	(	PUNCT
iajs-805	147	18	1	1	X
iajs-805	147	19	)	)	SYM
iajs-805	147	20	2	2	NUM
iajs-805	147	21	y(h	y(h	NOUN
iajs-805	147	22	)	)	PUNCT
iajs-805	147	23	2	2	NUM
iajs-805	147	24	(	(	PUNCT
iajs-805	147	25	k	k	NOUN
iajs-805	147	26	2	2	NUM
iajs-805	147	27	)	)	PUNCT
iajs-805	147	28	6	6	NUM
iajs-805	147	29	(	(	PUNCT
iajs-805	147	30	k	k	NOUN
iajs-805	147	31	1	1	NUM
iajs-805	147	32	)	)	PUNCT
iajs-805	147	33	7	7	NUM
iajs-805	147	34	(	(	PUNCT
iajs-805	147	35	k)1	k)1	NOUN
iajs-805	147	36	2	2	NUM
iajs-805	147	37	k	k	PROPN
iajs-805	147	38	kh	kh	PROPN
iajs-805	147	39	k	k	PROPN
iajs-805	147	40	h	h	PROPN
iajs-805	147	41	k1	k1	PROPN
iajs-805	147	42	2	2	NUM
iajs-805	147	43			NOUN
iajs-805	147	44			PROPN
iajs-805	147	45			NOUN
iajs-805	147	46			NOUN
iajs-805	147	47			PUNCT
iajs-805	148	1			PROPN
iajs-805	148	2			PROPN
iajs-805	149	1			PROPN
iajs-805	149	2			PRON
iajs-805	150	1			PROPN
iajs-805	150	2			PROPN
iajs-805	150	3			PUNCT
iajs-805	150	4			PUNCT
iajs-805	150	5			PROPN
iajs-805	150	6			VERB
iajs-805	150	7			VERB
iajs-805	150	8			PROPN
iajs-805	150	9			NUM
iajs-805	150	10			PROPN
iajs-805	150	11			PROPN
iajs-805	150	12			PROPN
iajs-805	150	13			PROPN
iajs-805	150	14			VERB
iajs-805	150	15			PROPN
iajs-805	150	16			PROPN
iajs-805	150	17			PROPN
iajs-805	151	1			PROPN
iajs-805	151	2			NOUN
iajs-805	152	1			PROPN
iajs-805	152	2			NOUN
iajs-805	152	3			PROPN
iajs-805	152	4			NOUN
iajs-805	152	5	…	…	PUNCT
iajs-805	152	6	(	(	PUNCT
iajs-805	152	7	14	14	NUM
iajs-805	152	8	)	)	PUNCT
iajs-805	152	9	where	where	SCONJ
iajs-805	152	10	(k	(k	PROPN
iajs-805	152	11	–	–	PUNCT
iajs-805	152	12	n	n	CCONJ
iajs-805	152	13	)	)	PUNCT
iajs-805	152	14	is	be	AUX
iajs-805	152	15	defined	define	VERB
iajs-805	152	16	in	in	ADP
iajs-805	152	17	equation	equation	NOUN
iajs-805	152	18	(	(	PUNCT
iajs-805	152	19	11	11	NUM
iajs-805	152	20	)	)	PUNCT
iajs-805	152	21	considering	considering	NOUN
iajs-805	152	22	,	,	PUNCT
iajs-805	152	23	the	the	DET
iajs-805	152	24	differential	differential	ADJ
iajs-805	152	25	transform	transform	NOUN
iajs-805	152	26	of	of	ADP
iajs-805	152	27	y(x	y(x	NOUN
iajs-805	152	28	)	)	PUNCT
iajs-805	152	29	at	at	ADP
iajs-805	152	30	x0	x0	PROPN
iajs-805	152	31	=	=	SYM
iajs-805	152	32	0	0	PROPN
iajs-805	152	33	,	,	PUNCT
iajs-805	152	34	the	the	DET
iajs-805	152	35	initial	initial	ADJ
iajs-805	152	36	conditions	condition	NOUN
iajs-805	152	37	in	in	ADP
iajs-805	152	38	equation	equation	NOUN
iajs-805	152	39	(	(	PUNCT
iajs-805	152	40	13	13	NUM
iajs-805	152	41	)	)	PUNCT
iajs-805	152	42	are	be	AUX
iajs-805	152	43	transformed	transform	VERB
iajs-805	152	44	into	into	ADP
iajs-805	152	45	:	:	PUNCT
iajs-805	152	46	y(0	y(0	PROPN
iajs-805	152	47	)	)	PUNCT
iajs-805	152	48	=	=	SYM
iajs-805	152	49	0	0	NUM
iajs-805	152	50	,	,	PUNCT
iajs-805	152	51	y(1	y(1	PROPN
iajs-805	152	52	)	)	PUNCT
iajs-805	152	53	=	=	NOUN
iajs-805	152	54	0	0	NUM
iajs-805	152	55	…	…	PUNCT
iajs-805	152	56	(	(	PUNCT
iajs-805	152	57	15	15	NUM
iajs-805	152	58	)	)	PUNCT
iajs-805	152	59	ibn	ibn	NOUN
iajs-805	152	60	alhaitham	alhaitham	NOUN
iajs-805	152	61	j.	j.	PROPN
iajs-805	152	62	for	for	ADP
iajs-805	152	63	pure	pure	ADJ
iajs-805	152	64	&	&	CCONJ
iajs-805	152	65	appl	appl	PROPN
iajs-805	152	66	.	.	PUNCT
iajs-805	153	1	sci	sci	PROPN
iajs-805	153	2	.	.	PUNCT
iajs-805	153	3	vol.24	vol.24	NOUN
iajs-805	153	4	(	(	PUNCT
iajs-805	153	5	3	3	NUM
iajs-805	153	6	)	)	PUNCT
iajs-805	153	7	2011	2011	NUM
iajs-805	153	8	taking	take	VERB
iajs-805	153	9	n	n	NOUN
iajs-805	153	10	=	=	SYM
iajs-805	153	11	3	3	NUM
iajs-805	153	12	,	,	PUNCT
iajs-805	153	13	we	we	PRON
iajs-805	153	14	obtain	obtain	VERB
iajs-805	153	15	the	the	DET
iajs-805	153	16	following	follow	VERB
iajs-805	153	17	system	system	NOUN
iajs-805	153	18	of	of	ADP
iajs-805	153	19	linear	linear	PROPN
iajs-805	153	20	algebraic	algebraic	ADJ
iajs-805	153	21	equations	equation	NOUN
iajs-805	153	22	by	by	ADP
iajs-805	153	23	using	use	VERB
iajs-805	153	24	equation	equation	NOUN
iajs-805	153	25	(	(	PUNCT
iajs-805	153	26	14	14	NUM
iajs-805	153	27	)	)	PUNCT
iajs-805	153	28	and	and	CCONJ
iajs-805	153	29	eq.(15	eq.(15	NOUN
iajs-805	153	30	)	)	PUNCT
iajs-805	153	31	for	for	ADP
iajs-805	153	32	k	k	PROPN
iajs-805	153	33	=	=	SYM
iajs-805	153	34	0	0	NUM
iajs-805	153	35	,	,	PUNCT
iajs-805	153	36	1	1	NUM
iajs-805	153	37	.	.	NOUN
iajs-805	153	38	7y(2	7y(2	NUM
iajs-805	153	39	)	)	PUNCT
iajs-805	153	40	–	–	PUNCT
iajs-805	153	41	9y(3	9y(3	NUM
iajs-805	153	42	)	)	PUNCT
iajs-805	153	43	=	=	SYM
iajs-805	153	44	7	7	NUM
iajs-805	153	45	–	–	PUNCT
iajs-805	153	46	6y(2	6y(2	NUM
iajs-805	153	47	)	)	PUNCT
iajs-805	154	1	+	+	CCONJ
iajs-805	154	2	21y(3	21y(3	X
iajs-805	154	3	)	)	PUNCT
iajs-805	154	4	=	=	SYM
iajs-805	154	5	–	–	PUNCT
iajs-805	154	6	6	6	NUM
iajs-805	154	7	solving	solve	VERB
iajs-805	154	8	this	this	DET
iajs-805	154	9	system	system	NOUN
iajs-805	154	10	,	,	PUNCT
iajs-805	154	11	we	we	PRON
iajs-805	154	12	obtain	obtain	VERB
iajs-805	154	13	:	:	PUNCT
iajs-805	154	14	y(2	y(2	NOUN
iajs-805	154	15	)	)	PUNCT
iajs-805	154	16	=	=	SYM
iajs-805	154	17	1	1	NUM
iajs-805	154	18	,	,	PUNCT
iajs-805	154	19	y(3	y(3	PROPN
iajs-805	154	20	)	)	PUNCT
iajs-805	155	1	=	=	SYM
iajs-805	155	2	0	0	NUM
iajs-805	155	3	similarly	similarly	ADV
iajs-805	155	4	,	,	PUNCT
iajs-805	155	5	we	we	PRON
iajs-805	155	6	have	have	VERB
iajs-805	155	7	y(k	y(k	NOUN
iajs-805	155	8	)	)	PUNCT
iajs-805	155	9	=	=	SYM
iajs-805	155	10	0	0	NUM
iajs-805	155	11	,	,	PUNCT
iajs-805	155	12	for	for	ADP
iajs-805	155	13	k	k	PROPN
iajs-805	155	14			PROPN
iajs-805	155	15	4	4	NUM
iajs-805	155	16	.	.	PUNCT
iajs-805	156	1	then	then	ADV
iajs-805	156	2	,	,	PUNCT
iajs-805	156	3	by	by	ADP
iajs-805	156	4	using	use	VERB
iajs-805	156	5	equation	equation	NOUN
iajs-805	156	6	(	(	PUNCT
iajs-805	156	7	4	4	NUM
iajs-805	156	8	)	)	PUNCT
iajs-805	156	9	,	,	PUNCT
iajs-805	156	10	we	we	PRON
iajs-805	156	11	obtain	obtain	VERB
iajs-805	156	12	the	the	DET
iajs-805	156	13	exact	exact	ADJ
iajs-805	156	14	solution	solution	NOUN
iajs-805	156	15	y(x	y(x	NOUN
iajs-805	156	16	)	)	PUNCT
iajs-805	157	1	=	=	SYM
iajs-805	157	2	x2	x2	PROPN
iajs-805	157	3	.	.	PUNCT
iajs-805	157	4	example	example	NOUN
iajs-805	158	1	3	3	NUM
iajs-805	158	2	:	:	PUNCT
iajs-805	158	3	consider	consider	VERB
iajs-805	158	4	the	the	DET
iajs-805	158	5	linear	linear	ADJ
iajs-805	158	6	differential	differential	ADJ
iajs-805	158	7	equation	equation	NOUN
iajs-805	158	8	of	of	ADP
iajs-805	158	9	third	third	ADJ
iajs-805	158	10	order	order	NOUN
iajs-805	158	11	3	3	NUM
iajs-805	158	12	x	x	SYM
iajs-805	158	13	0.3x	0.3x	NOUN
iajs-805	158	14	0.3	0.3	NUM
iajs-805	158	15	3	3	NUM
iajs-805	158	16	dy	dy	NOUN
iajs-805	158	17	y(x	y(x	PROPN
iajs-805	158	18	)	)	PUNCT
iajs-805	158	19	y	y	PROPN
iajs-805	158	20	(	(	PUNCT
iajs-805	158	21	)	)	PUNCT
iajs-805	158	22	,	,	PUNCT
iajs-805	158	23	0	0	NUM
iajs-805	158	24	x	x	SYM
iajs-805	158	25	1	1	NUM
iajs-805	158	26	...	...	PUNCT
iajs-805	158	27	(	(	PUNCT
iajs-805	158	28	16)e	16)e	NUM
iajs-805	158	29	dx	dx	PROPN
iajs-805	158	30			PROPN
iajs-805	158	31			PROPN
iajs-805	158	32			PROPN
iajs-805	158	33			NUM
iajs-805	158	34			NOUN
iajs-805	158	35	and	and	CCONJ
iajs-805	158	36	the	the	DET
iajs-805	158	37	following	follow	VERB
iajs-805	158	38	initial	initial	ADJ
iajs-805	158	39	conditions	condition	NOUN
iajs-805	158	40	y(0	y(0	PROPN
iajs-805	158	41	)	)	PUNCT
iajs-805	158	42	=	=	SYM
iajs-805	158	43	1	1	NUM
iajs-805	158	44	,	,	PUNCT
iajs-805	158	45	y'(0	y'(0	NOUN
iajs-805	158	46	)	)	PUNCT
iajs-805	158	47	=	=	PUNCT
iajs-805	158	48	–	–	PUNCT
iajs-805	158	49	1	1	NUM
iajs-805	158	50	,	,	PUNCT
iajs-805	158	51	y''(0	y''(0	NOUN
iajs-805	158	52	)	)	PUNCT
iajs-805	158	53	=	=	SYM
iajs-805	158	54	1	1	NUM
iajs-805	158	55	…	…	PUNCT
iajs-805	158	56	(	(	PUNCT
iajs-805	158	57	17	17	NUM
iajs-805	158	58	)	)	PUNCT
iajs-805	158	59	using	use	VERB
iajs-805	158	60	equation	equation	NOUN
iajs-805	158	61	(	(	PUNCT
iajs-805	158	62	3	3	NUM
iajs-805	158	63	)	)	PUNCT
iajs-805	158	64	,	,	PUNCT
iajs-805	158	65	the	the	DET
iajs-805	158	66	differential	differential	ADJ
iajs-805	158	67	transform	transform	NOUN
iajs-805	158	68	of	of	ADP
iajs-805	158	69	x	x	SYM
iajs-805	158	70	0.3	0.3	NUM
iajs-805	158	71	e	e	NOUN
iajs-805	158	72			PROPN
iajs-805	158	73			VERB
iajs-805	158	74	at	at	ADP
iajs-805	158	75	x0	x0	PROPN
iajs-805	158	76	=	=	SYM
iajs-805	158	77	0	0	NUM
iajs-805	158	78	are	be	AUX
iajs-805	158	79	obtained	obtain	VERB
iajs-805	158	80	to	to	PART
iajs-805	158	81	be	be	AUX
iajs-805	158	82	1	1	NUM
iajs-805	158	83	k	k	NOUN
iajs-805	158	84	0.3	0.3	NUM
iajs-805	158	85	(	(	PUNCT
iajs-805	158	86	)	)	PUNCT
iajs-805	159	1	(	(	PUNCT
iajs-805	159	2	1	1	X
iajs-805	159	3	)	)	PUNCT
iajs-805	159	4	k	k	AUX
iajs-805	159	5	!	!	PUNCT
iajs-805	159	6	e	e	NOUN
iajs-805	159	7	.then	.then	VERB
iajs-805	159	8	because	because	SCONJ
iajs-805	159	9	of	of	ADP
iajs-805	159	10	theorems	theorem	NOUN
iajs-805	159	11	(	(	PUNCT
iajs-805	159	12	3	3	NUM
iajs-805	159	13	)	)	PUNCT
iajs-805	159	14	and	and	CCONJ
iajs-805	159	15	(	(	PUNCT
iajs-805	159	16	6	6	X
iajs-805	159	17	)	)	PUNCT
iajs-805	159	18	the	the	DET
iajs-805	159	19	differential	differential	ADJ
iajs-805	159	20	transform	transform	NOUN
iajs-805	159	21	of	of	ADP
iajs-805	159	22	equation	equation	NOUN
iajs-805	159	23	(	(	PUNCT
iajs-805	159	24	16	16	NUM
iajs-805	159	25	)	)	PUNCT
iajs-805	159	26	is	be	AUX
iajs-805	159	27	:	:	PUNCT
iajs-805	159	28	1	1	NUM
iajs-805	159	29	hn	hn	PROPN
iajs-805	159	30	1h	1h	NUM
iajs-805	160	1	k	k	NOUN
iajs-805	160	2	h	h	PROPN
iajs-805	161	1	k	k	PROPN
iajs-805	161	2	k	k	PROPN
iajs-805	162	1	0.31	0.31	NUM
iajs-805	162	2	kh	kh	PROPN
iajs-805	162	3	k1	k1	PROPN
iajs-805	162	4	1	1	NUM
iajs-805	162	5	(	(	PUNCT
iajs-805	162	6	k	k	PROPN
iajs-805	162	7	1)(k	1)(k	NUM
iajs-805	162	8	2)(k	2)(k	NUM
iajs-805	162	9	3)y(k	3)y(k	NUM
iajs-805	162	10	3	3	NUM
iajs-805	162	11	)	)	PUNCT
iajs-805	162	12	y(k	y(k	PROPN
iajs-805	162	13	)	)	PUNCT
iajs-805	162	14	(	(	PUNCT
iajs-805	162	15	1	1	NUM
iajs-805	162	16	)	)	PUNCT
iajs-805	162	17	y(h	y(h	NOUN
iajs-805	162	18	)	)	PUNCT
iajs-805	162	19	(	(	PUNCT
iajs-805	162	20	1	1	X
iajs-805	162	21	)	)	PUNCT
iajs-805	162	22	e	e	NOUN
iajs-805	162	23	...	...	PUNCT
iajs-805	162	24	(	(	PUNCT
iajs-805	162	25	18)(0.3	18)(0.3	NUM
iajs-805	162	26	)	)	PUNCT
iajs-805	162	27	1	1	NUM
iajs-805	162	28	k	k	NOUN
iajs-805	162	29	!	!	PUNCT
iajs-805	162	30			NOUN
iajs-805	163	1			PROPN
iajs-805	163	2			PROPN
iajs-805	163	3			PROPN
iajs-805	164	1			PROPN
iajs-805	164	2			PROPN
iajs-805	165	1			PROPN
iajs-805	165	2			PROPN
iajs-805	165	3			NOUN
iajs-805	165	4			ADV
iajs-805	165	5			PROPN
iajs-805	165	6			PROPN
iajs-805	165	7			PROPN
iajs-805	165	8			PUNCT
iajs-805	165	9			PUNCT
iajs-805	165	10			PROPN
iajs-805	165	11			PROPN
iajs-805	165	12			ADP
iajs-805	165	13	considering	consider	VERB
iajs-805	165	14	,	,	PUNCT
iajs-805	165	15	the	the	DET
iajs-805	165	16	differential	differential	ADJ
iajs-805	165	17	transform	transform	NOUN
iajs-805	165	18	of	of	ADP
iajs-805	165	19	y(x	y(x	NOUN
iajs-805	165	20	)	)	PUNCT
iajs-805	165	21	at	at	ADP
iajs-805	165	22	x0	x0	PROPN
iajs-805	165	23	=	=	PUNCT
iajs-805	165	24	0	0	PROPN
iajs-805	166	1	the	the	DET
iajs-805	166	2	initial	initial	ADJ
iajs-805	166	3	conditions	condition	NOUN
iajs-805	166	4	in	in	ADP
iajs-805	166	5	equation	equation	NOUN
iajs-805	166	6	(	(	PUNCT
iajs-805	166	7	17	17	NUM
iajs-805	166	8	)	)	PUNCT
iajs-805	166	9	are	be	AUX
iajs-805	166	10	transformed	transform	VERB
iajs-805	166	11	into	into	ADP
iajs-805	166	12	:	:	PUNCT
iajs-805	166	13	1y(0	1y(0	NUM
iajs-805	166	14	)	)	PUNCT
iajs-805	166	15	0,y(1	0,y(1	NUM
iajs-805	166	16	)	)	PUNCT
iajs-805	166	17	1,y(2	1,y(2	NUM
iajs-805	166	18	)	)	PUNCT
iajs-805	166	19	,	,	PUNCT
iajs-805	166	20	...	...	PUNCT
iajs-805	166	21	(	(	PUNCT
iajs-805	166	22	19	19	NUM
iajs-805	166	23	)	)	SYM
iajs-805	166	24	2	2	NUM
iajs-805	166	25			PROPN
iajs-805	166	26			NOUN
iajs-805	166	27			NOUN
iajs-805	166	28	taking	taking	NOUN
iajs-805	166	29	n	n	NOUN
iajs-805	166	30	=	=	SYM
iajs-805	166	31	6	6	NUM
iajs-805	166	32	,	,	PUNCT
iajs-805	166	33	we	we	PRON
iajs-805	166	34	obtain	obtain	VERB
iajs-805	166	35	the	the	DET
iajs-805	166	36	following	follow	VERB
iajs-805	166	37	linear	linear	ADJ
iajs-805	166	38	algebraic	algebraic	ADJ
iajs-805	166	39	equations	equation	NOUN
iajs-805	166	40	system	system	NOUN
iajs-805	166	41	by	by	ADP
iajs-805	166	42	using	use	VERB
iajs-805	166	43	equation	equation	NOUN
iajs-805	166	44	(	(	PUNCT
iajs-805	166	45	18	18	NUM
iajs-805	166	46	)	)	PUNCT
iajs-805	166	47	and	and	CCONJ
iajs-805	166	48	equation	equation	NOUN
iajs-805	166	49	(	(	PUNCT
iajs-805	166	50	19	19	NUM
iajs-805	166	51	)	)	PUNCT
iajs-805	166	52	for	for	ADP
iajs-805	166	53	k	k	PROPN
iajs-805	166	54	=	=	SYM
iajs-805	166	55	0	0	NUM
iajs-805	166	56	,	,	PUNCT
iajs-805	166	57	1	1	NUM
iajs-805	166	58	,	,	PUNCT
iajs-805	166	59	2	2	NUM
iajs-805	166	60	,	,	PUNCT
iajs-805	166	61	3	3	NUM
iajs-805	166	62	.	.	NOUN
iajs-805	166	63	5.973y(3	5.973y(3	NUM
iajs-805	166	64	)	)	PUNCT
iajs-805	166	65	0.0081y(4	0.0081y(4	NUM
iajs-805	166	66	)	)	PUNCT
iajs-805	166	67	0.00243y(5	0.00243y(5	NUM
iajs-805	166	68	)	)	PUNCT
iajs-805	166	69	0.000729y(6	0.000729y(6	NUM
iajs-805	166	70	)	)	PUNCT
iajs-805	166	71	0.995141192	0.995141192	NUM
iajs-805	166	72	0.27y(3	0.27y(3	NOUN
iajs-805	166	73	)	)	PUNCT
iajs-805	166	74	23.892y(4	23.892y(4	NOUN
iajs-805	166	75	)	)	PUNCT
iajs-805	166	76	0.0405y(5	0.0405y(5	NUM
iajs-805	166	77	)	)	PUNCT
iajs-805	166	78	0.01458y(6	0.01458y(6	NOUN
iajs-805	166	79	)	)	PUNCT
iajs-805	167	1	0.950141192	0.950141192	NUM
iajs-805	167	2	0.9y(3	0.9y(3	NUM
iajs-805	167	3	)	)	PUNCT
iajs-805	167	4	0.54y(4	0.54y(4	NUM
iajs-805	167	5	)	)	PUNCT
iajs-805	167	6	59.73y(5	59.73y(5	NUM
iajs-805	167	7	)	)	PUNCT
iajs-805	167	8	0.1215y(6	0.1215y(6	NOUN
iajs-805	167	9	)	)	PUNCT
iajs-805	167	10	0.325070596	0.325070596	NUM
iajs-805	167	11	2y(3	2y(3	NUM
iajs-805	167	12	)	)	PUNCT
iajs-805	167	13	1.2y(4	1.2y(4	NUM
iajs-805	167	14	)	)	PUNCT
iajs-805	167	15	0.9y(5	0.9y(5	NUM
iajs-805	167	16	)	)	PUNCT
iajs-805	168	1	119.46y(6	119.46y(6	NUM
iajs-805	168	2	)	)	PUNCT
iajs-805	168	3	0.2	0.2	NUM
iajs-805	168	4			PUNCT
iajs-805	168	5			PROPN
iajs-805	168	6			VERB
iajs-805	168	7			PROPN
iajs-805	168	8			PROPN
iajs-805	168	9			ADV
iajs-805	168	10			VERB
iajs-805	168	11			PROPN
iajs-805	168	12			PROPN
iajs-805	168	13			PROPN
iajs-805	168	14			ADV
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iajs-805	168	33	)	)	PUNCT
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iajs-805	170	6			NOUN
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iajs-805	170	12	)	)	PUNCT
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iajs-805	170	22	3	3	NUM
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iajs-805	170	24	equation	equation	NOUN
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iajs-805	170	26	4	4	X
iajs-805	170	27	)	)	PUNCT
iajs-805	170	28	we	we	PRON
iajs-805	170	29	obtain	obtain	VERB
iajs-805	170	30	the	the	DET
iajs-805	170	31	following	follow	VERB
iajs-805	170	32	approximate	approximate	ADJ
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iajs-805	171	5	3	3	NUM
iajs-805	171	6	)	)	PUNCT
iajs-805	171	7	2011	2011	NUM
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iajs-805	171	19	60.001388386354x	60.001388386354x	NUM
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iajs-805	172	2			PROPN
iajs-805	172	3			VERB
iajs-805	172	4			PROPN
iajs-805	172	5			ADV
iajs-805	172	6			PROPN
iajs-805	172	7			ADV
iajs-805	172	8			VERB
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iajs-805	172	19	2	2	NUM
iajs-805	172	20	3	3	NUM
iajs-805	172	21	4	4	NUM
iajs-805	172	22	5y(x	5y(x	NUM
iajs-805	172	23	)	)	PUNCT
iajs-805	172	24	1	1	NUM
iajs-805	172	25	x	x	SYM
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iajs-805	172	28	0.04166666657x	0.04166666657x	VERB
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iajs-805	173	1	6	6	NUM
iajs-805	173	2	4	4	NUM
iajs-805	173	3	7	7	NUM
iajs-805	173	4	5	5	NUM
iajs-805	173	5	8	8	NUM
iajs-805	173	6	6	6	NUM
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iajs-805	173	9	10	10	NUM
iajs-805	173	10	x	x	SYM
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iajs-805	173	15	10	10	NUM
iajs-805	173	16	x	x	SYM
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iajs-805	173	18	10	10	NUM
iajs-805	173	19	8	8	NUM
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iajs-805	173	21	10	10	NUM
iajs-805	173	22	x	x	SYM
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iajs-805	173	24	10	10	NUM
iajs-805	173	25	x	x	NOUN
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iajs-805	174	1			NUM
iajs-805	174	2			PROPN
iajs-805	174	3			VERB
iajs-805	174	4			PROPN
iajs-805	174	5			VERB
iajs-805	174	6			PROPN
iajs-805	174	7			VERB
iajs-805	174	8			PROPN
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iajs-805	174	14			PROPN
iajs-805	174	15			PROPN
iajs-805	174	16			PROPN
iajs-805	174	17			PROPN
iajs-805	174	18			VERB
iajs-805	174	19			PROPN
iajs-805	174	20			PROPN
iajs-805	174	21			PROPN
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iajs-805	174	23	between	between	ADP
iajs-805	174	24	the	the	DET
iajs-805	174	25	numerical	numerical	ADJ
iajs-805	174	26	results	result	NOUN
iajs-805	174	27	for	for	ADP
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iajs-805	174	37	exact	exact	ADJ
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iajs-805	174	40	)	)	PUNCT
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iajs-805	175	4	,	,	PUNCT
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iajs-805	175	6	given	give	VERB
iajs-805	175	7	in	in	ADP
iajs-805	175	8	table	table	NOUN
iajs-805	175	9	(	(	PUNCT
iajs-805	175	10	1	1	NUM
iajs-805	175	11	)	)	PUNCT
iajs-805	175	12	.	.	PUNCT
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iajs-805	176	2	4	4	NUM
iajs-805	176	3	:	:	PUNCT
iajs-805	176	4	consider	consider	VERB
iajs-805	176	5	the	the	DET
iajs-805	176	6	nonlinear	nonlinear	ADJ
iajs-805	176	7	dde	dde	PROPN
iajs-805	176	8	with	with	ADP
iajs-805	176	9	multiple	multiple	ADJ
iajs-805	176	10	delays	delay	NOUN
iajs-805	176	11	:	:	PUNCT
iajs-805	177	1	2	2	NUM
iajs-805	177	2	x	x	SYM
iajs-805	177	3	x	x	SYM
iajs-805	177	4	x	x	SYM
iajs-805	177	5	2	2	NUM
iajs-805	177	6	d	d	SYM
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iajs-805	177	8	1	1	NUM
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iajs-805	177	10	)	)	PUNCT
iajs-805	177	11	.y(x	.y(x	X
iajs-805	177	12	)	)	PUNCT
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iajs-805	178	2	,	,	PUNCT
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iajs-805	178	4	x	x	SYM
iajs-805	178	5	1	1	NUM
iajs-805	178	6	...	...	PUNCT
iajs-805	178	7	(	(	PUNCT
iajs-805	178	8	20	20	NUM
iajs-805	178	9	)	)	PUNCT
iajs-805	178	10	4	4	NUM
iajs-805	178	11	4	4	NUM
iajs-805	178	12	2dx	2dx	NUM
iajs-805	178	13			PROPN
iajs-805	178	14			ADJ
iajs-805	178	15			ADJ
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iajs-805	178	17			PROPN
iajs-805	178	18			PROPN
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iajs-805	178	20			PART
iajs-805	178	21			NOUN
iajs-805	178	22			NOUN
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iajs-805	178	25	initial	initial	ADJ
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iajs-805	178	28	)	)	PUNCT
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iajs-805	178	36	,	,	PUNCT
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iajs-805	178	40	)	)	PUNCT
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iajs-805	178	44	3	3	NUM
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iajs-805	178	48	7	7	X
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iajs-805	178	57	)	)	PUNCT
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iajs-805	178	61	1	1	NUM
iajs-805	178	62	2	2	NUM
iajs-805	178	63	1	1	NUM
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iajs-805	178	65	1	1	NUM
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iajs-805	178	67	1	1	NUM
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iajs-805	183	1	k	k	NOUN
iajs-805	183	2	h	h	PROPN
iajs-805	184	1	k	k	PROPN
iajs-805	184	2	k	k	PROPN
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iajs-805	185	2	k	k	PROPN
iajs-805	185	3	1)(k	1)(k	NUM
iajs-805	185	4	2)y(k	2)y(k	NUM
iajs-805	185	5	2	2	NUM
iajs-805	185	6	)	)	PUNCT
iajs-805	185	7	y(k	y(k	PROPN
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iajs-805	185	10	1	1	X
iajs-805	185	11	)	)	PUNCT
iajs-805	185	12			VERB
iajs-805	185	13			PROPN
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iajs-805	185	15			PROPN
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iajs-805	185	17			ADV
iajs-805	185	18			CCONJ
iajs-805	185	19			PROPN
iajs-805	185	20			PUNCT
iajs-805	185	21			PUNCT
iajs-805	185	22			X
iajs-805	185	23			X
iajs-805	185	24			X
iajs-805	185	25	h	h	NOUN
iajs-805	185	26	h	h	NOUN
iajs-805	185	27	h	h	NOUN
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iajs-805	186	2	h	h	PROPN
iajs-805	187	1	k	k	PROPN
iajs-805	187	2	k1	k1	PROPN
iajs-805	187	3	2	2	NUM
iajs-805	187	4	1	1	NUM
iajs-805	187	5	1	1	NUM
iajs-805	187	6	1	1	NUM
iajs-805	187	7	h	h	NOUN
iajs-805	187	8	h1	h1	NOUN
iajs-805	187	9	2	2	NUM
iajs-805	187	10	k	k	PROPN
iajs-805	187	11	k	k	PROPN
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iajs-805	187	15	)	)	PUNCT
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iajs-805	187	19	(	(	PUNCT
iajs-805	187	20	)	)	PUNCT
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iajs-805	187	22	)	)	PUNCT
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iajs-805	187	25			NOUN
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iajs-805	187	30			PROPN
iajs-805	188	1			PROPN
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iajs-805	191	9	1	1	NUM
iajs-805	191	10	1d	1d	NUM
iajs-805	191	11	d	d	NOUN
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iajs-805	191	13	(	(	PUNCT
iajs-805	191	14	sin	sin	NOUN
iajs-805	191	15	cos	cos	PROPN
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iajs-805	191	17	]	]	PUNCT
iajs-805	192	1	[	[	PUNCT
iajs-805	192	2	(	(	PUNCT
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iajs-805	192	4	)	)	PUNCT
iajs-805	192	5	]	]	PUNCT
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iajs-805	192	7	k	k	NOUN
iajs-805	192	8	)	)	PUNCT
iajs-805	192	9	...	...	PUNCT
iajs-805	192	10	(	(	PUNCT
iajs-805	192	11	22	22	NUM
iajs-805	192	12	)	)	PUNCT
iajs-805	192	13	k	k	NOUN
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iajs-805	193	1	k	k	X
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iajs-805	194	1	2dx	2dx	NUM
iajs-805	194	2	dx	dx	PROPN
iajs-805	194	3			PROPN
iajs-805	194	4			PROPN
iajs-805	194	5			PROPN
iajs-805	194	6			VERB
iajs-805	194	7			PROPN
iajs-805	194	8	where	where	SCONJ
iajs-805	194	9	(k	(k	PROPN
iajs-805	194	10	–	–	PUNCT
iajs-805	194	11	n	n	CCONJ
iajs-805	194	12	)	)	PUNCT
iajs-805	194	13	is	be	AUX
iajs-805	194	14	defined	define	VERB
iajs-805	194	15	in	in	ADP
iajs-805	194	16	eq	eq	ADP
iajs-805	194	17	.	.	PUNCT
iajs-805	195	1	(	(	PUNCT
iajs-805	195	2	11	11	NUM
iajs-805	195	3	)	)	PUNCT
iajs-805	195	4	,	,	PUNCT
iajs-805	195	5	with	with	ADP
iajs-805	195	6	n	n	NOUN
iajs-805	195	7	=	=	SYM
iajs-805	195	8	0	0	NUM
iajs-805	195	9	.	.	PUNCT
iajs-805	196	1	the	the	DET
iajs-805	196	2	initial	initial	ADJ
iajs-805	196	3	conditions	condition	NOUN
iajs-805	196	4	in	in	ADP
iajs-805	196	5	eq	eq	ADP
iajs-805	196	6	.	.	PUNCT
iajs-805	197	1	(	(	PUNCT
iajs-805	197	2	21	21	NUM
iajs-805	197	3	)	)	PUNCT
iajs-805	197	4	are	be	AUX
iajs-805	197	5	transformed	transform	VERB
iajs-805	197	6	in	in	ADP
iajs-805	197	7	to	to	ADP
iajs-805	197	8	:	:	PUNCT
iajs-805	197	9	y(0	y(0	PROPN
iajs-805	197	10	)	)	PUNCT
iajs-805	197	11	=	=	SYM
iajs-805	197	12	1	1	NUM
iajs-805	197	13	,	,	PUNCT
iajs-805	197	14	y(1	y(1	PROPN
iajs-805	197	15	)	)	PUNCT
iajs-805	198	1	=	=	SYM
iajs-805	198	2	0	0	NUM
iajs-805	198	3	from	from	ADP
iajs-805	198	4	eq	eq	ADP
iajs-805	198	5	.	.	PUNCT
iajs-805	199	1	(	(	PUNCT
iajs-805	199	2	22	22	NUM
iajs-805	199	3	)	)	PUNCT
iajs-805	199	4	,	,	PUNCT
iajs-805	199	5	we	we	PRON
iajs-805	199	6	obtain	obtain	VERB
iajs-805	199	7	:	:	PUNCT
iajs-805	199	8	1	1	NUM
iajs-805	199	9	1	1	NUM
iajs-805	199	10	y(2	y(2	NOUN
iajs-805	199	11	)	)	PUNCT
iajs-805	199	12	,	,	PUNCT
iajs-805	199	13	y(3	y(3	PROPN
iajs-805	199	14	)	)	PUNCT
iajs-805	199	15	0	0	NUM
iajs-805	199	16	,	,	PUNCT
iajs-805	199	17	y(4	y(4	PROPN
iajs-805	199	18	)	)	PUNCT
iajs-805	199	19	,	,	PUNCT
iajs-805	199	20	y(5	y(5	PROPN
iajs-805	199	21	)	)	PUNCT
iajs-805	199	22	0	0	NUM
iajs-805	200	1	2	2	NUM
iajs-805	200	2	!	!	SYM
iajs-805	200	3	4	4	NUM
iajs-805	200	4	!	!	X
iajs-805	200	5			VERB
iajs-805	200	6			NOUN
iajs-805	201	1			NUM
iajs-805	202	1			NOUN
iajs-805	202	2			NUM
iajs-805	202	3	1	1	NUM
iajs-805	202	4	1	1	NUM
iajs-805	202	5	y(6	y(6	PROPN
iajs-805	202	6	)	)	PUNCT
iajs-805	202	7	,	,	PUNCT
iajs-805	202	8	y(3	y(3	PROPN
iajs-805	202	9	)	)	PUNCT
iajs-805	202	10	0,y(8	0,y(8	NOUN
iajs-805	202	11	)	)	PUNCT
iajs-805	202	12	,	,	PUNCT
iajs-805	202	13	y(9	y(9	PROPN
iajs-805	202	14	)	)	PUNCT
iajs-805	202	15	0	0	NUM
iajs-805	203	1	6	6	NUM
iajs-805	203	2	!	!	NOUN
iajs-805	203	3	8	8	NUM
iajs-805	203	4	!	!	SYM
iajs-805	203	5	1	1	NUM
iajs-805	203	6	1	1	NUM
iajs-805	203	7	y(10	y(10	NUM
iajs-805	203	8	)	)	PUNCT
iajs-805	203	9	,	,	PUNCT
iajs-805	203	10	y(11	y(11	NOUN
iajs-805	203	11	)	)	PUNCT
iajs-805	203	12	0	0	NUM
iajs-805	203	13	,	,	PUNCT
iajs-805	203	14	y(12	y(12	PROPN
iajs-805	203	15	)	)	PUNCT
iajs-805	203	16	,	,	PUNCT
iajs-805	203	17	y(13	y(13	PROPN
iajs-805	203	18	)	)	PUNCT
iajs-805	203	19	0	0	NUM
iajs-805	203	20	,	,	PUNCT
iajs-805	203	21	...	...	PUNCT
iajs-805	204	1	10	10	NUM
iajs-805	204	2	!	!	X
iajs-805	204	3	12	12	NUM
iajs-805	204	4	!	!	PUNCT
iajs-805	205	1			VERB
iajs-805	205	2			NUM
iajs-805	206	1			NUM
iajs-805	207	1			NUM
iajs-805	207	2			PROPN
iajs-805	207	3			NOUN
iajs-805	207	4			NOUN
iajs-805	208	1			NUM
iajs-805	208	2			PRON
iajs-805	208	3			NOUN
iajs-805	208	4	substituting	substitute	VERB
iajs-805	208	5	these	these	DET
iajs-805	208	6	values	value	NOUN
iajs-805	208	7	in	in	ADP
iajs-805	208	8	to	to	ADP
iajs-805	208	9	eq	eq	PROPN
iajs-805	208	10	.	.	PUNCT
iajs-805	209	1	(	(	PUNCT
iajs-805	209	2	4	4	NUM
iajs-805	209	3	)	)	PUNCT
iajs-805	209	4	,	,	PUNCT
iajs-805	209	5	we	we	PRON
iajs-805	209	6	obtain	obtain	VERB
iajs-805	209	7	the	the	DET
iajs-805	209	8	following	follow	VERB
iajs-805	209	9	analytical	analytical	ADJ
iajs-805	209	10	solution	solution	NOUN
iajs-805	209	11	,	,	PUNCT
iajs-805	209	12	2	2	NUM
iajs-805	209	13	4	4	NUM
iajs-805	209	14	6	6	NUM
iajs-805	209	15	8	8	NUM
iajs-805	209	16	10	10	NUM
iajs-805	209	17	121	121	NUM
iajs-805	209	18	1	1	NUM
iajs-805	209	19	1	1	NUM
iajs-805	209	20	1	1	NUM
iajs-805	209	21	1	1	NUM
iajs-805	209	22	1	1	NUM
iajs-805	209	23	y(x	y(x	NOUN
iajs-805	209	24	)	)	PUNCT
iajs-805	210	1	1	1	NUM
iajs-805	210	2	x	x	SYM
iajs-805	210	3	x	x	PUNCT
iajs-805	210	4	x	x	PUNCT
iajs-805	210	5	x	x	PUNCT
iajs-805	210	6	x	x	PUNCT
iajs-805	210	7	x	x	X
iajs-805	210	8	...	...	PUNCT
iajs-805	210	9	2	2	NUM
iajs-805	210	10	!	!	SYM
iajs-805	210	11	4	4	NUM
iajs-805	210	12	!	!	NOUN
iajs-805	210	13	6	6	NUM
iajs-805	210	14	!	!	NOUN
iajs-805	210	15	8	8	NUM
iajs-805	210	16	!	!	X
iajs-805	210	17	10	10	NUM
iajs-805	210	18	!	!	X
iajs-805	210	19	12	12	NUM
iajs-805	210	20	!	!	PUNCT
iajs-805	211	1			PROPN
iajs-805	211	2			PROPN
iajs-805	211	3			VERB
iajs-805	211	4			PROPN
iajs-805	211	5			VERB
iajs-805	211	6			PROPN
iajs-805	211	7			PROPN
iajs-805	211	8			PROPN
iajs-805	211	9	ibn	ibn	PROPN
iajs-805	211	10	alhaitham	alhaitham	PROPN
iajs-805	211	11	j.	j.	PROPN
iajs-805	211	12	for	for	ADP
iajs-805	211	13	pure	pure	ADJ
iajs-805	211	14	&	&	CCONJ
iajs-805	211	15	appl	appl	PROPN
iajs-805	211	16	.	.	PUNCT
iajs-805	212	1	sci	sci	PROPN
iajs-805	212	2	.	.	PUNCT
iajs-805	212	3	vol.24	vol.24	NOUN
iajs-805	212	4	(	(	PUNCT
iajs-805	212	5	3	3	NUM
iajs-805	212	6	)	)	PUNCT
iajs-805	212	7	2011	2011	NUM
iajs-805	212	8	which	which	PRON
iajs-805	212	9	is	be	AUX
iajs-805	212	10	formally	formally	ADV
iajs-805	212	11	the	the	DET
iajs-805	212	12	same	same	ADJ
iajs-805	212	13	as	as	ADP
iajs-805	212	14	maclaurin	maclaurin	NOUN
iajs-805	212	15	series	series	NOUN
iajs-805	212	16	of	of	ADP
iajs-805	212	17	cos	cos	PROPN
iajs-805	212	18	x.	x.	PROPN
iajs-805	212	19	in	in	ADP
iajs-805	212	20	fact	fact	NOUN
iajs-805	212	21	y(x	y(x	NOUN
iajs-805	212	22	)	)	PUNCT
iajs-805	212	23	=	=	PUNCT
iajs-805	213	1	cos	cos	ADP
iajs-805	213	2	x	x	NOUN
iajs-805	213	3	is	be	AUX
iajs-805	213	4	the	the	DET
iajs-805	213	5	exact	exact	ADJ
iajs-805	213	6	solution	solution	NOUN
iajs-805	213	7	for	for	ADP
iajs-805	213	8	eq	eq	PROPN
iajs-805	213	9	.	.	PUNCT
iajs-805	214	1	(	(	PUNCT
iajs-805	214	2	20	20	NUM
iajs-805	214	3	)	)	PUNCT
iajs-805	214	4	and	and	CCONJ
iajs-805	214	5	(	(	PUNCT
iajs-805	214	6	21	21	NUM
iajs-805	214	7	)	)	PUNCT
iajs-805	214	8	.	.	PUNCT
iajs-805	215	1	conclusions	conclusion	NOUN
iajs-805	215	2	in	in	ADP
iajs-805	215	3	this	this	DET
iajs-805	215	4	paper	paper	NOUN
iajs-805	215	5	the	the	DET
iajs-805	215	6	differential	differential	ADJ
iajs-805	215	7	transform	transform	NOUN
iajs-805	215	8	method	method	NOUN
iajs-805	215	9	is	be	AUX
iajs-805	215	10	developed	develop	VERB
iajs-805	215	11	for	for	ADP
iajs-805	215	12	solving	solve	VERB
iajs-805	215	13	differential	differential	ADJ
iajs-805	215	14	equations	equation	NOUN
iajs-805	215	15	with	with	ADP
iajs-805	215	16	multiple	multiple	ADJ
iajs-805	215	17	constant	constant	ADJ
iajs-805	215	18	delays	delay	NOUN
iajs-805	215	19	.	.	PUNCT
iajs-805	216	1	first	first	ADV
iajs-805	216	2	,	,	PUNCT
iajs-805	216	3	some	some	DET
iajs-805	216	4	new	new	ADJ
iajs-805	216	5	theorems	theorem	NOUN
iajs-805	216	6	are	be	AUX
iajs-805	216	7	provided	provide	VERB
iajs-805	216	8	and	and	CCONJ
iajs-805	216	9	then	then	ADV
iajs-805	216	10	used	use	VERB
iajs-805	216	11	to	to	PART
iajs-805	216	12	solve	solve	VERB
iajs-805	216	13	linear	linear	ADJ
iajs-805	216	14	and	and	CCONJ
iajs-805	216	15	nonlinear	nonlinear	ADJ
iajs-805	216	16	ddes	dde	NOUN
iajs-805	216	17	.	.	PUNCT
iajs-805	217	1	the	the	DET
iajs-805	217	2	obtained	obtain	VERB
iajs-805	217	3	results	result	NOUN
iajs-805	217	4	are	be	AUX
iajs-805	217	5	found	find	VERB
iajs-805	217	6	to	to	PART
iajs-805	217	7	be	be	AUX
iajs-805	217	8	very	very	ADV
iajs-805	217	9	accurate	accurate	ADJ
iajs-805	217	10	in	in	ADP
iajs-805	217	11	comparison	comparison	NOUN
iajs-805	217	12	with	with	ADP
iajs-805	217	13	the	the	DET
iajs-805	217	14	exact	exact	ADJ
iajs-805	217	15	solution	solution	NOUN
iajs-805	217	16	.	.	PUNCT
iajs-805	218	1	references	reference	NOUN
iajs-805	218	2	1	1	NUM
iajs-805	218	3	.	.	PUNCT
iajs-805	218	4	kurnaz	kurnaz	PROPN
iajs-805	218	5	,	,	PUNCT
iajs-805	218	6	a.	a.	NOUN
iajs-805	218	7	and	and	CCONJ
iajs-805	218	8	oturanç	oturanç	VERB
iajs-805	218	9	,	,	PUNCT
iajs-805	218	10	g.	g.	PROPN
iajs-805	218	11	(	(	PUNCT
iajs-805	218	12	2005)the	2005)the	DET
iajs-805	218	13	differential	differential	NOUN
iajs-805	218	14	transform	transform	NOUN
iajs-805	218	15	approximation	approximation	NOUN
iajs-805	218	16	for	for	ADP
iajs-805	218	17	the	the	DET
iajs-805	218	18	system	system	NOUN
iajs-805	218	19	of	of	ADP
iajs-805	218	20	ordinary	ordinary	ADJ
iajs-805	218	21	differential	differential	ADJ
iajs-805	218	22	equations	equation	NOUN
iajs-805	218	23	,	,	PUNCT
iajs-805	218	24	int	int	NOUN
iajs-805	218	25	.	.	PUNCT
iajs-805	219	1	j.	j.	PROPN
iajs-805	219	2	computer	computer	PROPN
iajs-805	219	3	math	math	PROPN
iajs-805	219	4	.	.	PUNCT
iajs-805	220	1	82:709–719	82:709–719	PROPN
iajs-805	220	2	.	.	PUNCT
iajs-805	221	1	2	2	NUM
iajs-805	221	2	.	.	X
iajs-805	221	3	zhou	zhou	PROPN
iajs-805	221	4	,	,	PUNCT
iajs-805	221	5	j.k	j.k	PROPN
iajs-805	221	6	.	.	PUNCT
iajs-805	222	1	(	(	PUNCT
iajs-805	222	2	1986)differential	1986)differential	ADJ
iajs-805	222	3	transformation	transformation	NOUN
iajs-805	222	4	and	and	CCONJ
iajs-805	222	5	its	its	PRON
iajs-805	222	6	application	application	NOUN
iajs-805	222	7	for	for	ADP
iajs-805	222	8	electrical	electrical	ADJ
iajs-805	222	9	circuit	circuit	NOUN
iajs-805	222	10	,	,	PUNCT
iajs-805	222	11	huazhong	huazhong	PROPN
iajs-805	222	12	university	university	PROPN
iajs-805	222	13	press	press	NOUN
iajs-805	222	14	,	,	PUNCT
iajs-805	222	15	wuhan	wuhan	PROPN
iajs-805	222	16	,	,	PUNCT
iajs-805	222	17	china	china	PROPN
iajs-805	222	18	,	,	PUNCT
iajs-805	222	19	3	3	X
iajs-805	222	20	.	.	X
iajs-805	223	1	evans	evans	PROPN
iajs-805	223	2	,	,	PUNCT
iajs-805	223	3	d.j	d.j	PROPN
iajs-805	223	4	.	.	PROPN
iajs-805	223	5	and	and	CCONJ
iajs-805	223	6	raslan	raslan	PROPN
iajs-805	223	7	,	,	PUNCT
iajs-805	223	8	k.r	k.r	PROPN
iajs-805	223	9	.	.	PROPN
iajs-805	224	1	(	(	PUNCT
iajs-805	224	2	2005)the	2005)the	NUM
iajs-805	224	3	adomian	adomian	NOUN
iajs-805	224	4	decomposition	decomposition	NOUN
iajs-805	224	5	method	method	NOUN
iajs-805	224	6	for	for	ADP
iajs-805	224	7	solving	solve	VERB
iajs-805	224	8	delay	delay	NOUN
iajs-805	224	9	differential	differential	ADJ
iajs-805	224	10	equation	equation	NOUN
iajs-805	224	11	,	,	PUNCT
iajs-805	224	12	int	int	NOUN
iajs-805	224	13	.	.	PUNCT
iajs-805	225	1	j.computer	j.computer	PROPN
iajs-805	225	2	math	math	NOUN
iajs-805	225	3	.	.	PUNCT
iajs-805	226	1	82	82	NUM
iajs-805	227	1	:	:	PUNCT
iajs-805	227	2	49–54	49–54	NUM
iajs-805	227	3	.	.	NOUN
iajs-805	228	1	4	4	NUM
iajs-805	228	2	.	.	NOUN
iajs-805	228	3	arikoglu	arikoglu	NOUN
iajs-805	228	4	and	and	CCONJ
iajs-805	228	5	özkol	özkol	NOUN
iajs-805	228	6	,	,	PUNCT
iajs-805	228	7	i.	i.	PROPN
iajs-805	228	8	(	(	PUNCT
iajs-805	228	9	2005	2005	NUM
iajs-805	228	10	)	)	PUNCT
iajs-805	229	1	solution	solution	NOUN
iajs-805	229	2	of	of	ADP
iajs-805	229	3	boundary	boundary	ADJ
iajs-805	229	4	value	value	NOUN
iajs-805	229	5	problems	problem	NOUN
iajs-805	229	6	for	for	ADP
iajs-805	229	7	integro	integro	ADJ
iajs-805	229	8	-	-	PUNCT
iajs-805	229	9	differential	differential	NOUN
iajs-805	229	10	equations	equation	NOUN
iajs-805	229	11	by	by	ADP
iajs-805	229	12	using	use	VERB
iajs-805	229	13	differential	differential	ADJ
iajs-805	229	14	transform	transform	NOUN
iajs-805	229	15	method	method	NOUN
iajs-805	229	16	,	,	PUNCT
iajs-805	229	17	appl	appl	PROPN
iajs-805	229	18	.	.	PROPN
iajs-805	229	19	math	math	PROPN
iajs-805	229	20	.	.	PUNCT
iajs-805	230	1	comput	comput	NOUN
iajs-805	230	2	168	168	NUM
iajs-805	230	3	:	:	PUNCT
iajs-805	230	4	1145	1145	NUM
iajs-805	230	5	-	-	SYM
iajs-805	230	6	1158	1158	NUM
iajs-805	230	7	.	.	PUNCT
iajs-805	231	1	5	5	NUM
iajs-805	231	2	.	.	X
iajs-805	231	3	ayaz	ayaz	PROPN
iajs-805	231	4	,	,	PUNCT
iajs-805	231	5	f.	f.	PROPN
iajs-805	231	6	(	(	PUNCT
iajs-805	231	7	2004	2004	NUM
iajs-805	231	8	)	)	PUNCT
iajs-805	231	9	solutions	solution	NOUN
iajs-805	231	10	of	of	ADP
iajs-805	231	11	the	the	DET
iajs-805	231	12	system	system	NOUN
iajs-805	231	13	of	of	ADP
iajs-805	231	14	differential	differential	ADJ
iajs-805	231	15	equations	equation	NOUN
iajs-805	231	16	by	by	ADP
iajs-805	231	17	differential	differential	ADJ
iajs-805	231	18	transform	transform	NOUN
iajs-805	231	19	method	method	NOUN
iajs-805	231	20	,	,	PUNCT
iajs-805	231	21	appl	appl	PROPN
iajs-805	231	22	.	.	PROPN
iajs-805	231	23	math	math	PROPN
iajs-805	231	24	.	.	PUNCT
iajs-805	232	1	comput	comput	NOUN
iajs-805	232	2	.	.	PUNCT
iajs-805	233	1	147:547–567	147:547–567	NUM
iajs-805	233	2	.	.	PUNCT
iajs-805	234	1	6	6	NUM
iajs-805	234	2	.	.	X
iajs-805	235	1	cooke	cooke	PROPN
iajs-805	235	2	,	,	PUNCT
iajs-805	235	3	k.l	k.l	PROPN
iajs-805	235	4	.	.	PROPN
iajs-805	235	5	and	and	CCONJ
iajs-805	235	6	yorke	yorke	PROPN
iajs-805	235	7	,	,	PUNCT
iajs-805	235	8	j.a	j.a	PROPN
iajs-805	235	9	.	.	PROPN
iajs-805	235	10	(	(	PUNCT
iajs-805	235	11	1973	1973	NUM
iajs-805	235	12	)	)	PUNCT
iajs-805	235	13	some	some	DET
iajs-805	235	14	equations	equation	NOUN
iajs-805	235	15	modelling	model	VERB
iajs-805	235	16	growth	growth	NOUN
iajs-805	235	17	processes	process	NOUN
iajs-805	235	18	and	and	CCONJ
iajs-805	235	19	gonorrhea	gonorrhea	NOUN
iajs-805	235	20	epidemics	epidemic	NOUN
iajs-805	235	21	,	,	PUNCT
iajs-805	235	22	m	m	VERB
iajs-805	235	23	ath	ath	NOUN
iajs-805	235	24	.	.	PUNCT
iajs-805	236	1	biosci.16	biosci.16	PROPN
iajs-805	236	2	:	:	PUNCT
iajs-805	237	1	75–101	75–101	NUM
iajs-805	237	2	.	.	PUNCT
iajs-805	238	1	ibn	ibn	PROPN
iajs-805	238	2	alhaitham	alhaitham	PROPN
iajs-805	238	3	j.	j.	PROPN
iajs-805	238	4	for	for	ADP
iajs-805	238	5	pure	pure	ADJ
iajs-805	238	6	&	&	CCONJ
iajs-805	238	7	appl	appl	PROPN
iajs-805	238	8	.	.	PUNCT
iajs-805	239	1	sci	sci	PROPN
iajs-805	239	2	.	.	PUNCT
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iajs-805	239	5	3	3	NUM
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iajs-805	239	7	2011	2011	NUM
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iajs-805	239	10	1):comparison	1):comparison	NUM
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iajs-805	239	24	0.2	0.2	NUM
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iajs-805	241	7	1	1	NUM
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iajs-805	241	9	0.81873075	0.81873075	NUM
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iajs-805	242	1	0.54881163	0.54881163	NUM
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iajs-805	242	4	0.40656965	0.40656965	PROPN
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iajs-805	242	9	(	(	PUNCT
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iajs-805	242	11	مجلة	مجلة	VERB
iajs-805	242	12	ابن	ابن	PROPN
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iajs-805	242	14	للعلوم	للعلوم	PROPN
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iajs-805	243	2	توسیع	توسیع	PROPN
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iajs-805	244	2	التفاضلیة	التفاضلیة	PROPN
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iajs-805	244	5	التفاضلیة	التفاضلیة	PROPN
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iajs-805	244	8	فاضل	فاضل	PROPN
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iajs-805	244	10	فاضل	فاضل	PROPN
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iajs-805	244	14	محمد	محمد	ADJ
iajs-805	244	15	ابن	ابن	VERB
iajs-805	244	16	الهیثم	الهیثم	PROPN
iajs-805	244	17	،	،	PROPN
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iajs-805	244	20	–	–	PUNCT
iajs-805	244	21	قسم	قسم	PROPN
iajs-805	244	22	الریاضیات	الریاضیات	PROPN
iajs-805	244	23	،	،	PROPN
iajs-805	244	24	كلیة	كلیة	PROPN
iajs-805	244	25	التربیة	التربیة	PROPN
iajs-805	244	26	لعلوم	لعلوم	PROPN
iajs-805	244	27	،	،	PROPN
iajs-805	244	28	جامعة	جامعة	PROPN
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iajs-805	245	1	قسم	قسم	PROPN
iajs-805	245	2	الریاضیات	الریاضیات	PROPN
iajs-805	245	3	وتطبیقات	وتطبیقات	PROPN
iajs-805	245	4	الحاسوب	الحاسوب	PROPN
iajs-805	245	5	،	،	PROPN
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iajs-805	245	7	ا	ا	PROPN
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iajs-805	246	10	:	:	PUNCT
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iajs-805	246	12	البحث	البحث	VERB
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iajs-805	247	2	ةصالخال	ةصالخال	PROPN
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iajs-805	247	17	طر	طر	ADP
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iajs-805	247	21	هذا	هذا	NOUN
iajs-805	247	22	البحث	البحث	NOUN
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iajs-805	248	5	العدید	العدید	VERB
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iajs-805	248	7	المسائل	المسائل	NOUN
iajs-805	248	8	الخطیة	الخطیة	VERB
iajs-805	248	9	وغیر	وغیر	ADJ
iajs-805	248	10	ملعستأ	ملعستأ	NOUN
iajs-805	248	11	.ةلطریقة	.ةلطریقة	PUNCT
iajs-805	248	12	التحویالت	التحویالت	ADJ
iajs-805	248	13	التفاضلی	التفاضلی	PROPN