id	sid	tid	token	lemma	pos
ejpam-418	1	1	5_418_kilicman.dvi	5_418_kilicman.dvi	NUM
ejpam-418	1	2	european	european	ADJ
ejpam-418	1	3	journal	journal	NOUN
ejpam-418	1	4	of	of	ADP
ejpam-418	1	5	pure	pure	ADJ
ejpam-418	1	6	and	and	CCONJ
ejpam-418	1	7	applied	apply	VERB
ejpam-418	1	8	mathematics	mathematic	NOUN
ejpam-418	1	9	vol	vol	NOUN
ejpam-418	1	10	.	.	PUNCT
ejpam-418	2	1	3	3	NUM
ejpam-418	2	2	,	,	PUNCT
ejpam-418	2	3	no	no	INTJ
ejpam-418	2	4	.	.	NOUN
ejpam-418	2	5	1	1	NUM
ejpam-418	2	6	,	,	PUNCT
ejpam-418	2	7	2010	2010	NUM
ejpam-418	2	8	,	,	PUNCT
ejpam-418	2	9	45	45	NUM
ejpam-418	2	10	-	-	SYM
ejpam-418	2	11	50	50	NUM
ejpam-418	2	12	issn	issn	PROPN
ejpam-418	2	13	1307	1307	NUM
ejpam-418	2	14	-	-	SYM
ejpam-418	2	15	5543	5543	NUM
ejpam-418	2	16	–	–	PUNCT
ejpam-418	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-418	2	18	on	on	ADP
ejpam-418	2	19	the	the	DET
ejpam-418	2	20	partial	partial	ADJ
ejpam-418	2	21	differential	differential	ADJ
ejpam-418	2	22	equations	equation	NOUN
ejpam-418	2	23	with	with	ADP
ejpam-418	2	24	non	non	ADJ
ejpam-418	2	25	-	-	ADJ
ejpam-418	2	26	constant	constant	ADJ
ejpam-418	2	27	coefficients	coefficient	NOUN
ejpam-418	2	28	and	and	CCONJ
ejpam-418	2	29	convolution	convolution	NOUN
ejpam-418	2	30	method	method	PROPN
ejpam-418	2	31	adem	adem	PROPN
ejpam-418	2	32	kılıçman∗	kılıçman∗	PROPN
ejpam-418	2	33	and	and	CCONJ
ejpam-418	2	34	hassan	hassan	PROPN
ejpam-418	2	35	eltayeb	eltayeb	PROPN
ejpam-418	2	36	department	department	PROPN
ejpam-418	2	37	of	of	ADP
ejpam-418	2	38	mathematics	mathematics	PROPN
ejpam-418	2	39	and	and	CCONJ
ejpam-418	2	40	institute	institute	PROPN
ejpam-418	2	41	for	for	ADP
ejpam-418	2	42	mathematical	mathematical	ADJ
ejpam-418	2	43	research	research	NOUN
ejpam-418	2	44	,	,	PUNCT
ejpam-418	2	45	university	university	NOUN
ejpam-418	2	46	putra	putra	PROPN
ejpam-418	2	47	malaysia	malaysia	PROPN
ejpam-418	2	48	,	,	PUNCT
ejpam-418	2	49	43400	43400	NUM
ejpam-418	2	50	upm	upm	PROPN
ejpam-418	2	51	,	,	PUNCT
ejpam-418	2	52	serdang	serdang	PROPN
ejpam-418	2	53	,	,	PUNCT
ejpam-418	2	54	selangor	selangor	PROPN
ejpam-418	2	55	,	,	PUNCT
ejpam-418	2	56	malaysia	malaysia	PROPN
ejpam-418	2	57	abstract	abstract	NOUN
ejpam-418	2	58	.	.	PUNCT
ejpam-418	3	1	in	in	ADP
ejpam-418	3	2	this	this	DET
ejpam-418	3	3	study	study	NOUN
ejpam-418	3	4	we	we	PRON
ejpam-418	3	5	consider	consider	VERB
ejpam-418	3	6	the	the	DET
ejpam-418	3	7	linear	linear	ADJ
ejpam-418	3	8	second	second	ADJ
ejpam-418	3	9	order	order	NOUN
ejpam-418	3	10	partial	partial	ADJ
ejpam-418	3	11	differential	differential	ADJ
ejpam-418	3	12	equations	equation	NOUN
ejpam-418	3	13	with	with	ADP
ejpam-418	3	14	nonhomogenous	nonhomogenous	ADJ
ejpam-418	3	15	forcing	forcing	NOUN
ejpam-418	3	16	term	term	NOUN
ejpam-418	3	17	and	and	CCONJ
ejpam-418	3	18	having	have	VERB
ejpam-418	3	19	singular	singular	ADJ
ejpam-418	3	20	variable	variable	ADJ
ejpam-418	3	21	data	datum	NOUN
ejpam-418	3	22	.	.	PUNCT
ejpam-418	4	1	in	in	ADP
ejpam-418	4	2	the	the	DET
ejpam-418	4	3	special	special	ADJ
ejpam-418	4	4	case	case	NOUN
ejpam-418	4	5	we	we	PRON
ejpam-418	4	6	solve	solve	VERB
ejpam-418	4	7	the	the	DET
ejpam-418	4	8	one	one	NUM
ejpam-418	4	9	dimensional	dimensional	ADJ
ejpam-418	4	10	wave	wave	NOUN
ejpam-418	4	11	equation	equation	NOUN
ejpam-418	4	12	by	by	ADP
ejpam-418	4	13	using	use	VERB
ejpam-418	4	14	the	the	DET
ejpam-418	4	15	double	double	ADJ
ejpam-418	4	16	integral	integral	ADJ
ejpam-418	4	17	transform	transform	NOUN
ejpam-418	4	18	.	.	PUNCT
ejpam-418	5	1	2000	2000	NUM
ejpam-418	5	2	mathematics	mathematic	NOUN
ejpam-418	5	3	subject	subject	NOUN
ejpam-418	5	4	classifications	classification	NOUN
ejpam-418	5	5	:	:	PUNCT
ejpam-418	5	6	primary	primary	ADJ
ejpam-418	5	7	35qxx	35qxx	NOUN
ejpam-418	5	8	,	,	PUNCT
ejpam-418	5	9	44a12	44a12	NUM
ejpam-418	5	10	;	;	PUNCT
ejpam-418	5	11	secondary	secondary	ADJ
ejpam-418	5	12	44a35	44a35	NUM
ejpam-418	5	13	key	key	ADJ
ejpam-418	5	14	words	word	NOUN
ejpam-418	5	15	and	and	CCONJ
ejpam-418	5	16	phrases	phrase	NOUN
ejpam-418	5	17	:	:	PUNCT
ejpam-418	5	18	pde	pde	NOUN
ejpam-418	5	19	with	with	ADP
ejpam-418	5	20	constant	constant	ADJ
ejpam-418	5	21	coefficients	coefficient	NOUN
ejpam-418	5	22	,	,	PUNCT
ejpam-418	5	23	polynomial	polynomial	ADJ
ejpam-418	5	24	coeeficients	coeeficient	NOUN
ejpam-418	5	25	,	,	PUNCT
ejpam-418	5	26	double	double	ADJ
ejpam-418	5	27	convolution	convolution	NOUN
ejpam-418	5	28	,	,	PUNCT
ejpam-418	5	29	double	double	ADJ
ejpam-418	5	30	laplace	laplace	NOUN
ejpam-418	5	31	transform	transform	NOUN
ejpam-418	5	32	.	.	PUNCT
ejpam-418	6	1	1	1	X
ejpam-418	6	2	.	.	X
ejpam-418	6	3	introduction	introduction	NOUN
ejpam-418	6	4	a	a	DET
ejpam-418	6	5	number	number	NOUN
ejpam-418	6	6	of	of	ADP
ejpam-418	6	7	problems	problem	NOUN
ejpam-418	6	8	in	in	ADP
ejpam-418	6	9	engineering	engineering	NOUN
ejpam-418	6	10	give	give	VERB
ejpam-418	6	11	rise	rise	NOUN
ejpam-418	6	12	to	to	ADP
ejpam-418	6	13	the	the	DET
ejpam-418	6	14	following	follow	VERB
ejpam-418	6	15	well	well	ADV
ejpam-418	6	16	-	-	PUNCT
ejpam-418	6	17	known	know	VERB
ejpam-418	6	18	partial	partial	ADJ
ejpam-418	6	19	differential	differential	NOUN
ejpam-418	6	20	equations	equation	NOUN
ejpam-418	6	21	:	:	PUNCT
ejpam-418	6	22	wave	wave	NOUN
ejpam-418	6	23	equation	equation	NOUN
ejpam-418	6	24	,	,	PUNCT
ejpam-418	6	25	one	one	NUM
ejpam-418	6	26	dimensional	dimensional	ADJ
ejpam-418	6	27	heat	heat	NOUN
ejpam-418	6	28	flow	flow	NOUN
ejpam-418	6	29	,	,	PUNCT
ejpam-418	6	30	two	two	NUM
ejpam-418	6	31	dimensional	dimensional	ADJ
ejpam-418	6	32	heat	heat	NOUN
ejpam-418	6	33	flow	flow	NOUN
ejpam-418	6	34	,	,	PUNCT
ejpam-418	6	35	which	which	PRON
ejpam-418	6	36	in	in	ADP
ejpam-418	6	37	steady	steady	ADJ
ejpam-418	6	38	state	state	NOUN
ejpam-418	6	39	becomes	become	VERB
ejpam-418	6	40	the	the	DET
ejpam-418	6	41	two	two	NUM
ejpam-418	6	42	dimensional	dimensional	ADJ
ejpam-418	6	43	laplace	laplace	NOUN
ejpam-418	6	44	’s	’s	PART
ejpam-418	6	45	equation	equation	NOUN
ejpam-418	6	46	,	,	PUNCT
ejpam-418	6	47	poisson	poisson	PROPN
ejpam-418	6	48	’s	’s	PART
ejpam-418	6	49	equation	equation	NOUN
ejpam-418	6	50	,	,	PUNCT
ejpam-418	6	51	these	these	DET
ejpam-418	6	52	equation	equation	NOUN
ejpam-418	6	53	arises	arise	VERB
ejpam-418	6	54	in	in	ADP
ejpam-418	6	55	electrostatics	electrostatic	NOUN
ejpam-418	6	56	and	and	CCONJ
ejpam-418	6	57	elasticity	elasticity	NOUN
ejpam-418	6	58	theory	theory	NOUN
ejpam-418	6	59	and	and	CCONJ
ejpam-418	6	60	transmission	transmission	NOUN
ejpam-418	6	61	line	line	NOUN
ejpam-418	6	62	equation	equation	NOUN
ejpam-418	6	63	.	.	PUNCT
ejpam-418	7	1	in	in	ADP
ejpam-418	7	2	a	a	DET
ejpam-418	7	3	long	long	ADJ
ejpam-418	7	4	electrical	electrical	ADJ
ejpam-418	7	5	cable	cable	NOUN
ejpam-418	7	6	or	or	CCONJ
ejpam-418	7	7	a	a	DET
ejpam-418	7	8	telephone	telephone	NOUN
ejpam-418	7	9	wire	wire	NOUN
ejpam-418	7	10	both	both	CCONJ
ejpam-418	7	11	the	the	DET
ejpam-418	7	12	current	current	ADJ
ejpam-418	7	13	and	and	CCONJ
ejpam-418	7	14	voltage	voltage	NOUN
ejpam-418	7	15	depend	depend	VERB
ejpam-418	7	16	upon	upon	SCONJ
ejpam-418	7	17	position	position	NOUN
ejpam-418	7	18	along	along	ADP
ejpam-418	7	19	the	the	DET
ejpam-418	7	20	wire	wire	NOUN
ejpam-418	7	21	as	as	ADV
ejpam-418	7	22	well	well	ADV
ejpam-418	7	23	as	as	ADP
ejpam-418	7	24	the	the	DET
ejpam-418	7	25	time	time	NOUN
ejpam-418	7	26	.	.	PUNCT
ejpam-418	8	1	by	by	ADP
ejpam-418	8	2	using	use	VERB
ejpam-418	8	3	basic	basic	ADJ
ejpam-418	8	4	laws	law	NOUN
ejpam-418	8	5	of	of	ADP
ejpam-418	8	6	electrical	electrical	ADJ
ejpam-418	8	7	circuit	circuit	NOUN
ejpam-418	8	8	theory	theory	NOUN
ejpam-418	8	9	,	,	PUNCT
ejpam-418	8	10	that	that	SCONJ
ejpam-418	8	11	the	the	DET
ejpam-418	8	12	electrical	electrical	ADJ
ejpam-418	8	13	current	current	ADJ
ejpam-418	8	14	i(x	i(x	PROPN
ejpam-418	8	15	,	,	PUNCT
ejpam-418	8	16	t	t	PROPN
ejpam-418	8	17	)	)	PUNCT
ejpam-418	8	18	satisfies	satisfy	VERB
ejpam-418	8	19	the	the	DET
ejpam-418	8	20	pde	pde	PROPN
ejpam-418	8	21	∂	∂	NOUN
ejpam-418	8	22	2i	2i	NUM
ejpam-418	8	23	∂	∂	NUM
ejpam-418	9	1	x2	x2	NOUN
ejpam-418	9	2	=	=	SYM
ejpam-418	9	3	lc	lc	PROPN
ejpam-418	9	4	∂	∂	NUM
ejpam-418	9	5	2i	2i	PROPN
ejpam-418	9	6	∂	∂	NOUN
ejpam-418	9	7	t2	t2	NOUN
ejpam-418	9	8	+	+	CCONJ
ejpam-418	9	9	(	(	PUNCT
ejpam-418	9	10	rc	rc	PROPN
ejpam-418	9	11	+	+	CCONJ
ejpam-418	9	12	gl	gl	PROPN
ejpam-418	9	13	)	)	PUNCT
ejpam-418	9	14	∂	∂	NOUN
ejpam-418	10	1	i	i	NOUN
ejpam-418	10	2	∂	∂	NOUN
ejpam-418	10	3	t	t	PROPN
ejpam-418	10	4	+	+	CCONJ
ejpam-418	10	5	rgi	rgi	PROPN
ejpam-418	10	6	.	.	PROPN
ejpam-418	11	1	(	(	PUNCT
ejpam-418	11	2	1	1	X
ejpam-418	11	3	)	)	PUNCT
ejpam-418	11	4	where	where	SCONJ
ejpam-418	11	5	the	the	DET
ejpam-418	11	6	constant	constant	ADJ
ejpam-418	11	7	r	r	NOUN
ejpam-418	11	8	,	,	PUNCT
ejpam-418	11	9	l	l	NOUN
ejpam-418	11	10	,	,	PUNCT
ejpam-418	11	11	c	c	PROPN
ejpam-418	11	12	and	and	CCONJ
ejpam-418	11	13	g	g	PROPN
ejpam-418	11	14	are	be	AUX
ejpam-418	11	15	the	the	DET
ejpam-418	11	16	resistance	resistance	NOUN
ejpam-418	11	17	,	,	PUNCT
ejpam-418	11	18	inductance	inductance	NOUN
ejpam-418	11	19	,	,	PUNCT
ejpam-418	11	20	capacitance	capacitance	NOUN
ejpam-418	11	21	and	and	CCONJ
ejpam-418	11	22	leakage	leakage	NOUN
ejpam-418	11	23	conductance	conductance	NOUN
ejpam-418	11	24	and	and	CCONJ
ejpam-418	11	25	the	the	DET
ejpam-418	11	26	distance	distance	NOUN
ejpam-418	11	27	measured	measure	VERB
ejpam-418	11	28	along	along	ADP
ejpam-418	11	29	the	the	DET
ejpam-418	11	30	length	length	NOUN
ejpam-418	11	31	of	of	ADP
ejpam-418	11	32	the	the	DET
ejpam-418	11	33	cable	cable	NOUN
ejpam-418	11	34	represented	represent	VERB
ejpam-418	11	35	by	by	ADP
ejpam-418	11	36	x	x	X
ejpam-418	11	37	.	.	PUNCT
ejpam-418	12	1	the	the	DET
ejpam-418	12	2	voltage	voltage	NOUN
ejpam-418	12	3	also	also	ADV
ejpam-418	12	4	satisfies	satisfy	VERB
ejpam-418	12	5	equation	equation	NOUN
ejpam-418	12	6	(	(	PUNCT
ejpam-418	12	7	1	1	NUM
ejpam-418	12	8	)	)	PUNCT
ejpam-418	12	9	.	.	PUNCT
ejpam-418	13	1	several	several	ADJ
ejpam-418	13	2	special	special	ADJ
ejpam-418	13	3	cases	case	NOUN
ejpam-418	13	4	of	of	ADP
ejpam-418	13	5	(	(	PUNCT
ejpam-418	13	6	1	1	X
ejpam-418	13	7	)	)	PUNCT
ejpam-418	13	8	arise	arise	NOUN
ejpam-418	13	9	in	in	ADP
ejpam-418	13	10	particular	particular	ADJ
ejpam-418	13	11	situations	situation	NOUN
ejpam-418	13	12	,	,	PUNCT
ejpam-418	13	13	∗corresponding	∗corresponde	VERB
ejpam-418	13	14	author	author	NOUN
ejpam-418	13	15	.	.	PUNCT
ejpam-418	14	1	email	email	NOUN
ejpam-418	14	2	addresses	address	NOUN
ejpam-418	14	3	:	:	PUNCT
ejpam-418	14	4	akili	akili	NOUN
ejpam-418	14	5	man�putra.upm.edu.my	man�putra.upm.edu.my	NOUN
ejpam-418	14	6	(	(	PUNCT
ejpam-418	14	7	a.	a.	NOUN
ejpam-418	14	8	kılıçman	kılıçman	PROPN
ejpam-418	14	9	)	)	PUNCT
ejpam-418	14	10	,	,	PUNCT
ejpam-418	14	11	eltayeb�putra.upm.edu.my	eltayeb�putra.upm.edu.my	PROPN
ejpam-418	14	12	(	(	PUNCT
ejpam-418	14	13	h.	h.	PROPN
ejpam-418	14	14	eltayeb	eltayeb	PROPN
ejpam-418	14	15	)	)	PUNCT
ejpam-418	14	16	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-418	15	1	45	45	NUM
ejpam-418	15	2	c	c	NOUN
ejpam-418	15	3	©	©	PROPN
ejpam-418	15	4	2009	2009	NUM
ejpam-418	15	5	ejpam	ejpam	NOUN
ejpam-418	15	6	all	all	DET
ejpam-418	15	7	rights	right	NOUN
ejpam-418	15	8	reserved	reserve	VERB
ejpam-418	15	9	.	.	PUNCT
ejpam-418	16	1	a.	a.	PROPN
ejpam-418	16	2	kılıçman	kılıçman	PROPN
ejpam-418	16	3	,	,	PUNCT
ejpam-418	16	4	h.	h.	PROPN
ejpam-418	16	5	eltayeb	eltayeb	PROPN
ejpam-418	16	6	/	/	SYM
ejpam-418	16	7	eur	eur	PROPN
ejpam-418	16	8	.	.	PUNCT
ejpam-418	17	1	j.	j.	PROPN
ejpam-418	17	2	pure	pure	PROPN
ejpam-418	17	3	appl	appl	PROPN
ejpam-418	17	4	.	.	PROPN
ejpam-418	17	5	math	math	PROPN
ejpam-418	17	6	,	,	PUNCT
ejpam-418	17	7	3	3	NUM
ejpam-418	17	8	(	(	PUNCT
ejpam-418	17	9	2010	2010	NUM
ejpam-418	17	10	)	)	PUNCT
ejpam-418	17	11	,	,	PUNCT
ejpam-418	17	12	45	45	NUM
ejpam-418	17	13	-	-	SYM
ejpam-418	17	14	50	50	NUM
ejpam-418	17	15	46	46	NUM
ejpam-418	17	16	for	for	ADP
ejpam-418	17	17	example	example	NOUN
ejpam-418	17	18	,	,	PUNCT
ejpam-418	17	19	for	for	ADP
ejpam-418	17	20	a	a	DET
ejpam-418	17	21	submarine	submarine	NOUN
ejpam-418	17	22	cable	cable	NOUN
ejpam-418	17	23	g	g	NOUN
ejpam-418	17	24	is	be	AUX
ejpam-418	17	25	negligible	negligible	ADJ
ejpam-418	17	26	and	and	CCONJ
ejpam-418	17	27	frequencies	frequency	NOUN
ejpam-418	17	28	are	be	AUX
ejpam-418	17	29	low	low	ADJ
ejpam-418	17	30	so	so	ADV
ejpam-418	17	31	inductive	inductive	ADJ
ejpam-418	17	32	effects	effect	NOUN
ejpam-418	17	33	can	can	AUX
ejpam-418	17	34	also	also	ADV
ejpam-418	17	35	be	be	AUX
ejpam-418	17	36	neglected	neglect	VERB
ejpam-418	17	37	,	,	PUNCT
ejpam-418	17	38	so	so	SCONJ
ejpam-418	17	39	that	that	SCONJ
ejpam-418	17	40	one	one	PRON
ejpam-418	17	41	may	may	AUX
ejpam-418	17	42	place	place	VERB
ejpam-418	17	43	g	g	NOUN
ejpam-418	17	44	=	=	PUNCT
ejpam-418	17	45	l	l	NOUN
ejpam-418	17	46	=	=	PUNCT
ejpam-418	17	47	0	0	X
ejpam-418	17	48	.	.	PUNCT
ejpam-418	18	1	in	in	ADP
ejpam-418	18	2	this	this	DET
ejpam-418	18	3	case	case	NOUN
ejpam-418	18	4	equation	equation	NOUN
ejpam-418	18	5	(	(	PUNCT
ejpam-418	18	6	1	1	X
ejpam-418	18	7	)	)	PUNCT
ejpam-418	18	8	becomes	become	VERB
ejpam-418	18	9	∂	∂	NUM
ejpam-418	18	10	2i	2i	NUM
ejpam-418	18	11	∂	∂	NUM
ejpam-418	18	12	x2	x2	PROPN
ejpam-418	18	13	=	=	SYM
ejpam-418	18	14	rc	rc	PROPN
ejpam-418	18	15	∂	∂	PROPN
ejpam-418	19	1	i	i	PROPN
ejpam-418	19	2	∂	∂	NOUN
ejpam-418	19	3	t	t	NOUN
ejpam-418	19	4	,	,	PUNCT
ejpam-418	19	5	(	(	PUNCT
ejpam-418	19	6	2	2	X
ejpam-418	19	7	)	)	PUNCT
ejpam-418	19	8	which	which	PRON
ejpam-418	19	9	is	be	AUX
ejpam-418	19	10	called	call	VERB
ejpam-418	19	11	the	the	DET
ejpam-418	19	12	submarine	submarine	NOUN
ejpam-418	19	13	equation	equation	NOUN
ejpam-418	19	14	or	or	CCONJ
ejpam-418	19	15	telegraph	telegraph	NOUN
ejpam-418	19	16	equation	equation	NOUN
ejpam-418	19	17	,	,	PUNCT
ejpam-418	19	18	then	then	ADV
ejpam-418	19	19	we	we	PRON
ejpam-418	19	20	see	see	VERB
ejpam-418	19	21	that	that	DET
ejpam-418	19	22	equation	equation	NOUN
ejpam-418	19	23	(	(	PUNCT
ejpam-418	19	24	2	2	X
ejpam-418	19	25	)	)	PUNCT
ejpam-418	19	26	satisfies	satisfy	VERB
ejpam-418	19	27	the	the	DET
ejpam-418	19	28	one	one	NUM
ejpam-418	19	29	dimensional	dimensional	ADJ
ejpam-418	19	30	heat	heat	NOUN
ejpam-418	19	31	equation	equation	NOUN
ejpam-418	19	32	.	.	PUNCT
ejpam-418	20	1	for	for	ADP
ejpam-418	20	2	high	high	ADJ
ejpam-418	20	3	frequency	frequency	NOUN
ejpam-418	20	4	alternating	alternate	VERB
ejpam-418	20	5	current	current	ADJ
ejpam-418	20	6	,	,	PUNCT
ejpam-418	20	7	again	again	ADV
ejpam-418	20	8	with	with	ADP
ejpam-418	20	9	negligible	negligible	ADJ
ejpam-418	20	10	leakage	leakage	NOUN
ejpam-418	20	11	,	,	PUNCT
ejpam-418	20	12	then	then	ADV
ejpam-418	20	13	equation	equation	NOUN
ejpam-418	20	14	(	(	PUNCT
ejpam-418	20	15	1	1	X
ejpam-418	20	16	)	)	PUNCT
ejpam-418	20	17	can	can	AUX
ejpam-418	20	18	be	be	AUX
ejpam-418	20	19	approximated	approximate	VERB
ejpam-418	20	20	by	by	ADP
ejpam-418	20	21	∂	∂	NUM
ejpam-418	20	22	2i	2i	NUM
ejpam-418	20	23	∂	∂	NUM
ejpam-418	20	24	x2	x2	NOUN
ejpam-418	20	25	=	=	SYM
ejpam-418	20	26	lc	lc	PROPN
ejpam-418	20	27	∂	∂	NUM
ejpam-418	20	28	2i	2i	PROPN
ejpam-418	20	29	∂	∂	NUM
ejpam-418	20	30	t2	t2	NOUN
ejpam-418	20	31	,	,	PUNCT
ejpam-418	20	32	(	(	PUNCT
ejpam-418	20	33	3	3	X
ejpam-418	20	34	)	)	PUNCT
ejpam-418	20	35	which	which	PRON
ejpam-418	20	36	is	be	AUX
ejpam-418	20	37	called	call	VERB
ejpam-418	20	38	the	the	DET
ejpam-418	20	39	high	high	ADJ
ejpam-418	20	40	frequency	frequency	NOUN
ejpam-418	20	41	line	line	NOUN
ejpam-418	20	42	equation	equation	NOUN
ejpam-418	20	43	,	,	PUNCT
ejpam-418	20	44	also	also	ADV
ejpam-418	20	45	this	this	DET
ejpam-418	20	46	equation	equation	NOUN
ejpam-418	20	47	satisfy	satisfy	VERB
ejpam-418	20	48	the	the	DET
ejpam-418	20	49	one	one	NUM
ejpam-418	20	50	dimensional	dimensional	ADJ
ejpam-418	20	51	wave	wave	NOUN
ejpam-418	20	52	equation	equation	NOUN
ejpam-418	20	53	.	.	PUNCT
ejpam-418	21	1	another	another	DET
ejpam-418	21	2	application	application	NOUN
ejpam-418	21	3	of	of	ADP
ejpam-418	21	4	wave	wave	NOUN
ejpam-418	21	5	equation	equation	NOUN
ejpam-418	21	6	,	,	PUNCT
ejpam-418	21	7	wave	wave	NOUN
ejpam-418	21	8	propagation	propagation	NOUN
ejpam-418	21	9	under	under	ADP
ejpam-418	21	10	moving	move	VERB
ejpam-418	21	11	load	load	NOUN
ejpam-418	21	12	is	be	AUX
ejpam-418	21	13	considered	consider	VERB
ejpam-418	21	14	in	in	ADP
ejpam-418	21	15	the	the	DET
ejpam-418	21	16	present	present	ADJ
ejpam-418	21	17	study	study	NOUN
ejpam-418	21	18	.	.	PUNCT
ejpam-418	22	1	in	in	ADP
ejpam-418	22	2	[	[	X
ejpam-418	22	3	1	1	NUM
ejpam-418	22	4	]	]	PUNCT
ejpam-418	22	5	,	,	PUNCT
ejpam-418	22	6	james	james	PROPN
ejpam-418	22	7	discussed	discuss	VERB
ejpam-418	22	8	the	the	DET
ejpam-418	22	9	basic	basic	ADJ
ejpam-418	22	10	equation	equation	NOUN
ejpam-418	22	11	of	of	ADP
ejpam-418	22	12	moving	move	VERB
ejpam-418	22	13	load	load	NOUN
ejpam-418	22	14	in	in	ADP
ejpam-418	22	15	wave	wave	NOUN
ejpam-418	22	16	equation	equation	NOUN
ejpam-418	22	17	with	with	ADP
ejpam-418	22	18	a	a	DET
ejpam-418	22	19	non	non	ADJ
ejpam-418	22	20	-	-	ADJ
ejpam-418	22	21	homogenous	homogenous	ADJ
ejpam-418	22	22	forcing	forcing	NOUN
ejpam-418	22	23	term	term	NOUN
ejpam-418	22	24	,	,	PUNCT
ejpam-418	22	25	ut	ut	PROPN
ejpam-418	22	26	t	t	PROPN
ejpam-418	22	27	−	−	PROPN
ejpam-418	22	28	c2ux	c2ux	NOUN
ejpam-418	22	29	x	x	X
ejpam-418	22	30	=	=	SYM
ejpam-418	22	31	f	f	X
ejpam-418	22	32	(	(	PUNCT
ejpam-418	22	33	x	x	PROPN
ejpam-418	22	34	,	,	PUNCT
ejpam-418	22	35	t	t	PROPN
ejpam-418	22	36	)	)	PUNCT
ejpam-418	22	37	,	,	PUNCT
ejpam-418	22	38	t	t	X
ejpam-418	22	39	>	>	X
ejpam-418	22	40	0	0	PROPN
ejpam-418	22	41	,	,	PUNCT
ejpam-418	22	42	0≤	0≤	NUM
ejpam-418	22	43	x	x	SYM
ejpam-418	22	44	≤	≤	NUM
ejpam-418	22	45	l	l	NOUN
ejpam-418	22	46	u(x	u(x	NOUN
ejpam-418	22	47	,	,	PUNCT
ejpam-418	22	48	0	0	NUM
ejpam-418	22	49	)	)	PUNCT
ejpam-418	22	50	=	=	SYM
ejpam-418	22	51	0	0	NUM
ejpam-418	22	52	,	,	PUNCT
ejpam-418	22	53	ut(x	ut(x	PUNCT
ejpam-418	22	54	,	,	PUNCT
ejpam-418	22	55	0	0	NUM
ejpam-418	22	56	)	)	PUNCT
ejpam-418	22	57	=	=	SYM
ejpam-418	22	58	0	0	X
ejpam-418	23	1	u(0	u(0	PROPN
ejpam-418	23	2	,	,	PUNCT
ejpam-418	23	3	t	t	PROPN
ejpam-418	23	4	)	)	PUNCT
ejpam-418	23	5	=	=	SYM
ejpam-418	23	6	0	0	NUM
ejpam-418	23	7	,	,	PUNCT
ejpam-418	23	8	u(l	u(l	PROPN
ejpam-418	23	9	,	,	PUNCT
ejpam-418	23	10	t	t	PROPN
ejpam-418	23	11	)	)	PUNCT
ejpam-418	23	12	=	=	SYM
ejpam-418	23	13	0	0	NUM
ejpam-418	23	14	,	,	PUNCT
ejpam-418	23	15	(	(	PUNCT
ejpam-418	23	16	4	4	NUM
ejpam-418	23	17	)	)	PUNCT
ejpam-418	23	18	by	by	ADP
ejpam-418	23	19	using	use	VERB
ejpam-418	23	20	single	single	ADJ
ejpam-418	23	21	laplace	laplace	NOUN
ejpam-418	23	22	transform	transform	NOUN
ejpam-418	23	23	.	.	PUNCT
ejpam-418	24	1	in	in	ADP
ejpam-418	24	2	the	the	DET
ejpam-418	24	3	next	next	ADJ
ejpam-418	24	4	we	we	PRON
ejpam-418	24	5	will	will	AUX
ejpam-418	24	6	generalize	generalize	VERB
ejpam-418	24	7	the	the	DET
ejpam-418	24	8	james	james	PROPN
ejpam-418	24	9	’s	’s	PART
ejpam-418	24	10	setting	setting	NOUN
ejpam-418	24	11	and	and	CCONJ
ejpam-418	24	12	will	will	AUX
ejpam-418	24	13	solve	solve	VERB
ejpam-418	24	14	by	by	ADP
ejpam-418	24	15	using	use	VERB
ejpam-418	24	16	double	double	ADJ
ejpam-418	24	17	laplace	laplace	NOUN
ejpam-418	24	18	transform(dlt	transform(dlt	PROPN
ejpam-418	24	19	)	)	PUNCT
ejpam-418	24	20	with	with	ADP
ejpam-418	24	21	moving	move	VERB
ejpam-418	24	22	data	datum	NOUN
ejpam-418	24	23	as	as	SCONJ
ejpam-418	24	24	follows	follow	VERB
ejpam-418	24	25	ut	ut	PROPN
ejpam-418	24	26	t	t	PROPN
ejpam-418	24	27	−	−	PROPN
ejpam-418	25	1	ux	ux	NOUN
ejpam-418	26	1	x	x	X
ejpam-418	27	1	=	=	SYM
ejpam-418	28	1	f	f	X
ejpam-418	29	1	(	(	PUNCT
ejpam-418	30	1	x	x	PROPN
ejpam-418	30	2	,	,	PUNCT
ejpam-418	30	3	t	t	PROPN
ejpam-418	30	4	)	)	PUNCT
ejpam-418	30	5	,	,	PUNCT
ejpam-418	30	6	t	t	X
ejpam-418	30	7	>	>	X
ejpam-418	30	8	0	0	PROPN
ejpam-418	30	9	,	,	PUNCT
ejpam-418	30	10	x	x	X
ejpam-418	30	11	>	>	X
ejpam-418	30	12	0	0	PUNCT
ejpam-418	31	1	u(0	u(0	PROPN
ejpam-418	31	2	,	,	PUNCT
ejpam-418	31	3	t	t	PROPN
ejpam-418	31	4	)	)	PUNCT
ejpam-418	31	5	=	=	SYM
ejpam-418	31	6	g1(t	g1(t	NOUN
ejpam-418	31	7	)	)	PUNCT
ejpam-418	31	8	,	,	PUNCT
ejpam-418	31	9	u(x	u(x	PROPN
ejpam-418	31	10	,	,	PUNCT
ejpam-418	31	11	0	0	NUM
ejpam-418	31	12	)	)	PUNCT
ejpam-418	31	13	=	=	SYM
ejpam-418	31	14	h1(x	h1(x	NOUN
ejpam-418	31	15	)	)	PUNCT
ejpam-418	31	16	ux	ux	NOUN
ejpam-418	31	17	(	(	PUNCT
ejpam-418	31	18	0	0	NUM
ejpam-418	31	19	,	,	PUNCT
ejpam-418	31	20	t	t	PROPN
ejpam-418	31	21	)	)	PUNCT
ejpam-418	31	22	=	=	SYM
ejpam-418	32	1	g′1(t	g′1(t	NUM
ejpam-418	32	2	)	)	PUNCT
ejpam-418	32	3	,	,	PUNCT
ejpam-418	32	4	ut(x	ut(x	NOUN
ejpam-418	32	5	,	,	PUNCT
ejpam-418	32	6	0	0	NUM
ejpam-418	32	7	)	)	PUNCT
ejpam-418	32	8	=	=	SYM
ejpam-418	32	9	h′1(x	h′1(x	NOUN
ejpam-418	32	10	)	)	PUNCT
ejpam-418	32	11	.	.	PUNCT
ejpam-418	33	1	(	(	PUNCT
ejpam-418	33	2	5	5	X
ejpam-418	33	3	)	)	PUNCT
ejpam-418	33	4	where	where	SCONJ
ejpam-418	33	5	c	c	NOUN
ejpam-418	33	6	=	=	SYM
ejpam-418	33	7	1	1	X
ejpam-418	33	8	.	.	PUNCT
ejpam-418	33	9	now	now	ADV
ejpam-418	33	10	let	let	VERB
ejpam-418	33	11	us	we	PRON
ejpam-418	33	12	slightly	slightly	ADV
ejpam-418	33	13	modify	modify	VERB
ejpam-418	33	14	and	and	CCONJ
ejpam-418	33	15	consider	consider	VERB
ejpam-418	33	16	high	high	ADJ
ejpam-418	33	17	frequency	frequency	NOUN
ejpam-418	33	18	line	line	NOUN
ejpam-418	33	19	equation	equation	NOUN
ejpam-418	33	20	as	as	ADP
ejpam-418	33	21	follow	follow	NOUN
ejpam-418	33	22	∂	∂	NUM
ejpam-418	33	23	2i	2i	NUM
ejpam-418	33	24	∂	∂	NUM
ejpam-418	34	1	t2	t2	PROPN
ejpam-418	34	2	−	−	PROPN
ejpam-418	34	3	∂	∂	NUM
ejpam-418	34	4	2i	2i	NUM
ejpam-418	34	5	∂	∂	NUM
ejpam-418	34	6	x2	x2	NOUN
ejpam-418	34	7	=	=	PUNCT
ejpam-418	34	8	h(x)⊗h(t	h(x)⊗h(t	PROPN
ejpam-418	34	9	)	)	PUNCT
ejpam-418	34	10	,	,	PUNCT
ejpam-418	34	11	t	t	PROPN
ejpam-418	34	12	,	,	PUNCT
ejpam-418	34	13	x	x	X
ejpam-418	34	14	>	>	X
ejpam-418	34	15	0	0	NUM
ejpam-418	34	16	,	,	PUNCT
ejpam-418	34	17	(	(	PUNCT
ejpam-418	34	18	6	6	NUM
ejpam-418	34	19	)	)	PUNCT
ejpam-418	34	20	where	where	SCONJ
ejpam-418	34	21	the	the	DET
ejpam-418	34	22	symbol	symbol	NOUN
ejpam-418	34	23	⊗	⊗	PROPN
ejpam-418	34	24	represents	represent	VERB
ejpam-418	34	25	tensor	tensor	NOUN
ejpam-418	34	26	product	product	NOUN
ejpam-418	34	27	and	and	CCONJ
ejpam-418	34	28	h	h	NOUN
ejpam-418	34	29	heaviside	heaviside	ADJ
ejpam-418	34	30	function	function	NOUN
ejpam-418	34	31	,	,	PUNCT
ejpam-418	34	32	under	under	ADP
ejpam-418	34	33	the	the	DET
ejpam-418	34	34	initial	initial	ADJ
ejpam-418	34	35	conditions	condition	NOUN
ejpam-418	34	36	i(0	i(0	PROPN
ejpam-418	34	37	,	,	PUNCT
ejpam-418	34	38	t	t	PROPN
ejpam-418	34	39	)	)	PUNCT
ejpam-418	34	40	=	=	SYM
ejpam-418	34	41	δ(t	δ(t	PROPN
ejpam-418	34	42	)	)	PUNCT
ejpam-418	34	43	,	,	PUNCT
ejpam-418	34	44	i(x	i(x	PROPN
ejpam-418	34	45	,	,	PUNCT
ejpam-418	34	46	0	0	NUM
ejpam-418	34	47	)	)	PUNCT
ejpam-418	34	48	=	=	SYM
ejpam-418	34	49	δ(x	δ(x	NOUN
ejpam-418	34	50	)	)	PUNCT
ejpam-418	34	51	ix(0	ix(0	PROPN
ejpam-418	34	52	,	,	PUNCT
ejpam-418	34	53	t	t	PROPN
ejpam-418	34	54	)	)	PUNCT
ejpam-418	34	55	=	=	SYM
ejpam-418	34	56	δ	δ	PROPN
ejpam-418	34	57	′(t	′(t	PROPN
ejpam-418	34	58	)	)	PUNCT
ejpam-418	34	59	,	,	PUNCT
ejpam-418	34	60	it(x	it(x	NOUN
ejpam-418	34	61	,	,	PUNCT
ejpam-418	34	62	0	0	X
ejpam-418	34	63	)	)	PUNCT
ejpam-418	34	64	=	=	SYM
ejpam-418	34	65	δ′(x	δ′(x	NOUN
ejpam-418	34	66	)	)	PUNCT
ejpam-418	34	67	.	.	PUNCT
ejpam-418	35	1	(	(	PUNCT
ejpam-418	35	2	7	7	X
ejpam-418	35	3	)	)	PUNCT
ejpam-418	35	4	a.	a.	NOUN
ejpam-418	35	5	kılıçman	kılıçman	PROPN
ejpam-418	35	6	,	,	PUNCT
ejpam-418	35	7	h.	h.	PROPN
ejpam-418	35	8	eltayeb	eltayeb	PROPN
ejpam-418	35	9	/	/	SYM
ejpam-418	35	10	eur	eur	PROPN
ejpam-418	35	11	.	.	PUNCT
ejpam-418	36	1	j.	j.	PROPN
ejpam-418	36	2	pure	pure	PROPN
ejpam-418	36	3	appl	appl	PROPN
ejpam-418	36	4	.	.	PROPN
ejpam-418	36	5	math	math	PROPN
ejpam-418	36	6	,	,	PUNCT
ejpam-418	36	7	3	3	NUM
ejpam-418	36	8	(	(	PUNCT
ejpam-418	36	9	2010	2010	NUM
ejpam-418	36	10	)	)	PUNCT
ejpam-418	36	11	,	,	PUNCT
ejpam-418	36	12	45	45	NUM
ejpam-418	36	13	-	-	SYM
ejpam-418	36	14	50	50	NUM
ejpam-418	36	15	47	47	NUM
ejpam-418	36	16	here	here	ADV
ejpam-418	36	17	we	we	PRON
ejpam-418	36	18	consider	consider	VERB
ejpam-418	36	19	i	i	PRON
ejpam-418	36	20	inductance	inductance	VERB
ejpam-418	36	21	and	and	CCONJ
ejpam-418	36	22	capacitance	capacitance	NOUN
ejpam-418	36	23	to	to	PART
ejpam-418	36	24	be	be	AUX
ejpam-418	36	25	each	each	PRON
ejpam-418	36	26	equal	equal	ADJ
ejpam-418	36	27	to	to	ADP
ejpam-418	36	28	unity	unity	NOUN
ejpam-418	36	29	and	and	CCONJ
ejpam-418	36	30	δ	δ	PRON
ejpam-418	36	31	the	the	DET
ejpam-418	36	32	dirac	dirac	PROPN
ejpam-418	36	33	delta	delta	PROPN
ejpam-418	36	34	function	function	NOUN
ejpam-418	36	35	.	.	PUNCT
ejpam-418	37	1	we	we	PRON
ejpam-418	37	2	solve	solve	VERB
ejpam-418	37	3	this	this	DET
ejpam-418	37	4	equation	equation	NOUN
ejpam-418	37	5	,	,	PUNCT
ejpam-418	37	6	by	by	ADP
ejpam-418	37	7	using	use	VERB
ejpam-418	37	8	dlt	dlt	PROPN
ejpam-418	37	9	technique	technique	NOUN
ejpam-418	37	10	as	as	ADP
ejpam-418	37	11	follow	follow	NOUN
ejpam-418	37	12	:	:	PUNCT
ejpam-418	37	13	taking	take	VERB
ejpam-418	37	14	the	the	DET
ejpam-418	37	15	dlt	dlt	PROPN
ejpam-418	37	16	of	of	ADP
ejpam-418	37	17	the	the	DET
ejpam-418	37	18	equation	equation	NOUN
ejpam-418	37	19	(	(	PUNCT
ejpam-418	37	20	6	6	NUM
ejpam-418	37	21	)	)	PUNCT
ejpam-418	37	22	,	,	PUNCT
ejpam-418	37	23	we	we	PRON
ejpam-418	37	24	get	get	VERB
ejpam-418	37	25	s2	s2	NOUN
ejpam-418	37	26	i(s	i(s	NOUN
ejpam-418	37	27	,	,	PUNCT
ejpam-418	37	28	p)−	p)−	NOUN
ejpam-418	37	29	si(p	si(p	NOUN
ejpam-418	37	30	,	,	PUNCT
ejpam-418	37	31	0)−	0)−	NUM
ejpam-418	37	32	∂	∂	NUM
ejpam-418	37	33	∂	∂	NUM
ejpam-418	37	34	t	t	NOUN
ejpam-418	37	35	i(p	i(p	NOUN
ejpam-418	37	36	,	,	PUNCT
ejpam-418	37	37	0)−	0)−	NUM
ejpam-418	37	38	(	(	PUNCT
ejpam-418	37	39	p2	p2	PROPN
ejpam-418	37	40	i(s	i(s	NOUN
ejpam-418	37	41	,	,	PUNCT
ejpam-418	37	42	p)−	p)−	PROPN
ejpam-418	37	43	pi(0	pi(0	PROPN
ejpam-418	37	44	,	,	PUNCT
ejpam-418	37	45	s)−	s)−	PROPN
ejpam-418	37	46	∂	∂	NUM
ejpam-418	37	47	∂	∂	NOUN
ejpam-418	37	48	x	x	X
ejpam-418	37	49	i(0	i(0	PROPN
ejpam-418	37	50	,	,	PUNCT
ejpam-418	37	51	s	s	NOUN
ejpam-418	37	52	)	)	PUNCT
ejpam-418	37	53	)	)	PUNCT
ejpam-418	38	1	=	=	SYM
ejpam-418	38	2	1	1	NUM
ejpam-418	38	3	sp	sp	NOUN
ejpam-418	38	4	,	,	PUNCT
ejpam-418	38	5	(	(	PUNCT
ejpam-418	38	6	8)	8)	NUM
ejpam-418	38	7	and	and	CCONJ
ejpam-418	38	8	on	on	ADP
ejpam-418	38	9	taking	take	VERB
ejpam-418	38	10	single	single	ADJ
ejpam-418	38	11	laplace	laplace	NOUN
ejpam-418	38	12	transform	transform	NOUN
ejpam-418	38	13	for	for	ADP
ejpam-418	38	14	initial	initial	ADJ
ejpam-418	38	15	data	datum	NOUN
ejpam-418	38	16	i.e.	i.e.	X
ejpam-418	38	17	(	(	PUNCT
ejpam-418	38	18	7	7	NUM
ejpam-418	38	19	)	)	PUNCT
ejpam-418	38	20	,	,	PUNCT
ejpam-418	38	21	we	we	PRON
ejpam-418	38	22	get	get	VERB
ejpam-418	38	23	i(0	i(0	PROPN
ejpam-418	38	24	,	,	PUNCT
ejpam-418	38	25	s	s	NOUN
ejpam-418	38	26	)	)	PUNCT
ejpam-418	38	27	=	=	SYM
ejpam-418	38	28	1	1	NUM
ejpam-418	38	29	,	,	PUNCT
ejpam-418	38	30	i(p	i(p	NOUN
ejpam-418	38	31	,	,	PUNCT
ejpam-418	38	32	0	0	NUM
ejpam-418	38	33	)	)	PUNCT
ejpam-418	38	34	=	=	SYM
ejpam-418	38	35	1	1	NUM
ejpam-418	38	36	,	,	PUNCT
ejpam-418	38	37	it(p	it(p	NOUN
ejpam-418	38	38	,	,	PUNCT
ejpam-418	38	39	0	0	NUM
ejpam-418	38	40	)	)	PUNCT
ejpam-418	38	41	=	=	SYM
ejpam-418	39	1	p	p	NOUN
ejpam-418	39	2	and	and	CCONJ
ejpam-418	39	3	ix	ix	INTJ
ejpam-418	39	4	(	(	PUNCT
ejpam-418	39	5	0	0	NUM
ejpam-418	39	6	,	,	PUNCT
ejpam-418	39	7	s	s	PART
ejpam-418	39	8	)	)	PUNCT
ejpam-418	39	9	=	=	SYM
ejpam-418	40	1	s.	s.	PROPN
ejpam-418	40	2	(	(	PUNCT
ejpam-418	40	3	9	9	X
ejpam-418	40	4	)	)	PUNCT
ejpam-418	40	5	substituting	substituting	NOUN
ejpam-418	40	6	(	(	PUNCT
ejpam-418	40	7	5	5	NUM
ejpam-418	40	8	)	)	PUNCT
ejpam-418	40	9	into	into	ADP
ejpam-418	40	10	(	(	PUNCT
ejpam-418	40	11	8)	8)	NUM
ejpam-418	40	12	,	,	PUNCT
ejpam-418	40	13	we	we	PRON
ejpam-418	40	14	obtain	obtain	VERB
ejpam-418	40	15	i(p	i(p	NOUN
ejpam-418	40	16	,	,	PUNCT
ejpam-418	40	17	s	s	PART
ejpam-418	40	18	)	)	PUNCT
ejpam-418	40	19	=	=	SYM
ejpam-418	41	1	1	1	NUM
ejpam-418	41	2	sp(s2	sp(s2	NOUN
ejpam-418	41	3	−	−	PROPN
ejpam-418	41	4	p2	p2	NOUN
ejpam-418	41	5	)	)	PUNCT
ejpam-418	41	6	.	.	PUNCT
ejpam-418	42	1	(	(	PUNCT
ejpam-418	42	2	10	10	NUM
ejpam-418	42	3	)	)	PUNCT
ejpam-418	42	4	now	now	ADV
ejpam-418	42	5	,	,	PUNCT
ejpam-418	42	6	on	on	ADP
ejpam-418	42	7	using	use	VERB
ejpam-418	42	8	double	double	ADJ
ejpam-418	42	9	inverse	inverse	NOUN
ejpam-418	42	10	laplace	laplace	NOUN
ejpam-418	42	11	transform	transform	NOUN
ejpam-418	42	12	for	for	ADP
ejpam-418	42	13	both	both	DET
ejpam-418	42	14	sides	side	NOUN
ejpam-418	42	15	of	of	ADP
ejpam-418	42	16	equation	equation	NOUN
ejpam-418	42	17	(	(	PUNCT
ejpam-418	42	18	10	10	NUM
ejpam-418	42	19	)	)	PUNCT
ejpam-418	42	20	we	we	PRON
ejpam-418	42	21	obtain	obtain	VERB
ejpam-418	42	22	the	the	DET
ejpam-418	42	23	solution	solution	NOUN
ejpam-418	42	24	which	which	PRON
ejpam-418	42	25	is	be	AUX
ejpam-418	42	26	known	know	VERB
ejpam-418	42	27	as	as	ADP
ejpam-418	42	28	current	current	ADJ
ejpam-418	42	29	in	in	ADP
ejpam-418	42	30	the	the	DET
ejpam-418	42	31	form	form	NOUN
ejpam-418	42	32	of	of	ADP
ejpam-418	42	33	i(x	i(x	PROPN
ejpam-418	42	34	,	,	PUNCT
ejpam-418	42	35	t	t	PROPN
ejpam-418	42	36	)	)	PUNCT
ejpam-418	42	37	=	=	SYM
ejpam-418	42	38	1	1	NUM
ejpam-418	42	39	2	2	NUM
ejpam-418	42	40	t2	t2	NOUN
ejpam-418	42	41	.	.	PUNCT
ejpam-418	43	1	now	now	ADV
ejpam-418	43	2	,	,	PUNCT
ejpam-418	43	3	let	let	VERB
ejpam-418	43	4	us	we	PRON
ejpam-418	43	5	reconsider	reconsider	VERB
ejpam-418	43	6	the	the	DET
ejpam-418	43	7	equation	equation	NOUN
ejpam-418	43	8	(	(	PUNCT
ejpam-418	43	9	5	5	NUM
ejpam-418	43	10	)	)	PUNCT
ejpam-418	43	11	,	,	PUNCT
ejpam-418	43	12	and	and	CCONJ
ejpam-418	43	13	multiply	multiply	VERB
ejpam-418	43	14	the	the	DET
ejpam-418	43	15	left	left	ADJ
ejpam-418	43	16	hand	hand	NOUN
ejpam-418	43	17	side	side	NOUN
ejpam-418	43	18	of	of	ADP
ejpam-418	43	19	this	this	DET
ejpam-418	43	20	equation	equation	NOUN
ejpam-418	43	21	by	by	ADP
ejpam-418	43	22	the	the	DET
ejpam-418	43	23	polynomial	polynomial	ADJ
ejpam-418	43	24	ψ(x	ψ(x	PROPN
ejpam-418	43	25	,	,	PUNCT
ejpam-418	43	26	t	t	PROPN
ejpam-418	43	27	)	)	PUNCT
ejpam-418	43	28	in	in	ADP
ejpam-418	43	29	order	order	NOUN
ejpam-418	43	30	to	to	PART
ejpam-418	43	31	have	have	AUX
ejpam-418	43	32	non	non	ADJ
ejpam-418	43	33	-	-	ADJ
ejpam-418	43	34	constant	constant	ADJ
ejpam-418	43	35	coefficients	coefficient	NOUN
ejpam-418	43	36	on	on	ADP
ejpam-418	43	37	applying	apply	VERB
ejpam-418	43	38	double	double	ADJ
ejpam-418	43	39	convolutions	convolution	NOUN
ejpam-418	43	40	,	,	PUNCT
ejpam-418	43	41	we	we	PRON
ejpam-418	43	42	get	get	VERB
ejpam-418	43	43	ψ(x	ψ(x	PROPN
ejpam-418	43	44	,	,	PUNCT
ejpam-418	43	45	t	t	PROPN
ejpam-418	43	46	)	)	PUNCT
ejpam-418	43	47	∗	∗	NOUN
ejpam-418	43	48	∗	∗	PROPN
ejpam-418	43	49	�	�	PROPN
ejpam-418	43	50	ut	ut	PROPN
ejpam-418	43	51	t	t	PROPN
ejpam-418	44	1	−	−	PROPN
ejpam-418	44	2	ux	ux	PROPN
ejpam-418	44	3	x	x	SYM
ejpam-418	44	4	�	�	PROPN
ejpam-418	44	5	=	=	SYM
ejpam-418	44	6	f	f	PROPN
ejpam-418	44	7	(	(	PUNCT
ejpam-418	44	8	x	x	PROPN
ejpam-418	44	9	,	,	PUNCT
ejpam-418	44	10	t	t	PROPN
ejpam-418	44	11	)	)	PUNCT
ejpam-418	44	12	(	(	PUNCT
ejpam-418	44	13	11	11	NUM
ejpam-418	44	14	)	)	PUNCT
ejpam-418	44	15	under	under	ADP
ejpam-418	44	16	the	the	DET
ejpam-418	44	17	same	same	ADJ
ejpam-418	44	18	initial	initial	ADJ
ejpam-418	44	19	conditions	condition	NOUN
ejpam-418	44	20	.	.	PUNCT
ejpam-418	45	1	now	now	ADV
ejpam-418	45	2	by	by	ADP
ejpam-418	45	3	taking	take	VERB
ejpam-418	45	4	double	double	ADJ
ejpam-418	45	5	laplace	laplace	NOUN
ejpam-418	45	6	transform	transform	NOUN
ejpam-418	45	7	for	for	ADP
ejpam-418	45	8	the	the	DET
ejpam-418	45	9	equation	equation	NOUN
ejpam-418	45	10	(	(	PUNCT
ejpam-418	45	11	11	11	NUM
ejpam-418	45	12	)	)	PUNCT
ejpam-418	45	13	and	and	CCONJ
ejpam-418	45	14	single	single	ADJ
ejpam-418	45	15	laplace	laplace	NOUN
ejpam-418	45	16	transform	transform	NOUN
ejpam-418	45	17	for	for	ADP
ejpam-418	45	18	initial	initial	ADJ
ejpam-418	45	19	conditions	condition	NOUN
ejpam-418	45	20	,	,	PUNCT
ejpam-418	45	21	the	the	DET
ejpam-418	45	22	solution	solution	NOUN
ejpam-418	45	23	of	of	ADP
ejpam-418	45	24	equation	equation	NOUN
ejpam-418	45	25	(	(	PUNCT
ejpam-418	45	26	11	11	NUM
ejpam-418	45	27	)	)	PUNCT
ejpam-418	45	28	given	give	VERB
ejpam-418	45	29	by	by	ADP
ejpam-418	45	30	u(x	u(x	NOUN
ejpam-418	45	31	,	,	PUNCT
ejpam-418	45	32	t	t	NOUN
ejpam-418	45	33	)	)	PUNCT
ejpam-418	45	34	=	=	PUNCT
ejpam-418	45	35	l−1	l−1	PROPN
ejpam-418	45	36	s	s	PART
ejpam-418	45	37	l−1	l−1	PROPN
ejpam-418	45	38	p	p	NOUN
ejpam-418	45	39			NOUN
ejpam-418	45	40			ADJ
ejpam-418	45	41			ADJ
ejpam-418	45	42			ADJ
ejpam-418	45	43			NUM
ejpam-418	45	44	sh1(p	sh1(p	NOUN
ejpam-418	45	45	)	)	PUNCT
ejpam-418	45	46	�	�	PROPN
ejpam-418	45	47	s2	s2	NOUN
ejpam-418	45	48	−	−	PROPN
ejpam-418	45	49	p2	p2	PROPN
ejpam-418	45	50	�	�	PROPN
ejpam-418	45	51	−	−	ADP
ejpam-418	45	52	pg1(s	pg1(s	PROPN
ejpam-418	45	53	)	)	PUNCT
ejpam-418	45	54	�	�	PROPN
ejpam-418	45	55	s2	s2	NOUN
ejpam-418	45	56	−	−	PROPN
ejpam-418	45	57	p2	p2	PROPN
ejpam-418	45	58	�	�	PROPN
ejpam-418	45	59	+	+	CCONJ
ejpam-418	45	60	ph1(p)−h1(0	ph1(p)−h1(0	PROPN
ejpam-418	45	61	)	)	PUNCT
ejpam-418	45	62	�	�	PROPN
ejpam-418	45	63	s2	s2	PROPN
ejpam-418	45	64	−	−	PROPN
ejpam-418	45	65	p2	p2	PROPN
ejpam-418	45	66	�	�	PROPN
ejpam-418	46	1	−	−	PROPN
ejpam-418	46	2	sg1(s)−	sg1(s)−	PROPN
ejpam-418	46	3	g1(0	g1(0	PROPN
ejpam-418	46	4	)	)	PUNCT
ejpam-418	46	5	�	�	PROPN
ejpam-418	46	6	s2	s2	PROPN
ejpam-418	46	7	−	−	PROPN
ejpam-418	46	8	p2	p2	PROPN
ejpam-418	46	9	�	�	PROPN
ejpam-418	46	10	+	+	CCONJ
ejpam-418	46	11	f(p	f(p	PROPN
ejpam-418	46	12	,	,	PUNCT
ejpam-418	46	13	s	s	PART
ejpam-418	46	14	)	)	PUNCT
ejpam-418	46	15	�	�	PROPN
ejpam-418	46	16	s2	s2	NOUN
ejpam-418	46	17	−	−	PROPN
ejpam-418	46	18	p2	p2	PROPN
ejpam-418	46	19	�	�	PROPN
ejpam-418	46	20	ψ(p	ψ(p	PROPN
ejpam-418	46	21	,	,	PUNCT
ejpam-418	46	22	s	s	X
ejpam-418	46	23	)	)	PUNCT
ejpam-418	46	24			PROPN
ejpam-418	47	1			PROPN
ejpam-418	47	2			PROPN
ejpam-418	47	3			PROPN
ejpam-418	47	4			PROPN
ejpam-418	47	5	(	(	PUNCT
ejpam-418	47	6	12	12	NUM
ejpam-418	47	7	)	)	PUNCT
ejpam-418	47	8	provided	provide	VERB
ejpam-418	47	9	the	the	DET
ejpam-418	47	10	inverse	inverse	NOUN
ejpam-418	47	11	double	double	ADJ
ejpam-418	47	12	laplace	laplace	NOUN
ejpam-418	47	13	transform	transform	NOUN
ejpam-418	47	14	exist	exist	VERB
ejpam-418	47	15	.	.	PUNCT
ejpam-418	48	1	in	in	ADP
ejpam-418	48	2	[	[	X
ejpam-418	48	3	2	2	NUM
ejpam-418	48	4	]	]	PUNCT
ejpam-418	48	5	and	and	CCONJ
ejpam-418	48	6	[	[	X
ejpam-418	48	7	3	3	X
ejpam-418	48	8	]	]	PUNCT
ejpam-418	48	9	the	the	DET
ejpam-418	48	10	authors	author	NOUN
ejpam-418	48	11	consider	consider	VERB
ejpam-418	48	12	the	the	DET
ejpam-418	48	13	convolution	convolution	NOUN
ejpam-418	48	14	terms	term	NOUN
ejpam-418	48	15	are	be	AUX
ejpam-418	48	16	polynomials	polynomial	NOUN
ejpam-418	48	17	.	.	PUNCT
ejpam-418	49	1	in	in	ADP
ejpam-418	49	2	the	the	DET
ejpam-418	49	3	next	next	ADJ
ejpam-418	49	4	we	we	PRON
ejpam-418	49	5	compare	compare	VERB
ejpam-418	49	6	two	two	NUM
ejpam-418	49	7	solutions	solution	NOUN
ejpam-418	49	8	of	of	ADP
ejpam-418	49	9	the	the	DET
ejpam-418	49	10	equations	equation	NOUN
ejpam-418	49	11	(	(	PUNCT
ejpam-418	49	12	5	5	NUM
ejpam-418	49	13	)	)	PUNCT
ejpam-418	49	14	and	and	CCONJ
ejpam-418	49	15	(	(	PUNCT
ejpam-418	49	16	11	11	NUM
ejpam-418	49	17	)	)	PUNCT
ejpam-418	49	18	.	.	PUNCT
ejpam-418	50	1	now	now	ADV
ejpam-418	50	2	consider	consider	VERB
ejpam-418	50	3	the	the	DET
ejpam-418	50	4	equations	equation	NOUN
ejpam-418	50	5	(	(	PUNCT
ejpam-418	50	6	5	5	NUM
ejpam-418	50	7	)	)	PUNCT
ejpam-418	50	8	and	and	CCONJ
ejpam-418	50	9	(	(	PUNCT
ejpam-418	50	10	11	11	NUM
ejpam-418	50	11	)	)	PUNCT
ejpam-418	50	12	have	have	VERB
ejpam-418	50	13	solutions	solution	NOUN
ejpam-418	50	14	f(x	f(x	PROPN
ejpam-418	50	15	,	,	PUNCT
ejpam-418	50	16	t	t	PROPN
ejpam-418	50	17	)	)	PUNCT
ejpam-418	50	18	and	and	CCONJ
ejpam-418	50	19	k(x	k(x	PROPN
ejpam-418	50	20	,	,	PUNCT
ejpam-418	50	21	t	t	PROPN
ejpam-418	50	22	)	)	PUNCT
ejpam-418	50	23	respectively	respectively	ADV
ejpam-418	50	24	,	,	PUNCT
ejpam-418	50	25	then	then	ADV
ejpam-418	50	26	we	we	PRON
ejpam-418	50	27	can	can	AUX
ejpam-418	50	28	easily	easily	ADV
ejpam-418	50	29	check	check	VERB
ejpam-418	50	30	whether	whether	SCONJ
ejpam-418	50	31	f(x	f(x	PROPN
ejpam-418	50	32	,	,	PUNCT
ejpam-418	50	33	t	t	PROPN
ejpam-418	50	34	)	)	PUNCT
ejpam-418	50	35	∗	∗	NOUN
ejpam-418	50	36	∗k(x	∗k(x	PROPN
ejpam-418	50	37	,	,	PUNCT
ejpam-418	50	38	t	t	PROPN
ejpam-418	50	39	)	)	PUNCT
ejpam-418	50	40	is	be	AUX
ejpam-418	50	41	a	a	DET
ejpam-418	50	42	solution	solution	NOUN
ejpam-418	50	43	for	for	ADP
ejpam-418	50	44	a	a	DET
ejpam-418	50	45	similar	similar	ADJ
ejpam-418	50	46	type	type	NOUN
ejpam-418	50	47	of	of	ADP
ejpam-418	50	48	wave	wave	NOUN
ejpam-418	50	49	equation	equation	NOUN
ejpam-418	50	50	.	.	PUNCT
ejpam-418	51	1	since	since	SCONJ
ejpam-418	51	2	f(x	f(x	PROPN
ejpam-418	51	3	,	,	PUNCT
ejpam-418	51	4	t	t	PROPN
ejpam-418	51	5	)	)	PUNCT
ejpam-418	51	6	and	and	CCONJ
ejpam-418	51	7	k(x	k(x	PROPN
ejpam-418	51	8	,	,	PUNCT
ejpam-418	51	9	t	t	PROPN
ejpam-418	51	10	)	)	PUNCT
ejpam-418	51	11	are	be	AUX
ejpam-418	51	12	solutions	solution	NOUN
ejpam-418	51	13	,	,	PUNCT
ejpam-418	51	14	by	by	ADP
ejpam-418	51	15	substitution	substitution	NOUN
ejpam-418	51	16	we	we	PRON
ejpam-418	51	17	obtain	obtain	VERB
ejpam-418	51	18	(	(	PUNCT
ejpam-418	51	19	f(x	f(x	PROPN
ejpam-418	51	20	,	,	PUNCT
ejpam-418	51	21	t	t	PROPN
ejpam-418	51	22	)	)	PUNCT
ejpam-418	51	23	∗	∗	NOUN
ejpam-418	51	24	∗k(x	∗k(x	PROPN
ejpam-418	51	25	,	,	PUNCT
ejpam-418	51	26	t))t	t))t	NOUN
ejpam-418	51	27	t	t	NOUN
ejpam-418	51	28	−	−	PROPN
ejpam-418	51	29	(	(	PUNCT
ejpam-418	51	30	f(x	f(x	PROPN
ejpam-418	51	31	,	,	PUNCT
ejpam-418	51	32	t	t	PROPN
ejpam-418	51	33	)	)	PUNCT
ejpam-418	51	34	∗	∗	NOUN
ejpam-418	51	35	∗k(x	∗k(x	PROPN
ejpam-418	51	36	,	,	PUNCT
ejpam-418	51	37	t))x	t))x	NOUN
ejpam-418	51	38	x	x	PUNCT
ejpam-418	51	39	?	?	PUNCT
ejpam-418	52	1	=	=	PUNCT
ejpam-418	52	2	f	f	X
ejpam-418	52	3	(	(	PUNCT
ejpam-418	52	4	x	x	PROPN
ejpam-418	52	5	,	,	PUNCT
ejpam-418	52	6	t	t	PROPN
ejpam-418	52	7	)	)	PUNCT
ejpam-418	52	8	.	.	PUNCT
ejpam-418	53	1	(	(	PUNCT
ejpam-418	53	2	13	13	NUM
ejpam-418	53	3	)	)	PUNCT
ejpam-418	53	4	on	on	ADP
ejpam-418	53	5	using	use	VERB
ejpam-418	53	6	the	the	DET
ejpam-418	53	7	definition	definition	NOUN
ejpam-418	53	8	of	of	ADP
ejpam-418	53	9	partial	partial	ADJ
ejpam-418	53	10	derivative	derivative	NOUN
ejpam-418	53	11	with	with	ADP
ejpam-418	53	12	convolution	convolution	NOUN
ejpam-418	53	13	,	,	PUNCT
ejpam-418	53	14	we	we	PRON
ejpam-418	53	15	have	have	VERB
ejpam-418	53	16	ft	ft	ADP
ejpam-418	53	17	t(x	t(x	PROPN
ejpam-418	53	18	,	,	PUNCT
ejpam-418	53	19	t	t	PROPN
ejpam-418	53	20	)	)	PUNCT
ejpam-418	53	21	∗	∗	NOUN
ejpam-418	53	22	∗k(x	∗k(x	PROPN
ejpam-418	53	23	,	,	PUNCT
ejpam-418	53	24	t)−	t)−	PROPN
ejpam-418	53	25	fx	fx	NOUN
ejpam-418	53	26	x	x	SYM
ejpam-418	53	27	(	(	PUNCT
ejpam-418	53	28	x	x	X
ejpam-418	53	29	,	,	PUNCT
ejpam-418	53	30	t	t	PROPN
ejpam-418	53	31	)	)	PUNCT
ejpam-418	53	32	∗	∗	NOUN
ejpam-418	53	33	∗k(x	∗k(x	PROPN
ejpam-418	53	34	,	,	PUNCT
ejpam-418	53	35	t	t	PROPN
ejpam-418	53	36	)	)	PUNCT
ejpam-418	54	1	=	=	SYM
ejpam-418	54	2	f(x	f(x	PROPN
ejpam-418	54	3	,	,	PUNCT
ejpam-418	54	4	t	t	PROPN
ejpam-418	54	5	)	)	PUNCT
ejpam-418	54	6	∗	∗	NOUN
ejpam-418	54	7	∗kt	∗kt	NUM
ejpam-418	55	1	t(x	t(x	PROPN
ejpam-418	55	2	,	,	PUNCT
ejpam-418	55	3	t)−	t)−	PROPN
ejpam-418	55	4	f(x	f(x	PROPN
ejpam-418	55	5	,	,	PUNCT
ejpam-418	55	6	t	t	PROPN
ejpam-418	55	7	)	)	PUNCT
ejpam-418	55	8	∗	∗	NOUN
ejpam-418	55	9	∗kx	∗kx	PROPN
ejpam-418	55	10	x(x	x(x	PROPN
ejpam-418	55	11	,	,	PUNCT
ejpam-418	55	12	t	t	PROPN
ejpam-418	55	13	)	)	PUNCT
ejpam-418	55	14	a.	a.	NOUN
ejpam-418	55	15	kılıçman	kılıçman	PROPN
ejpam-418	55	16	,	,	PUNCT
ejpam-418	55	17	h.	h.	PROPN
ejpam-418	55	18	eltayeb	eltayeb	PROPN
ejpam-418	55	19	/	/	SYM
ejpam-418	55	20	eur	eur	PROPN
ejpam-418	55	21	.	.	PUNCT
ejpam-418	56	1	j.	j.	PROPN
ejpam-418	56	2	pure	pure	PROPN
ejpam-418	56	3	appl	appl	PROPN
ejpam-418	56	4	.	.	PROPN
ejpam-418	56	5	math	math	PROPN
ejpam-418	56	6	,	,	PUNCT
ejpam-418	56	7	3	3	NUM
ejpam-418	56	8	(	(	PUNCT
ejpam-418	56	9	2010	2010	NUM
ejpam-418	56	10	)	)	PUNCT
ejpam-418	56	11	,	,	PUNCT
ejpam-418	56	12	45	45	NUM
ejpam-418	56	13	-	-	SYM
ejpam-418	56	14	50	50	NUM
ejpam-418	56	15	48	48	NUM
ejpam-418	56	16	then	then	ADV
ejpam-418	56	17	the	the	DET
ejpam-418	56	18	equation	equation	NOUN
ejpam-418	56	19	(	(	PUNCT
ejpam-418	56	20	13	13	NUM
ejpam-418	56	21	)	)	PUNCT
ejpam-418	56	22	can	can	AUX
ejpam-418	56	23	be	be	AUX
ejpam-418	56	24	written	write	VERB
ejpam-418	56	25	in	in	ADP
ejpam-418	56	26	the	the	DET
ejpam-418	56	27	form	form	NOUN
ejpam-418	56	28	f(x	f(x	PROPN
ejpam-418	56	29	,	,	PUNCT
ejpam-418	56	30	t	t	PROPN
ejpam-418	56	31	)	)	PUNCT
ejpam-418	56	32	∗	∗	NOUN
ejpam-418	56	33	∗	∗	X
ejpam-418	56	34	�	�	PROPN
ejpam-418	56	35	kt	kt	PROPN
ejpam-418	56	36	t(x	t(x	PROPN
ejpam-418	56	37	,	,	PUNCT
ejpam-418	56	38	t)−	t)−	PROPN
ejpam-418	56	39	kx	kx	PROPN
ejpam-418	56	40	x(x	x(x	PROPN
ejpam-418	56	41	,	,	PUNCT
ejpam-418	56	42	t	t	PROPN
ejpam-418	56	43	)	)	PUNCT
ejpam-418	56	44	�	�	PROPN
ejpam-418	56	45	?	?	PUNCT
ejpam-418	57	1	=	=	PUNCT
ejpam-418	57	2	f	f	X
ejpam-418	57	3	(	(	PUNCT
ejpam-418	57	4	x	x	PROPN
ejpam-418	57	5	,	,	PUNCT
ejpam-418	57	6	t	t	PROPN
ejpam-418	57	7	)	)	PUNCT
ejpam-418	57	8	(	(	PUNCT
ejpam-418	57	9	14	14	NUM
ejpam-418	57	10	)	)	PUNCT
ejpam-418	57	11	or	or	CCONJ
ejpam-418	57	12	�	�	PROPN
ejpam-418	57	13	ft	ft	PROPN
ejpam-418	57	14	t(x	t(x	PROPN
ejpam-418	57	15	,	,	PUNCT
ejpam-418	57	16	t)−	t)−	PROPN
ejpam-418	57	17	fx	fx	NOUN
ejpam-418	57	18	x	x	SYM
ejpam-418	57	19	(	(	PUNCT
ejpam-418	57	20	x	x	SYM
ejpam-418	57	21	,	,	PUNCT
ejpam-418	57	22	t	t	PROPN
ejpam-418	57	23	)	)	PUNCT
ejpam-418	57	24	�	�	PROPN
ejpam-418	57	25	∗	∗	NOUN
ejpam-418	57	26	∗k(x	∗k(x	PROPN
ejpam-418	57	27	,	,	PUNCT
ejpam-418	57	28	t	t	PROPN
ejpam-418	57	29	)	)	PUNCT
ejpam-418	57	30	?	?	PUNCT
ejpam-418	58	1	=	=	PUNCT
ejpam-418	58	2	f	f	X
ejpam-418	58	3	(	(	PUNCT
ejpam-418	58	4	x	x	PROPN
ejpam-418	58	5	,	,	PUNCT
ejpam-418	58	6	t	t	PROPN
ejpam-418	58	7	)	)	PUNCT
ejpam-418	58	8	(	(	PUNCT
ejpam-418	58	9	15	15	NUM
ejpam-418	58	10	)	)	PUNCT
ejpam-418	58	11	by	by	ADP
ejpam-418	58	12	substituting	substitute	VERB
ejpam-418	58	13	we	we	PRON
ejpam-418	58	14	obtain	obtain	VERB
ejpam-418	58	15	f(x	f(x	PROPN
ejpam-418	58	16	,	,	PUNCT
ejpam-418	58	17	t	t	PROPN
ejpam-418	58	18	)	)	PUNCT
ejpam-418	58	19	∗	∗	NOUN
ejpam-418	58	20	∗	∗	NOUN
ejpam-418	58	21	1	1	NUM
ejpam-418	58	22	i	i	NOUN
ejpam-418	58	23	!	!	PUNCT
ejpam-418	59	1	j	j	PROPN
ejpam-418	59	2	!	!	PUNCT
ejpam-418	60	1	f	f	PROPN
ejpam-418	61	1	(	(	PUNCT
ejpam-418	61	2	x	x	PROPN
ejpam-418	61	3	,	,	PUNCT
ejpam-418	61	4	t	t	PROPN
ejpam-418	61	5	)	)	PUNCT
ejpam-418	61	6	6=	6=	ADP
ejpam-418	61	7	f	f	PROPN
ejpam-418	61	8	(	(	PUNCT
ejpam-418	61	9	x	x	PROPN
ejpam-418	61	10	,	,	PUNCT
ejpam-418	61	11	t	t	PROPN
ejpam-418	61	12	)	)	PUNCT
ejpam-418	61	13	(	(	PUNCT
ejpam-418	61	14	16	16	NUM
ejpam-418	61	15	)	)	PUNCT
ejpam-418	61	16	and	and	CCONJ
ejpam-418	61	17	f	f	PROPN
ejpam-418	61	18	(	(	PUNCT
ejpam-418	61	19	x	x	PROPN
ejpam-418	61	20	,	,	PUNCT
ejpam-418	61	21	t	t	PROPN
ejpam-418	61	22	)	)	PUNCT
ejpam-418	61	23	∗	∗	NOUN
ejpam-418	61	24	∗k(x	∗k(x	PROPN
ejpam-418	61	25	,	,	PUNCT
ejpam-418	61	26	t	t	PROPN
ejpam-418	61	27	)	)	PUNCT
ejpam-418	61	28	6=	6=	ADP
ejpam-418	62	1	f	f	PROPN
ejpam-418	62	2	(	(	PUNCT
ejpam-418	62	3	x	x	PROPN
ejpam-418	62	4	,	,	PUNCT
ejpam-418	62	5	t	t	PROPN
ejpam-418	62	6	)	)	PUNCT
ejpam-418	62	7	(	(	PUNCT
ejpam-418	62	8	17	17	NUM
ejpam-418	62	9	)	)	PUNCT
ejpam-418	62	10	thus	thus	ADV
ejpam-418	62	11	the	the	DET
ejpam-418	62	12	convolution	convolution	NOUN
ejpam-418	62	13	f(x	f(x	PROPN
ejpam-418	62	14	,	,	PUNCT
ejpam-418	62	15	t	t	PROPN
ejpam-418	62	16	)	)	PUNCT
ejpam-418	62	17	∗	∗	NOUN
ejpam-418	62	18	∗k(x	∗k(x	PROPN
ejpam-418	62	19	,	,	PUNCT
ejpam-418	62	20	t	t	PROPN
ejpam-418	62	21	)	)	PUNCT
ejpam-418	62	22	is	be	AUX
ejpam-418	62	23	not	not	PART
ejpam-418	62	24	a	a	DET
ejpam-418	62	25	solution	solution	NOUN
ejpam-418	62	26	for	for	ADP
ejpam-418	62	27	equations	equation	NOUN
ejpam-418	62	28	(	(	PUNCT
ejpam-418	62	29	5	5	NUM
ejpam-418	62	30	)	)	PUNCT
ejpam-418	62	31	and	and	CCONJ
ejpam-418	62	32	(	(	PUNCT
ejpam-418	62	33	11	11	NUM
ejpam-418	62	34	)	)	PUNCT
ejpam-418	62	35	.	.	PUNCT
ejpam-418	63	1	but	but	CCONJ
ejpam-418	63	2	it	it	PRON
ejpam-418	63	3	is	be	AUX
ejpam-418	63	4	a	a	DET
ejpam-418	63	5	solution	solution	NOUN
ejpam-418	63	6	for	for	ADP
ejpam-418	63	7	another	another	DET
ejpam-418	63	8	type	type	NOUN
ejpam-418	63	9	of	of	ADP
ejpam-418	63	10	equation	equation	NOUN
ejpam-418	63	11	as	as	ADP
ejpam-418	63	12	in	in	ADP
ejpam-418	63	13	the	the	DET
ejpam-418	63	14	following	follow	VERB
ejpam-418	63	15	theorem	theorem	PROPN
ejpam-418	63	16	.	.	PUNCT
ejpam-418	63	17	theorem	theorem	NOUN
ejpam-418	63	18	1	1	NUM
ejpam-418	63	19	.	.	PUNCT
ejpam-418	64	1	let	let	VERB
ejpam-418	64	2	f(x	f(x	PROPN
ejpam-418	64	3	,	,	PUNCT
ejpam-418	64	4	t	t	PROPN
ejpam-418	64	5	)	)	PUNCT
ejpam-418	64	6	be	be	AUX
ejpam-418	64	7	a	a	DET
ejpam-418	64	8	solution	solution	NOUN
ejpam-418	64	9	of	of	ADP
ejpam-418	64	10	ut	ut	PROPN
ejpam-418	64	11	t	t	PROPN
ejpam-418	65	1	−	−	PROPN
ejpam-418	65	2	ux	ux	NOUN
ejpam-418	65	3	x	x	X
ejpam-418	65	4	=	=	SYM
ejpam-418	65	5	f	f	X
ejpam-418	65	6	(	(	PUNCT
ejpam-418	65	7	x	x	PROPN
ejpam-418	65	8	,	,	PUNCT
ejpam-418	65	9	t	t	PROPN
ejpam-418	65	10	)	)	PUNCT
ejpam-418	65	11	and	and	CCONJ
ejpam-418	65	12	similarly	similarly	ADV
ejpam-418	65	13	k(x	k(x	PROPN
ejpam-418	65	14	,	,	PUNCT
ejpam-418	65	15	t	t	PROPN
ejpam-418	65	16	)	)	PUNCT
ejpam-418	65	17	be	be	AUX
ejpam-418	65	18	a	a	DET
ejpam-418	65	19	solution	solution	NOUN
ejpam-418	65	20	for	for	ADP
ejpam-418	65	21	p(x	p(x	PROPN
ejpam-418	65	22	,	,	PUNCT
ejpam-418	65	23	t	t	PROPN
ejpam-418	65	24	)	)	PUNCT
ejpam-418	65	25	∗	∗	NOUN
ejpam-418	65	26	∗	∗	PROPN
ejpam-418	65	27	�	�	PROPN
ejpam-418	65	28	ut	ut	PROPN
ejpam-418	65	29	t	t	PROPN
ejpam-418	66	1	−	−	PROPN
ejpam-418	66	2	ux	ux	PROPN
ejpam-418	66	3	x	x	SYM
ejpam-418	66	4	�	�	PROPN
ejpam-418	66	5	=	=	SYM
ejpam-418	66	6	f	f	PROPN
ejpam-418	66	7	(	(	PUNCT
ejpam-418	66	8	x	x	PROPN
ejpam-418	66	9	,	,	PUNCT
ejpam-418	66	10	t	t	PROPN
ejpam-418	66	11	)	)	PUNCT
ejpam-418	66	12	(	(	PUNCT
ejpam-418	66	13	x	x	X
ejpam-418	66	14	,	,	PUNCT
ejpam-418	66	15	t	t	PROPN
ejpam-418	66	16	)	)	PUNCT
ejpam-418	66	17	∈	∈	PROPN
ejpam-418	66	18	r2	r2	NOUN
ejpam-418	66	19	+	+	CCONJ
ejpam-418	66	20	under	under	ADP
ejpam-418	66	21	the	the	DET
ejpam-418	66	22	initial	initial	ADJ
ejpam-418	66	23	conditions	condition	NOUN
ejpam-418	66	24	u(0	u(0	PROPN
ejpam-418	66	25	,	,	PUNCT
ejpam-418	66	26	t	t	PROPN
ejpam-418	66	27	)	)	PUNCT
ejpam-418	66	28	=	=	SYM
ejpam-418	66	29	g1(t	g1(t	NOUN
ejpam-418	66	30	)	)	PUNCT
ejpam-418	66	31	,	,	PUNCT
ejpam-418	66	32	u(x	u(x	PROPN
ejpam-418	66	33	,	,	PUNCT
ejpam-418	66	34	0	0	NUM
ejpam-418	66	35	)	)	PUNCT
ejpam-418	66	36	=	=	SYM
ejpam-418	66	37	h1(x	h1(x	NOUN
ejpam-418	66	38	)	)	PUNCT
ejpam-418	66	39	ux(0	ux(0	PROPN
ejpam-418	66	40	,	,	PUNCT
ejpam-418	66	41	t	t	PROPN
ejpam-418	66	42	)	)	PUNCT
ejpam-418	66	43	=	=	SYM
ejpam-418	67	1	g′1(t	g′1(t	NUM
ejpam-418	67	2	)	)	PUNCT
ejpam-418	67	3	,	,	PUNCT
ejpam-418	67	4	ut(x	ut(x	NOUN
ejpam-418	67	5	,	,	PUNCT
ejpam-418	67	6	0	0	NUM
ejpam-418	67	7	)	)	PUNCT
ejpam-418	67	8	=	=	SYM
ejpam-418	67	9	h′1(x	h′1(x	NOUN
ejpam-418	67	10	)	)	PUNCT
ejpam-418	67	11	then	then	ADV
ejpam-418	67	12	f(x	f(x	PROPN
ejpam-418	67	13	,	,	PUNCT
ejpam-418	67	14	t	t	PROPN
ejpam-418	67	15	)	)	PUNCT
ejpam-418	67	16	∗	∗	NOUN
ejpam-418	67	17	∗k(x	∗k(x	PROPN
ejpam-418	67	18	,	,	PUNCT
ejpam-418	67	19	t	t	PROPN
ejpam-418	67	20	)	)	PUNCT
ejpam-418	67	21	is	be	AUX
ejpam-418	67	22	a	a	DET
ejpam-418	67	23	solution	solution	NOUN
ejpam-418	67	24	for	for	ADP
ejpam-418	67	25	the	the	DET
ejpam-418	67	26	following	follow	VERB
ejpam-418	67	27	type	type	NOUN
ejpam-418	67	28	of	of	ADP
ejpam-418	67	29	equation	equation	NOUN
ejpam-418	68	1	ut	ut	PROPN
ejpam-418	68	2	t(x	t(x	PROPN
ejpam-418	68	3	,	,	PUNCT
ejpam-418	68	4	t)−	t)−	PROPN
ejpam-418	68	5	ux	ux	PROPN
ejpam-418	68	6	x(x	x(x	PROPN
ejpam-418	68	7	,	,	PUNCT
ejpam-418	68	8	t)−	t)−	PROPN
ejpam-418	68	9	θ(x	θ(x	PROPN
ejpam-418	68	10	,	,	PUNCT
ejpam-418	68	11	t	t	PROPN
ejpam-418	68	12	)	)	PUNCT
ejpam-418	69	1	=	=	SYM
ejpam-418	69	2	f	f	X
ejpam-418	69	3	(	(	PUNCT
ejpam-418	69	4	x	x	PROPN
ejpam-418	69	5	,	,	PUNCT
ejpam-418	69	6	t	t	PROPN
ejpam-418	69	7	)	)	PUNCT
ejpam-418	69	8	(	(	PUNCT
ejpam-418	69	9	x	x	X
ejpam-418	69	10	,	,	PUNCT
ejpam-418	69	11	t	t	PROPN
ejpam-418	69	12	)	)	PUNCT
ejpam-418	69	13	∈	∈	PROPN
ejpam-418	69	14	r2	r2	NOUN
ejpam-418	69	15	+	+	CCONJ
ejpam-418	69	16	(	(	PUNCT
ejpam-418	69	17	18	18	NUM
ejpam-418	69	18	)	)	PUNCT
ejpam-418	69	19	where	where	SCONJ
ejpam-418	69	20	the	the	DET
ejpam-418	69	21	initial	initial	ADJ
ejpam-418	69	22	conditions	condition	NOUN
ejpam-418	69	23	as	as	ADP
ejpam-418	69	24	above	above	ADV
ejpam-418	69	25	and	and	CCONJ
ejpam-418	69	26	p(x	p(x	PROPN
ejpam-418	69	27	,	,	PUNCT
ejpam-418	69	28	t	t	PROPN
ejpam-418	69	29	)	)	PUNCT
ejpam-418	69	30	is	be	AUX
ejpam-418	69	31	a	a	DET
ejpam-418	69	32	polynomial	polynomial	ADJ
ejpam-418	69	33	.	.	PUNCT
ejpam-418	70	1	proof	proof	NOUN
ejpam-418	70	2	.	.	PUNCT
ejpam-418	71	1	since	since	SCONJ
ejpam-418	71	2	f(x	f(x	PROPN
ejpam-418	71	3	,	,	PUNCT
ejpam-418	71	4	t	t	PROPN
ejpam-418	71	5	)	)	PUNCT
ejpam-418	71	6	is	be	AUX
ejpam-418	71	7	a	a	DET
ejpam-418	71	8	solution	solution	NOUN
ejpam-418	71	9	of	of	ADP
ejpam-418	71	10	equation	equation	NOUN
ejpam-418	71	11	(	(	PUNCT
ejpam-418	71	12	5	5	NUM
ejpam-418	71	13	)	)	PUNCT
ejpam-418	71	14	then	then	ADV
ejpam-418	71	15	ft	ft	PROPN
ejpam-418	71	16	t(x	t(x	PROPN
ejpam-418	71	17	,	,	PUNCT
ejpam-418	71	18	t)−	t)−	PROPN
ejpam-418	71	19	fx	fx	NOUN
ejpam-418	72	1	x	x	SYM
ejpam-418	72	2	(	(	PUNCT
ejpam-418	72	3	x	x	X
ejpam-418	72	4	,	,	PUNCT
ejpam-418	72	5	t	t	PROPN
ejpam-418	72	6	)	)	PUNCT
ejpam-418	72	7	=	=	SYM
ejpam-418	73	1	f	f	X
ejpam-418	73	2	(	(	PUNCT
ejpam-418	73	3	x	x	PROPN
ejpam-418	73	4	,	,	PUNCT
ejpam-418	73	5	t	t	PROPN
ejpam-418	73	6	)	)	PUNCT
ejpam-418	73	7	(	(	PUNCT
ejpam-418	73	8	19	19	NUM
ejpam-418	73	9	)	)	PUNCT
ejpam-418	73	10	true	true	ADJ
ejpam-418	73	11	and	and	CCONJ
ejpam-418	73	12	k(x	k(x	PROPN
ejpam-418	73	13	,	,	PUNCT
ejpam-418	73	14	t	t	PROPN
ejpam-418	73	15	)	)	PUNCT
ejpam-418	73	16	is	be	AUX
ejpam-418	73	17	a	a	DET
ejpam-418	73	18	solution	solution	NOUN
ejpam-418	73	19	of	of	ADP
ejpam-418	73	20	equation	equation	NOUN
ejpam-418	73	21	(	(	PUNCT
ejpam-418	73	22	11	11	NUM
ejpam-418	73	23	)	)	PUNCT
ejpam-418	73	24	rendering	render	VERB
ejpam-418	73	25	kt	kt	ADP
ejpam-418	73	26	t(x	t(x	PROPN
ejpam-418	73	27	,	,	PUNCT
ejpam-418	73	28	t)−	t)−	PROPN
ejpam-418	73	29	kx	kx	PROPN
ejpam-418	73	30	x(x	x(x	PROPN
ejpam-418	73	31	,	,	PUNCT
ejpam-418	73	32	t	t	PROPN
ejpam-418	73	33	)	)	PUNCT
ejpam-418	73	34	=	=	SYM
ejpam-418	73	35	1	1	NUM
ejpam-418	73	36	i	i	NOUN
ejpam-418	73	37	!	!	PUNCT
ejpam-418	74	1	j	j	PROPN
ejpam-418	74	2	!	!	PUNCT
ejpam-418	75	1	f	f	PROPN
ejpam-418	76	1	(	(	PUNCT
ejpam-418	76	2	x	x	PROPN
ejpam-418	76	3	,	,	PUNCT
ejpam-418	76	4	t	t	PROPN
ejpam-418	76	5	)	)	PUNCT
ejpam-418	76	6	.	.	PUNCT
ejpam-418	77	1	(	(	PUNCT
ejpam-418	77	2	20	20	NUM
ejpam-418	77	3	)	)	PUNCT
ejpam-418	77	4	to	to	PART
ejpam-418	77	5	be	be	AUX
ejpam-418	77	6	true	true	ADJ
ejpam-418	77	7	.	.	PUNCT
ejpam-418	78	1	now	now	ADV
ejpam-418	78	2	it	it	PRON
ejpam-418	78	3	follows	follow	VERB
ejpam-418	78	4	(	(	PUNCT
ejpam-418	78	5	f(x	f(x	PROPN
ejpam-418	78	6	,	,	PUNCT
ejpam-418	78	7	t	t	PROPN
ejpam-418	78	8	)	)	PUNCT
ejpam-418	78	9	∗	∗	NOUN
ejpam-418	78	10	∗k(x	∗k(x	PROPN
ejpam-418	78	11	,	,	PUNCT
ejpam-418	78	12	t))t	t))t	NOUN
ejpam-418	78	13	t	t	NOUN
ejpam-418	78	14	−	−	PROPN
ejpam-418	79	1	(	(	PUNCT
ejpam-418	79	2	f(x	f(x	PROPN
ejpam-418	79	3	,	,	PUNCT
ejpam-418	79	4	t	t	PROPN
ejpam-418	79	5	)	)	PUNCT
ejpam-418	79	6	∗	∗	NOUN
ejpam-418	79	7	∗k(x	∗k(x	PROPN
ejpam-418	79	8	,	,	PUNCT
ejpam-418	79	9	t))x	t))x	NOUN
ejpam-418	79	10	x	x	PUNCT
ejpam-418	79	11	−	−	PROPN
ejpam-418	79	12	θ(x	θ(x	PROPN
ejpam-418	79	13	,	,	PUNCT
ejpam-418	79	14	t	t	PROPN
ejpam-418	79	15	)	)	PUNCT
ejpam-418	80	1	=	=	SYM
ejpam-418	80	2	f	f	X
ejpam-418	80	3	(	(	PUNCT
ejpam-418	80	4	x	x	PROPN
ejpam-418	80	5	,	,	PUNCT
ejpam-418	80	6	t	t	PROPN
ejpam-418	80	7	)	)	PUNCT
ejpam-418	80	8	.	.	PUNCT
ejpam-418	81	1	(	(	PUNCT
ejpam-418	81	2	21	21	NUM
ejpam-418	81	3	)	)	PUNCT
ejpam-418	81	4	a.	a.	NOUN
ejpam-418	81	5	kılıçman	kılıçman	PROPN
ejpam-418	81	6	,	,	PUNCT
ejpam-418	81	7	h.	h.	PROPN
ejpam-418	81	8	eltayeb	eltayeb	PROPN
ejpam-418	81	9	/	/	SYM
ejpam-418	81	10	eur	eur	PROPN
ejpam-418	81	11	.	.	PUNCT
ejpam-418	82	1	j.	j.	PROPN
ejpam-418	82	2	pure	pure	PROPN
ejpam-418	82	3	appl	appl	PROPN
ejpam-418	82	4	.	.	PROPN
ejpam-418	82	5	math	math	PROPN
ejpam-418	82	6	,	,	PUNCT
ejpam-418	82	7	3	3	NUM
ejpam-418	82	8	(	(	PUNCT
ejpam-418	82	9	2010	2010	NUM
ejpam-418	82	10	)	)	PUNCT
ejpam-418	82	11	,	,	PUNCT
ejpam-418	82	12	45	45	NUM
ejpam-418	82	13	-	-	SYM
ejpam-418	82	14	50	50	NUM
ejpam-418	82	15	49	49	NUM
ejpam-418	82	16	on	on	ADP
ejpam-418	82	17	using	use	VERB
ejpam-418	82	18	partial	partial	ADJ
ejpam-418	82	19	derivative	derivative	NOUN
ejpam-418	82	20	of	of	ADP
ejpam-418	82	21	convolution	convolution	NOUN
ejpam-418	82	22	,	,	PUNCT
ejpam-418	82	23	we	we	PRON
ejpam-418	82	24	have	have	VERB
ejpam-418	82	25	ft	ft	ADP
ejpam-418	82	26	t(x	t(x	PROPN
ejpam-418	82	27	,	,	PUNCT
ejpam-418	82	28	t	t	PROPN
ejpam-418	82	29	)	)	PUNCT
ejpam-418	82	30	∗	∗	NOUN
ejpam-418	82	31	∗k(x	∗k(x	PROPN
ejpam-418	82	32	,	,	PUNCT
ejpam-418	82	33	t)−	t)−	PROPN
ejpam-418	82	34	fx	fx	NOUN
ejpam-418	82	35	x	x	SYM
ejpam-418	82	36	(	(	PUNCT
ejpam-418	82	37	x	x	X
ejpam-418	82	38	,	,	PUNCT
ejpam-418	82	39	t	t	PROPN
ejpam-418	82	40	)	)	PUNCT
ejpam-418	82	41	∗	∗	NOUN
ejpam-418	82	42	∗k(x	∗k(x	PROPN
ejpam-418	82	43	,	,	PUNCT
ejpam-418	82	44	t	t	PROPN
ejpam-418	82	45	)	)	PUNCT
ejpam-418	83	1	=	=	SYM
ejpam-418	83	2	f(x	f(x	PROPN
ejpam-418	83	3	,	,	PUNCT
ejpam-418	83	4	t	t	PROPN
ejpam-418	83	5	)	)	PUNCT
ejpam-418	83	6	∗	∗	NOUN
ejpam-418	83	7	∗kt	∗kt	NUM
ejpam-418	84	1	t(x	t(x	PROPN
ejpam-418	84	2	,	,	PUNCT
ejpam-418	84	3	t)−	t)−	PROPN
ejpam-418	84	4	f(x	f(x	PROPN
ejpam-418	84	5	,	,	PUNCT
ejpam-418	84	6	t	t	PROPN
ejpam-418	84	7	)	)	PUNCT
ejpam-418	84	8	∗	∗	NOUN
ejpam-418	84	9	∗kx	∗kx	PROPN
ejpam-418	84	10	x(x	x(x	PROPN
ejpam-418	84	11	,	,	PUNCT
ejpam-418	84	12	t	t	PROPN
ejpam-418	84	13	)	)	PUNCT
ejpam-418	84	14	(	(	PUNCT
ejpam-418	84	15	22	22	NUM
ejpam-418	84	16	)	)	PUNCT
ejpam-418	84	17	then	then	ADV
ejpam-418	84	18	the	the	DET
ejpam-418	84	19	equation	equation	NOUN
ejpam-418	84	20	(	(	PUNCT
ejpam-418	84	21	21	21	NUM
ejpam-418	84	22	)	)	PUNCT
ejpam-418	84	23	can	can	AUX
ejpam-418	84	24	be	be	AUX
ejpam-418	84	25	written	write	VERB
ejpam-418	84	26	in	in	ADP
ejpam-418	84	27	the	the	DET
ejpam-418	84	28	form	form	NOUN
ejpam-418	84	29	�	�	PROPN
ejpam-418	84	30	ft	ft	ADP
ejpam-418	84	31	t(x	t(x	PROPN
ejpam-418	84	32	,	,	PUNCT
ejpam-418	84	33	t)−	t)−	PROPN
ejpam-418	84	34	fx	fx	NOUN
ejpam-418	84	35	x	x	SYM
ejpam-418	84	36	(	(	PUNCT
ejpam-418	84	37	x	x	SYM
ejpam-418	84	38	,	,	PUNCT
ejpam-418	84	39	t	t	PROPN
ejpam-418	84	40	)	)	PUNCT
ejpam-418	84	41	�	�	PROPN
ejpam-418	84	42	∗	∗	NOUN
ejpam-418	84	43	∗k(x	∗k(x	PROPN
ejpam-418	84	44	,	,	PUNCT
ejpam-418	84	45	t)−	t)−	PROPN
ejpam-418	84	46	θ(x	θ(x	PROPN
ejpam-418	84	47	,	,	PUNCT
ejpam-418	84	48	t	t	PROPN
ejpam-418	84	49	)	)	PUNCT
ejpam-418	85	1	=	=	SYM
ejpam-418	85	2	f	f	X
ejpam-418	85	3	(	(	PUNCT
ejpam-418	85	4	x	x	PROPN
ejpam-418	85	5	,	,	PUNCT
ejpam-418	85	6	t	t	PROPN
ejpam-418	85	7	)	)	PUNCT
ejpam-418	85	8	.	.	PUNCT
ejpam-418	86	1	(	(	PUNCT
ejpam-418	86	2	23	23	NUM
ejpam-418	86	3	)	)	PUNCT
ejpam-418	86	4	by	by	ADP
ejpam-418	86	5	substituting	substitute	VERB
ejpam-418	86	6	equation	equation	NOUN
ejpam-418	86	7	(	(	PUNCT
ejpam-418	86	8	19	19	NUM
ejpam-418	86	9	)	)	PUNCT
ejpam-418	86	10	in	in	ADP
ejpam-418	86	11	(	(	PUNCT
ejpam-418	86	12	23	23	NUM
ejpam-418	86	13	)	)	PUNCT
ejpam-418	86	14	we	we	PRON
ejpam-418	86	15	have	have	AUX
ejpam-418	86	16	f	f	X
ejpam-418	86	17	(	(	PUNCT
ejpam-418	86	18	x	x	PROPN
ejpam-418	86	19	,	,	PUNCT
ejpam-418	86	20	t	t	PROPN
ejpam-418	86	21	)	)	PUNCT
ejpam-418	86	22	∗	∗	NOUN
ejpam-418	86	23	∗k(x	∗k(x	PROPN
ejpam-418	86	24	,	,	PUNCT
ejpam-418	86	25	t)−	t)−	PROPN
ejpam-418	86	26	θ(x	θ(x	PROPN
ejpam-418	86	27	,	,	PUNCT
ejpam-418	86	28	t	t	PROPN
ejpam-418	86	29	)	)	PUNCT
ejpam-418	87	1	=	=	SYM
ejpam-418	87	2	f	f	X
ejpam-418	87	3	(	(	PUNCT
ejpam-418	87	4	x	x	PROPN
ejpam-418	87	5	,	,	PUNCT
ejpam-418	87	6	t	t	PROPN
ejpam-418	87	7	)	)	PUNCT
ejpam-418	87	8	.	.	PUNCT
ejpam-418	88	1	(	(	PUNCT
ejpam-418	88	2	24	24	NUM
ejpam-418	88	3	)	)	PUNCT
ejpam-418	88	4	thus	thus	ADV
ejpam-418	88	5	we	we	PRON
ejpam-418	88	6	see	see	VERB
ejpam-418	88	7	that	that	SCONJ
ejpam-418	88	8	the	the	DET
ejpam-418	88	9	convolution	convolution	NOUN
ejpam-418	88	10	f(x	f(x	PROPN
ejpam-418	88	11	,	,	PUNCT
ejpam-418	88	12	t	t	PROPN
ejpam-418	88	13	)	)	PUNCT
ejpam-418	88	14	∗	∗	NOUN
ejpam-418	88	15	∗k(x	∗k(x	PROPN
ejpam-418	88	16	,	,	PUNCT
ejpam-418	88	17	t	t	PROPN
ejpam-418	88	18	)	)	PUNCT
ejpam-418	88	19	is	be	AUX
ejpam-418	88	20	a	a	DET
ejpam-418	88	21	solution	solution	NOUN
ejpam-418	88	22	of	of	ADP
ejpam-418	88	23	equation	equation	NOUN
ejpam-418	88	24	(	(	PUNCT
ejpam-418	88	25	18	18	NUM
ejpam-418	88	26	)	)	PUNCT
ejpam-418	88	27	.	.	PUNCT
ejpam-418	89	1	we	we	PRON
ejpam-418	89	2	can	can	AUX
ejpam-418	89	3	also	also	ADV
ejpam-418	89	4	apply	apply	VERB
ejpam-418	89	5	the	the	DET
ejpam-418	89	6	same	same	ADJ
ejpam-418	89	7	method	method	NOUN
ejpam-418	89	8	to	to	PART
ejpam-418	89	9	solve	solve	VERB
ejpam-418	89	10	non	non	ADJ
ejpam-418	89	11	-	-	ADJ
ejpam-418	89	12	homogenous	homogenous	ADJ
ejpam-418	89	13	one	one	NUM
ejpam-418	89	14	dimensional	dimensional	ADJ
ejpam-418	89	15	heat	heat	NOUN
ejpam-418	89	16	equation	equation	NOUN
ejpam-418	89	17	with	with	ADP
ejpam-418	89	18	non	non	ADJ
ejpam-418	89	19	-	-	ADJ
ejpam-418	89	20	constant	constant	ADJ
ejpam-418	89	21	coefficient	coefficient	NOUN
ejpam-418	89	22	as	as	ADV
ejpam-418	89	23	well	well	ADV
ejpam-418	89	24	as	as	ADP
ejpam-418	89	25	for	for	ADP
ejpam-418	89	26	laplace	laplace	NOUN
ejpam-418	89	27	’s	’s	PART
ejpam-418	89	28	equation	equation	NOUN
ejpam-418	89	29	in	in	ADP
ejpam-418	89	30	two	two	NUM
ejpam-418	89	31	dimensions	dimension	NOUN
ejpam-418	89	32	.	.	PUNCT
ejpam-418	90	1	in	in	ADP
ejpam-418	90	2	the	the	DET
ejpam-418	90	3	next	next	ADJ
ejpam-418	90	4	we	we	PRON
ejpam-418	90	5	consider	consider	VERB
ejpam-418	90	6	the	the	DET
ejpam-418	90	7	one	one	NUM
ejpam-418	90	8	dimensional	dimensional	ADJ
ejpam-418	90	9	wave	wave	NOUN
ejpam-418	90	10	equation	equation	NOUN
ejpam-418	90	11	in	in	ADP
ejpam-418	90	12	the	the	DET
ejpam-418	90	13	form	form	NOUN
ejpam-418	90	14	ut	ut	PROPN
ejpam-418	90	15	t	t	PROPN
ejpam-418	90	16	−	−	PROPN
ejpam-418	91	1	ux	ux	NOUN
ejpam-418	92	1	x	x	X
ejpam-418	93	1	=	=	SYM
ejpam-418	94	1	ex+t	ex+t	PROPN
ejpam-418	95	1	(	(	PUNCT
ejpam-418	96	1	t	t	PROPN
ejpam-418	96	2	,	,	PUNCT
ejpam-418	96	3	x	x	NOUN
ejpam-418	96	4	)	)	PUNCT
ejpam-418	96	5	∈	∈	NOUN
ejpam-418	96	6	r2	r2	NOUN
ejpam-418	96	7	+	+	CCONJ
ejpam-418	96	8	(	(	PUNCT
ejpam-418	96	9	25	25	NUM
ejpam-418	96	10	)	)	PUNCT
ejpam-418	96	11	u(x	u(x	NOUN
ejpam-418	96	12	,	,	PUNCT
ejpam-418	96	13	0	0	NUM
ejpam-418	96	14	)	)	PUNCT
ejpam-418	96	15	=	=	SYM
ejpam-418	96	16	xex	xex	X
ejpam-418	96	17	,	,	PUNCT
ejpam-418	96	18	ut(x	ut(x	NOUN
ejpam-418	96	19	,	,	PUNCT
ejpam-418	96	20	0	0	NUM
ejpam-418	96	21	)	)	PUNCT
ejpam-418	96	22	=	=	VERB
ejpam-418	96	23	xex	xex	PROPN
ejpam-418	97	1	+	+	CCONJ
ejpam-418	97	2	ex	ex	X
ejpam-418	97	3	(	(	PUNCT
ejpam-418	97	4	26	26	NUM
ejpam-418	97	5	)	)	PUNCT
ejpam-418	97	6	u(0	u(0	PROPN
ejpam-418	97	7	,	,	PUNCT
ejpam-418	97	8	t	t	PROPN
ejpam-418	97	9	)	)	PUNCT
ejpam-418	97	10	=	=	SYM
ejpam-418	97	11	tet	tet	NOUN
ejpam-418	97	12	,	,	PUNCT
ejpam-418	97	13	ux(0	ux(0	PROPN
ejpam-418	97	14	,	,	PUNCT
ejpam-418	97	15	t	t	PROPN
ejpam-418	97	16	)	)	PUNCT
ejpam-418	97	17	=	=	SYM
ejpam-418	97	18	tet	tet	NOUN
ejpam-418	98	1	+	+	CCONJ
ejpam-418	98	2	et	et	PROPN
ejpam-418	98	3	(	(	PUNCT
ejpam-418	98	4	27	27	NUM
ejpam-418	98	5	)	)	PUNCT
ejpam-418	98	6	by	by	ADP
ejpam-418	98	7	taking	take	VERB
ejpam-418	98	8	double	double	ADJ
ejpam-418	98	9	laplace	laplace	NOUN
ejpam-418	98	10	transform	transform	NOUN
ejpam-418	98	11	for	for	ADP
ejpam-418	98	12	equation	equation	NOUN
ejpam-418	98	13	(	(	PUNCT
ejpam-418	98	14	25	25	NUM
ejpam-418	98	15	)	)	PUNCT
ejpam-418	98	16	and	and	CCONJ
ejpam-418	98	17	single	single	ADJ
ejpam-418	98	18	laplace	laplace	NOUN
ejpam-418	98	19	transform	transform	NOUN
ejpam-418	98	20	for	for	ADP
ejpam-418	98	21	equations	equation	NOUN
ejpam-418	98	22	(	(	PUNCT
ejpam-418	98	23	26	26	NUM
ejpam-418	98	24	)	)	PUNCT
ejpam-418	98	25	and	and	CCONJ
ejpam-418	98	26	(	(	PUNCT
ejpam-418	98	27	27	27	NUM
ejpam-418	98	28	)	)	PUNCT
ejpam-418	98	29	,	,	PUNCT
ejpam-418	98	30	we	we	PRON
ejpam-418	98	31	obtain	obtain	VERB
ejpam-418	98	32	u(p	u(p	NOUN
ejpam-418	98	33	,	,	PUNCT
ejpam-418	98	34	s	s	PART
ejpam-418	98	35	)	)	PUNCT
ejpam-418	98	36	=	=	SYM
ejpam-418	98	37	s	s	PART
ejpam-418	98	38	�	�	PROPN
ejpam-418	98	39	p−	p−	PROPN
ejpam-418	98	40	1	1	NUM
ejpam-418	98	41	�	�	SYM
ejpam-418	98	42	2	2	NUM
ejpam-418	98	43	�	�	PROPN
ejpam-418	98	44	s2	s2	NOUN
ejpam-418	98	45	−	−	PROPN
ejpam-418	98	46	p2	p2	PROPN
ejpam-418	98	47	�	�	PROPN
ejpam-418	98	48	+	+	CCONJ
ejpam-418	98	49	p	p	PROPN
ejpam-418	98	50	�	�	PROPN
ejpam-418	98	51	p−	p−	PROPN
ejpam-418	98	52	1	1	NUM
ejpam-418	98	53	�	�	SYM
ejpam-418	98	54	2	2	NUM
ejpam-418	98	55	�	�	PROPN
ejpam-418	98	56	s2	s2	NOUN
ejpam-418	98	57	−	−	PROPN
ejpam-418	98	58	p2	p2	PROPN
ejpam-418	98	59	�	�	PROPN
ejpam-418	99	1	−	−	PROPN
ejpam-418	99	2	p	p	NOUN
ejpam-418	99	3	(	(	PUNCT
ejpam-418	99	4	s−	s−	PROPN
ejpam-418	99	5	1)2	1)2	NUM
ejpam-418	99	6	�	�	PROPN
ejpam-418	99	7	s2	s2	PROPN
ejpam-418	99	8	−	−	PROPN
ejpam-418	99	9	p2	p2	PROPN
ejpam-418	99	10	�	�	PROPN
ejpam-418	100	1	−	−	NOUN
ejpam-418	100	2	s	s	PART
ejpam-418	100	3	(	(	PUNCT
ejpam-418	100	4	s−	s−	PROPN
ejpam-418	100	5	1)2	1)2	NUM
ejpam-418	100	6	�	�	PROPN
ejpam-418	100	7	s2	s2	PROPN
ejpam-418	100	8	−	−	PROPN
ejpam-418	100	9	p2	p2	PROPN
ejpam-418	100	10	�	�	PROPN
ejpam-418	101	1	+	+	CCONJ
ejpam-418	101	2	1	1	NUM
ejpam-418	101	3	(	(	PUNCT
ejpam-418	101	4	p−	p−	NOUN
ejpam-418	101	5	1)(s−	1)(s−	NUM
ejpam-418	101	6	1	1	NUM
ejpam-418	101	7	)	)	PUNCT
ejpam-418	101	8	�	�	PROPN
ejpam-418	101	9	s2	s2	PROPN
ejpam-418	101	10	−	−	PROPN
ejpam-418	101	11	p2	p2	PROPN
ejpam-418	101	12	�	�	PROPN
ejpam-418	101	13	.	.	PUNCT
ejpam-418	102	1	(	(	PUNCT
ejpam-418	102	2	28	28	NUM
ejpam-418	102	3	)	)	PUNCT
ejpam-418	102	4	on	on	ADP
ejpam-418	102	5	using	use	VERB
ejpam-418	102	6	the	the	DET
ejpam-418	102	7	double	double	ADJ
ejpam-418	102	8	inverse	inverse	NOUN
ejpam-418	102	9	laplace	laplace	NOUN
ejpam-418	102	10	transform	transform	NOUN
ejpam-418	102	11	for	for	ADP
ejpam-418	102	12	equation	equation	NOUN
ejpam-418	102	13	(	(	PUNCT
ejpam-418	102	14	28	28	NUM
ejpam-418	102	15	)	)	PUNCT
ejpam-418	102	16	,	,	PUNCT
ejpam-418	102	17	we	we	PRON
ejpam-418	102	18	obtain	obtain	VERB
ejpam-418	102	19	the	the	DET
ejpam-418	102	20	solution	solution	NOUN
ejpam-418	102	21	of	of	ADP
ejpam-418	102	22	equation	equation	NOUN
ejpam-418	102	23	(	(	PUNCT
ejpam-418	102	24	25	25	NUM
ejpam-418	102	25	)	)	PUNCT
ejpam-418	102	26	as	as	SCONJ
ejpam-418	102	27	follows	follow	VERB
ejpam-418	102	28	u(x	u(x	PROPN
ejpam-418	102	29	,	,	PUNCT
ejpam-418	102	30	t	t	PROPN
ejpam-418	102	31	)	)	PUNCT
ejpam-418	102	32	=	=	SYM
ejpam-418	102	33	3	3	NUM
ejpam-418	102	34	2	2	NUM
ejpam-418	102	35	et+x	et+x	NOUN
ejpam-418	102	36	t	t	NOUN
ejpam-418	102	37	+	+	CCONJ
ejpam-418	102	38	et+x	et+x	PROPN
ejpam-418	102	39	x	x	PUNCT
ejpam-418	103	1	−	−	PROPN
ejpam-418	103	2	1	1	NUM
ejpam-418	103	3	4	4	NUM
ejpam-418	103	4	et+x	et+x	NOUN
ejpam-418	103	5	+	+	CCONJ
ejpam-418	103	6	1	1	NUM
ejpam-418	103	7	4	4	NUM
ejpam-418	103	8	e−t+x	e−t+x	NOUN
ejpam-418	103	9	.	.	PUNCT
ejpam-418	104	1	(	(	PUNCT
ejpam-418	104	2	29	29	NUM
ejpam-418	104	3	)	)	PUNCT
ejpam-418	104	4	we	we	PRON
ejpam-418	104	5	note	note	VERB
ejpam-418	104	6	that	that	SCONJ
ejpam-418	104	7	in	in	ADP
ejpam-418	104	8	the	the	DET
ejpam-418	104	9	literature	literature	NOUN
ejpam-418	104	10	there	there	PRON
ejpam-418	104	11	is	be	VERB
ejpam-418	104	12	no	no	DET
ejpam-418	104	13	systematic	systematic	ADJ
ejpam-418	104	14	way	way	NOUN
ejpam-418	104	15	to	to	PART
ejpam-418	104	16	generate	generate	VERB
ejpam-418	104	17	a	a	DET
ejpam-418	104	18	partial	partial	ADJ
ejpam-418	104	19	differential	differential	NOUN
ejpam-418	104	20	equation	equation	NOUN
ejpam-418	104	21	with	with	ADP
ejpam-418	104	22	variable	variable	ADJ
ejpam-418	104	23	coefficients	coefficient	NOUN
ejpam-418	104	24	from	from	ADP
ejpam-418	104	25	the	the	DET
ejpam-418	104	26	pde	pde	NOUN
ejpam-418	104	27	with	with	ADP
ejpam-418	104	28	constant	constant	ADJ
ejpam-418	104	29	coefficients	coefficient	NOUN
ejpam-418	104	30	,	,	PUNCT
ejpam-418	104	31	however	however	ADV
ejpam-418	104	32	the	the	DET
ejpam-418	104	33	most	most	ADJ
ejpam-418	104	34	of	of	ADP
ejpam-418	104	35	the	the	DET
ejpam-418	104	36	partial	partial	ADJ
ejpam-418	104	37	differential	differential	ADJ
ejpam-418	104	38	equations	equation	NOUN
ejpam-418	104	39	with	with	ADP
ejpam-418	104	40	variable	variable	ADJ
ejpam-418	104	41	coefficients	coefficient	NOUN
ejpam-418	104	42	depend	depend	VERB
ejpam-418	104	43	on	on	ADP
ejpam-418	104	44	nature	nature	NOUN
ejpam-418	104	45	of	of	ADP
ejpam-418	104	46	particular	particular	ADJ
ejpam-418	104	47	problems	problem	NOUN
ejpam-418	104	48	,	,	PUNCT
ejpam-418	104	49	see	see	VERB
ejpam-418	104	50	[	[	X
ejpam-418	104	51	2	2	X
ejpam-418	104	52	]	]	PUNCT
ejpam-418	104	53	and	and	CCONJ
ejpam-418	104	54	[	[	X
ejpam-418	104	55	3	3	NUM
ejpam-418	104	56	]	]	PUNCT
ejpam-418	104	57	.	.	PUNCT
ejpam-418	105	1	in	in	ADP
ejpam-418	105	2	the	the	DET
ejpam-418	105	3	next	next	NOUN
ejpam-418	105	4	we	we	PRON
ejpam-418	105	5	use	use	VERB
ejpam-418	105	6	the	the	DET
ejpam-418	105	7	convolution	convolution	NOUN
ejpam-418	105	8	technique	technique	NOUN
ejpam-418	105	9	to	to	PART
ejpam-418	105	10	generate	generate	VERB
ejpam-418	105	11	a	a	DET
ejpam-418	105	12	pde	pde	NOUN
ejpam-418	105	13	with	with	ADP
ejpam-418	105	14	variable	variable	ADJ
ejpam-418	105	15	coefficients	coefficient	NOUN
ejpam-418	105	16	by	by	ADP
ejpam-418	105	17	using	use	VERB
ejpam-418	105	18	the	the	DET
ejpam-418	105	19	equation	equation	NOUN
ejpam-418	105	20	(	(	PUNCT
ejpam-418	105	21	25	25	NUM
ejpam-418	105	22	)	)	PUNCT
ejpam-418	105	23	and	and	CCONJ
ejpam-418	105	24	compare	compare	VERB
ejpam-418	105	25	the	the	DET
ejpam-418	105	26	solution	solution	NOUN
ejpam-418	105	27	with	with	ADP
ejpam-418	105	28	the	the	DET
ejpam-418	105	29	solution	solution	NOUN
ejpam-418	105	30	of	of	ADP
ejpam-418	105	31	the	the	DET
ejpam-418	105	32	equation	equation	NOUN
ejpam-418	105	33	(	(	PUNCT
ejpam-418	105	34	25	25	NUM
ejpam-418	105	35	)	)	PUNCT
ejpam-418	105	36	.	.	PUNCT
ejpam-418	106	1	now	now	ADV
ejpam-418	106	2	,	,	PUNCT
ejpam-418	106	3	if	if	SCONJ
ejpam-418	106	4	we	we	PRON
ejpam-418	106	5	consider	consider	VERB
ejpam-418	106	6	to	to	PART
ejpam-418	106	7	multiply	multiply	VERB
ejpam-418	106	8	the	the	DET
ejpam-418	106	9	left	left	ADJ
ejpam-418	106	10	hand	hand	NOUN
ejpam-418	106	11	side	side	NOUN
ejpam-418	106	12	of	of	ADP
ejpam-418	106	13	equation	equation	NOUN
ejpam-418	106	14	(	(	PUNCT
ejpam-418	106	15	25	25	NUM
ejpam-418	106	16	)	)	PUNCT
ejpam-418	106	17	by	by	ADP
ejpam-418	106	18	non	non	ADJ
ejpam-418	106	19	-	-	ADJ
ejpam-418	106	20	constant	constant	ADJ
ejpam-418	106	21	coefficient	coefficient	NOUN
ejpam-418	106	22	term	term	NOUN
ejpam-418	106	23	x3t2	x3t2	X
ejpam-418	106	24	and	and	CCONJ
ejpam-418	106	25	using	use	VERB
ejpam-418	106	26	the	the	DET
ejpam-418	106	27	double	double	ADJ
ejpam-418	106	28	convolution	convolution	NOUN
ejpam-418	106	29	with	with	ADP
ejpam-418	106	30	respect	respect	NOUN
ejpam-418	106	31	to	to	ADP
ejpam-418	106	32	x	x	PUNCT
ejpam-418	106	33	and	and	CCONJ
ejpam-418	106	34	t	t	PROPN
ejpam-418	106	35	respectively	respectively	ADV
ejpam-418	106	36	,	,	PUNCT
ejpam-418	106	37	then	then	ADV
ejpam-418	106	38	we	we	PRON
ejpam-418	106	39	have	have	VERB
ejpam-418	106	40	the	the	DET
ejpam-418	106	41	following	follow	VERB
ejpam-418	106	42	equation	equation	NOUN
ejpam-418	106	43	x3t2	x3t2	PUNCT
ejpam-418	106	44	∗	∗	PROPN
ejpam-418	106	45	∗	∗	PROPN
ejpam-418	106	46	�	�	PROPN
ejpam-418	106	47	ut	ut	PROPN
ejpam-418	106	48	t	t	PROPN
ejpam-418	106	49	−	−	PROPN
ejpam-418	106	50	ux	ux	PROPN
ejpam-418	106	51	x	x	SYM
ejpam-418	106	52	�	�	PROPN
ejpam-418	106	53	=	=	SYM
ejpam-418	106	54	ex+t	ex+t	PROPN
ejpam-418	106	55	(	(	PUNCT
ejpam-418	106	56	t	t	PROPN
ejpam-418	106	57	,	,	PUNCT
ejpam-418	106	58	x	x	NOUN
ejpam-418	106	59	)	)	PUNCT
ejpam-418	106	60	∈	∈	NOUN
ejpam-418	106	61	r2	r2	NOUN
ejpam-418	106	62	+	+	CCONJ
ejpam-418	106	63	(	(	PUNCT
ejpam-418	106	64	30	30	NUM
ejpam-418	106	65	)	)	PUNCT
ejpam-418	106	66	references	reference	VERB
ejpam-418	106	67	50	50	NUM
ejpam-418	106	68	u(x	u(x	NOUN
ejpam-418	106	69	,	,	PUNCT
ejpam-418	106	70	0	0	NUM
ejpam-418	106	71	)	)	PUNCT
ejpam-418	106	72	=	=	SYM
ejpam-418	106	73	xex	xex	X
ejpam-418	106	74	,	,	PUNCT
ejpam-418	106	75	ut(x	ut(x	NOUN
ejpam-418	106	76	,	,	PUNCT
ejpam-418	106	77	0	0	NUM
ejpam-418	106	78	)	)	PUNCT
ejpam-418	106	79	=	=	VERB
ejpam-418	106	80	xex	xex	PROPN
ejpam-418	107	1	+	+	CCONJ
ejpam-418	107	2	ex	ex	X
ejpam-418	107	3	(	(	PUNCT
ejpam-418	107	4	31	31	NUM
ejpam-418	107	5	)	)	PUNCT
ejpam-418	107	6	u(0	u(0	PROPN
ejpam-418	107	7	,	,	PUNCT
ejpam-418	107	8	t	t	PROPN
ejpam-418	107	9	)	)	PUNCT
ejpam-418	107	10	=	=	SYM
ejpam-418	107	11	tet	tet	NOUN
ejpam-418	107	12	,	,	PUNCT
ejpam-418	107	13	ux	ux	PROPN
ejpam-418	107	14	(	(	PUNCT
ejpam-418	107	15	0	0	NUM
ejpam-418	107	16	,	,	PUNCT
ejpam-418	107	17	t	t	PROPN
ejpam-418	107	18	)	)	PUNCT
ejpam-418	107	19	=	=	SYM
ejpam-418	107	20	tet	tet	NOUN
ejpam-418	107	21	+	+	CCONJ
ejpam-418	107	22	et	et	NOUN
ejpam-418	107	23	.	.	PUNCT
ejpam-418	108	1	(	(	PUNCT
ejpam-418	108	2	32	32	NUM
ejpam-418	108	3	)	)	PUNCT
ejpam-418	108	4	by	by	ADP
ejpam-418	108	5	using	use	VERB
ejpam-418	108	6	the	the	DET
ejpam-418	108	7	same	same	ADJ
ejpam-418	108	8	technique	technique	NOUN
ejpam-418	108	9	we	we	PRON
ejpam-418	108	10	obtain	obtain	VERB
ejpam-418	108	11	the	the	DET
ejpam-418	108	12	solution	solution	NOUN
ejpam-418	108	13	of	of	ADP
ejpam-418	108	14	equation	equation	NOUN
ejpam-418	108	15	(	(	PUNCT
ejpam-418	108	16	30	30	NUM
ejpam-418	108	17	)	)	PUNCT
ejpam-418	108	18	as	as	ADP
ejpam-418	108	19	v(t	v(t	NOUN
ejpam-418	108	20	,	,	PUNCT
ejpam-418	108	21	x	x	NOUN
ejpam-418	108	22	)	)	PUNCT
ejpam-418	108	23	=	=	SYM
ejpam-418	108	24	5	5	NUM
ejpam-418	108	25	48	48	NUM
ejpam-418	108	26	et+x	et+x	NOUN
ejpam-418	108	27	+	+	NUM
ejpam-418	108	28	et+x	et+x	PROPN
ejpam-418	108	29	x	x	PUNCT
ejpam-418	108	30	−	−	PROPN
ejpam-418	108	31	1	1	NUM
ejpam-418	108	32	48	48	NUM
ejpam-418	108	33	e−t+x	e−t+x	NOUN
ejpam-418	109	1	+	+	CCONJ
ejpam-418	109	2	25	25	NUM
ejpam-418	109	3	24	24	NUM
ejpam-418	109	4	et+x	et+x	NOUN
ejpam-418	109	5	t.	t.	NOUN
ejpam-418	109	6	(	(	PUNCT
ejpam-418	109	7	33	33	NUM
ejpam-418	109	8	)	)	PUNCT
ejpam-418	109	9	now	now	ADV
ejpam-418	109	10	when	when	SCONJ
ejpam-418	109	11	we	we	PRON
ejpam-418	109	12	compare	compare	VERB
ejpam-418	109	13	the	the	DET
ejpam-418	109	14	equations	equation	NOUN
ejpam-418	109	15	(	(	PUNCT
ejpam-418	109	16	29	29	NUM
ejpam-418	109	17	)	)	PUNCT
ejpam-418	109	18	and	and	CCONJ
ejpam-418	109	19	(	(	PUNCT
ejpam-418	109	20	33	33	NUM
ejpam-418	109	21	)	)	PUNCT
ejpam-418	109	22	we	we	PRON
ejpam-418	109	23	see	see	VERB
ejpam-418	109	24	the	the	DET
ejpam-418	109	25	relationship	relationship	NOUN
ejpam-418	109	26	between	between	ADP
ejpam-418	109	27	these	these	DET
ejpam-418	109	28	two	two	NUM
ejpam-418	109	29	solutions	solution	NOUN
ejpam-418	109	30	as	as	ADP
ejpam-418	109	31	in	in	ADP
ejpam-418	109	32	the	the	DET
ejpam-418	109	33	following	follow	VERB
ejpam-418	109	34	form	form	NOUN
ejpam-418	109	35	(	(	PUNCT
ejpam-418	109	36	x3t2	x3t2	NOUN
ejpam-418	109	37	)	)	PUNCT
ejpam-418	109	38	∗	∗	NOUN
ejpam-418	109	39	∗	∗	PROPN
ejpam-418	109	40	�	�	PROPN
ejpam-418	109	41	vt	vt	PROPN
ejpam-418	109	42	t	t	PROPN
ejpam-418	109	43	−	−	PROPN
ejpam-418	109	44	vx	vx	PROPN
ejpam-418	109	45	x	x	PROPN
ejpam-418	109	46	�	�	PROPN
ejpam-418	109	47	=	=	SYM
ejpam-418	109	48	�	�	PROPN
ejpam-418	109	49	ut	ut	PROPN
ejpam-418	109	50	t	t	PROPN
ejpam-418	110	1	−	−	PROPN
ejpam-418	111	1	ux	ux	PROPN
ejpam-418	111	2	x	x	SYM
ejpam-418	111	3	�	�	PROPN
ejpam-418	111	4	+	+	CCONJ
ejpam-418	111	5	θ(x	θ(x	PROPN
ejpam-418	111	6	,	,	PUNCT
ejpam-418	111	7	t	t	PROPN
ejpam-418	111	8	)	)	PUNCT
ejpam-418	111	9	.	.	PUNCT
ejpam-418	112	1	acknowledgements	acknowledgement	VERB
ejpam-418	112	2	the	the	DET
ejpam-418	112	3	authors	author	NOUN
ejpam-418	112	4	gratefully	gratefully	ADV
ejpam-418	112	5	acknowledge	acknowledge	VERB
ejpam-418	112	6	that	that	SCONJ
ejpam-418	112	7	this	this	DET
ejpam-418	112	8	research	research	NOUN
ejpam-418	112	9	was	be	AUX
ejpam-418	112	10	partially	partially	ADV
ejpam-418	112	11	supported	support	VERB
ejpam-418	112	12	by	by	ADP
ejpam-418	112	13	university	university	NOUN
ejpam-418	112	14	putra	putra	PROPN
ejpam-418	112	15	malaysia	malaysia	PROPN
ejpam-418	112	16	under	under	ADP
ejpam-418	112	17	the	the	DET
ejpam-418	112	18	research	research	NOUN
ejpam-418	112	19	university	university	NOUN
ejpam-418	112	20	grant	grant	NOUN
ejpam-418	112	21	scheme	scheme	NOUN
ejpam-418	112	22	05	05	NUM
ejpam-418	112	23	-	-	PUNCT
ejpam-418	112	24	01	01	NUM
ejpam-418	112	25	-	-	PUNCT
ejpam-418	112	26	09	09	NUM
ejpam-418	112	27	-	-	PUNCT
ejpam-418	112	28	0720ru	0720ru	NOUN
ejpam-418	112	29	.	.	PUNCT
ejpam-418	113	1	the	the	DET
ejpam-418	113	2	authors	author	NOUN
ejpam-418	113	3	also	also	ADV
ejpam-418	113	4	thank	thank	VERB
ejpam-418	113	5	the	the	DET
ejpam-418	113	6	referee(s	referee(s	NOUN
ejpam-418	113	7	)	)	PUNCT
ejpam-418	113	8	for	for	ADP
ejpam-418	113	9	very	very	ADV
ejpam-418	113	10	constructive	constructive	ADJ
ejpam-418	113	11	comments	comment	NOUN
ejpam-418	113	12	and	and	CCONJ
ejpam-418	113	13	suggestions	suggestion	NOUN
ejpam-418	113	14	.	.	PUNCT
ejpam-418	114	1	references	reference	NOUN
ejpam-418	114	2	[	[	X
ejpam-418	114	3	1	1	NUM
ejpam-418	114	4	]	]	X
ejpam-418	114	5	g.	g.	PROPN
ejpam-418	114	6	james	james	PROPN
ejpam-418	114	7	.	.	PUNCT
ejpam-418	115	1	advanced	advanced	ADJ
ejpam-418	115	2	modern	modern	ADJ
ejpam-418	115	3	engineering	engineering	NOUN
ejpam-418	115	4	mathematics	mathematic	NOUN
ejpam-418	115	5	,	,	PUNCT
ejpam-418	115	6	3rd	3rd	ADJ
ejpam-418	115	7	ed	ed	NOUN
ejpam-418	115	8	;	;	PUNCT
ejpam-418	115	9	pearson	pearson	PROPN
ejpam-418	115	10	education	education	PROPN
ejpam-418	115	11	limited	limit	VERB
ejpam-418	115	12	:	:	PUNCT
ejpam-418	115	13	new	new	PROPN
ejpam-418	115	14	york	york	PROPN
ejpam-418	115	15	,	,	PUNCT
ejpam-418	115	16	1999	1999	NUM
ejpam-418	115	17	.	.	PUNCT
ejpam-418	116	1	[	[	X
ejpam-418	116	2	2	2	X
ejpam-418	116	3	]	]	X
ejpam-418	116	4	h.	h.	PROPN
ejpam-418	116	5	eltayeb	eltayeb	PROPN
ejpam-418	116	6	and	and	CCONJ
ejpam-418	116	7	a.	a.	PROPN
ejpam-418	116	8	kılıçman	kılıçman	PROPN
ejpam-418	116	9	.	.	PUNCT
ejpam-418	117	1	a	a	DET
ejpam-418	117	2	note	note	NOUN
ejpam-418	117	3	on	on	ADP
ejpam-418	117	4	solutions	solution	NOUN
ejpam-418	117	5	of	of	ADP
ejpam-418	117	6	wave	wave	NOUN
ejpam-418	117	7	,	,	PUNCT
ejpam-418	117	8	laplace	laplace	NOUN
ejpam-418	117	9	’s	’s	PART
ejpam-418	117	10	and	and	CCONJ
ejpam-418	117	11	heat	heat	NOUN
ejpam-418	117	12	equations	equation	NOUN
ejpam-418	117	13	with	with	ADP
ejpam-418	117	14	convolution	convolution	NOUN
ejpam-418	117	15	terms	term	NOUN
ejpam-418	117	16	by	by	ADP
ejpam-418	117	17	using	use	VERB
ejpam-418	117	18	double	double	ADJ
ejpam-418	117	19	laplace	laplace	NOUN
ejpam-418	117	20	transform	transform	NOUN
ejpam-418	117	21	:	:	PUNCT
ejpam-418	117	22	appl	appl	PROPN
ejpam-418	117	23	.	.	PROPN
ejpam-418	117	24	math	math	PROPN
ejpam-418	117	25	.	.	PUNCT
ejpam-418	118	1	lett	lett	PROPN
ejpam-418	118	2	.	.	PUNCT
ejpam-418	119	1	21(12)(2008	21(12)(2008	NUM
ejpam-418	119	2	)	)	PUNCT
ejpam-418	119	3	,	,	PUNCT
ejpam-418	119	4	1324–1329	1324–1329	NUM
ejpam-418	119	5	.	.	PUNCT
ejpam-418	120	1	[	[	X
ejpam-418	120	2	3	3	NUM
ejpam-418	120	3	]	]	PUNCT
ejpam-418	120	4	a.	a.	NOUN
ejpam-418	120	5	kılıçman	kılıçman	NOUN
ejpam-418	120	6	and	and	CCONJ
ejpam-418	120	7	h.	h.	PROPN
ejpam-418	120	8	eltayeb	eltayeb	PROPN
ejpam-418	120	9	.	.	PUNCT
ejpam-418	121	1	a	a	DET
ejpam-418	121	2	note	note	NOUN
ejpam-418	121	3	on	on	ADP
ejpam-418	121	4	defining	define	VERB
ejpam-418	121	5	singular	singular	NOUN
ejpam-418	121	6	integral	integral	ADJ
ejpam-418	121	7	as	as	ADP
ejpam-418	121	8	distribution	distribution	NOUN
ejpam-418	121	9	and	and	CCONJ
ejpam-418	121	10	partial	partial	ADJ
ejpam-418	121	11	differential	differential	ADJ
ejpam-418	121	12	equations	equation	NOUN
ejpam-418	121	13	with	with	ADP
ejpam-418	121	14	convolution	convolution	NOUN
ejpam-418	121	15	term	term	NOUN
ejpam-418	121	16	:	:	PUNCT
ejpam-418	121	17	mathematical	mathematical	ADJ
ejpam-418	121	18	and	and	CCONJ
ejpam-418	121	19	computer	computer	NOUN
ejpam-418	121	20	modelling	model	VERB
ejpam-418	121	21	49(2009	49(2009	NUM
ejpam-418	121	22	)	)	PUNCT
ejpam-418	121	23	,	,	PUNCT
ejpam-418	121	24	327–336	327–336	NUM
ejpam-418	121	25	.	.	PUNCT