id	sid	tid	token	lemma	pos
ejpam-4468	1	1	european	european	PROPN
ejpam-4468	1	2	journal	journal	PROPN
ejpam-4468	1	3	of	of	ADP
ejpam-4468	1	4	pure	pure	ADJ
ejpam-4468	1	5	and	and	CCONJ
ejpam-4468	1	6	applied	apply	VERB
ejpam-4468	1	7	mathematics	mathematic	NOUN
ejpam-4468	1	8	vol	vol	NOUN
ejpam-4468	1	9	.	.	PROPN
ejpam-4468	2	1	15	15	NUM
ejpam-4468	2	2	,	,	PUNCT
ejpam-4468	2	3	no	no	INTJ
ejpam-4468	2	4	.	.	NOUN
ejpam-4468	2	5	4	4	NUM
ejpam-4468	2	6	,	,	PUNCT
ejpam-4468	2	7	2022	2022	NUM
ejpam-4468	2	8	,	,	PUNCT
ejpam-4468	2	9	1444	1444	NUM
ejpam-4468	2	10	-	-	SYM
ejpam-4468	2	11	1454	1454	NUM
ejpam-4468	2	12	issn	issn	PROPN
ejpam-4468	2	13	1307	1307	NUM
ejpam-4468	2	14	-	-	SYM
ejpam-4468	2	15	5543	5543	NUM
ejpam-4468	2	16	–	–	PUNCT
ejpam-4468	2	17	ejpam.com	ejpam.com	X
ejpam-4468	2	18	published	publish	VERB
ejpam-4468	2	19	by	by	ADP
ejpam-4468	2	20	new	new	PROPN
ejpam-4468	2	21	york	york	PROPN
ejpam-4468	2	22	business	business	PROPN
ejpam-4468	2	23	global	global	ADJ
ejpam-4468	2	24	exact	exact	ADJ
ejpam-4468	2	25	solution	solution	NOUN
ejpam-4468	2	26	of	of	ADP
ejpam-4468	2	27	burger	burger	NOUN
ejpam-4468	2	28	’s	’s	PART
ejpam-4468	2	29	equation	equation	NOUN
ejpam-4468	2	30	using	use	VERB
ejpam-4468	2	31	tensor	tensor	NOUN
ejpam-4468	2	32	product	product	NOUN
ejpam-4468	2	33	technique	technique	NOUN
ejpam-4468	2	34	ameerah	ameerah	PROPN
ejpam-4468	2	35	al	al	PROPN
ejpam-4468	2	36	-	-	PUNCT
ejpam-4468	2	37	jarrah1,∗	jarrah1,∗	PROPN
ejpam-4468	2	38	,	,	PUNCT
ejpam-4468	2	39	sharifa	sharifa	PROPN
ejpam-4468	2	40	alsharif1	alsharif1	PROPN
ejpam-4468	2	41	,	,	PUNCT
ejpam-4468	2	42	hasan	hasan	PROPN
ejpam-4468	2	43	almefleh1	almefleh1	PROPN
ejpam-4468	2	44	1	1	NUM
ejpam-4468	2	45	department	department	NOUN
ejpam-4468	2	46	of	of	ADP
ejpam-4468	2	47	mathematics	mathematic	NOUN
ejpam-4468	2	48	,	,	PUNCT
ejpam-4468	2	49	faculty	faculty	NOUN
ejpam-4468	2	50	of	of	ADP
ejpam-4468	2	51	science	science	NOUN
ejpam-4468	2	52	,	,	PUNCT
ejpam-4468	2	53	yarmouk	yarmouk	CCONJ
ejpam-4468	2	54	university	university	NOUN
ejpam-4468	2	55	,	,	PUNCT
ejpam-4468	2	56	irbid	irbid	PROPN
ejpam-4468	2	57	,	,	PUNCT
ejpam-4468	2	58	jordan	jordan	PROPN
ejpam-4468	2	59	abstract	abstract	PROPN
ejpam-4468	2	60	.	.	PUNCT
ejpam-4468	3	1	in	in	ADP
ejpam-4468	3	2	this	this	DET
ejpam-4468	3	3	paper	paper	NOUN
ejpam-4468	3	4	a	a	DET
ejpam-4468	3	5	new	new	ADJ
ejpam-4468	3	6	technique	technique	NOUN
ejpam-4468	3	7	using	use	VERB
ejpam-4468	3	8	tensor	tensor	NOUN
ejpam-4468	3	9	product	product	NOUN
ejpam-4468	3	10	is	be	AUX
ejpam-4468	3	11	presented	present	VERB
ejpam-4468	3	12	which	which	PRON
ejpam-4468	3	13	yields	yield	VERB
ejpam-4468	3	14	an	an	DET
ejpam-4468	3	15	exact	exact	ADJ
ejpam-4468	3	16	solution	solution	NOUN
ejpam-4468	3	17	to	to	ADP
ejpam-4468	3	18	burger	burger	NOUN
ejpam-4468	3	19	’s	’s	PART
ejpam-4468	3	20	equation	equation	NOUN
ejpam-4468	3	21	ut	ut	PROPN
ejpam-4468	4	1	+	+	CCONJ
ejpam-4468	4	2	αuux	αuux	NOUN
ejpam-4468	4	3	=	=	SYM
ejpam-4468	4	4	υuxx	υuxx	NOUN
ejpam-4468	4	5	which	which	PRON
ejpam-4468	4	6	is	be	AUX
ejpam-4468	4	7	one	one	NUM
ejpam-4468	4	8	of	of	ADP
ejpam-4468	4	9	the	the	DET
ejpam-4468	4	10	very	very	ADV
ejpam-4468	4	11	few	few	ADJ
ejpam-4468	4	12	nonlinear	nonlinear	ADJ
ejpam-4468	4	13	partial	partial	ADJ
ejpam-4468	4	14	differential	differential	ADJ
ejpam-4468	4	15	equations	equation	NOUN
ejpam-4468	4	16	that	that	PRON
ejpam-4468	4	17	can	can	AUX
ejpam-4468	4	18	be	be	AUX
ejpam-4468	4	19	solved	solve	VERB
ejpam-4468	4	20	analytically	analytically	ADV
ejpam-4468	4	21	.	.	PUNCT
ejpam-4468	5	1	more	more	ADJ
ejpam-4468	5	2	over	over	ADP
ejpam-4468	5	3	we	we	PRON
ejpam-4468	5	4	give	give	VERB
ejpam-4468	5	5	an	an	DET
ejpam-4468	5	6	atomic	atomic	ADJ
ejpam-4468	5	7	solution	solution	NOUN
ejpam-4468	5	8	for	for	ADP
ejpam-4468	5	9	linear	linear	ADJ
ejpam-4468	5	10	partial	partial	ADJ
ejpam-4468	5	11	differential	differential	NOUN
ejpam-4468	5	12	equations	equation	NOUN
ejpam-4468	5	13	with	with	ADP
ejpam-4468	5	14	and	and	CCONJ
ejpam-4468	5	15	without	without	ADP
ejpam-4468	5	16	variable	variable	ADJ
ejpam-4468	5	17	coefficient	coefficient	NOUN
ejpam-4468	5	18	terms	term	NOUN
ejpam-4468	5	19	.	.	PUNCT
ejpam-4468	6	1	2020	2020	NUM
ejpam-4468	6	2	mathematics	mathematic	NOUN
ejpam-4468	6	3	subject	subject	NOUN
ejpam-4468	6	4	classifications	classification	NOUN
ejpam-4468	6	5	:	:	PUNCT
ejpam-4468	6	6	46m05	46m05	NUM
ejpam-4468	6	7	,	,	PUNCT
ejpam-4468	6	8	35	35	NUM
ejpam-4468	6	9	-	-	SYM
ejpam-4468	6	10	xx	xx	NUM
ejpam-4468	6	11	,	,	PUNCT
ejpam-4468	6	12	46bxx	46bxx	NOUN
ejpam-4468	6	13	key	key	ADJ
ejpam-4468	6	14	words	word	NOUN
ejpam-4468	6	15	and	and	CCONJ
ejpam-4468	6	16	phrases	phrase	NOUN
ejpam-4468	6	17	:	:	PUNCT
ejpam-4468	6	18	burger	burger	NOUN
ejpam-4468	6	19	’s	’s	PART
ejpam-4468	6	20	equation	equation	NOUN
ejpam-4468	6	21	,	,	PUNCT
ejpam-4468	6	22	tensor	tensor	NOUN
ejpam-4468	6	23	product	product	NOUN
ejpam-4468	6	24	,	,	PUNCT
ejpam-4468	6	25	atom	atom	NOUN
ejpam-4468	6	26	solution	solution	NOUN
ejpam-4468	6	27	1	1	NUM
ejpam-4468	6	28	.	.	PUNCT
ejpam-4468	6	29	introduction	introduction	NOUN
ejpam-4468	6	30	one	one	NUM
ejpam-4468	6	31	of	of	ADP
ejpam-4468	6	32	the	the	DET
ejpam-4468	6	33	well	well	ADV
ejpam-4468	6	34	known	know	VERB
ejpam-4468	6	35	partial	partial	ADJ
ejpam-4468	6	36	differential	differential	NOUN
ejpam-4468	6	37	equations	equation	NOUN
ejpam-4468	6	38	which	which	PRON
ejpam-4468	6	39	governs	govern	VERB
ejpam-4468	6	40	a	a	DET
ejpam-4468	6	41	wide	wide	ADJ
ejpam-4468	6	42	variety	variety	NOUN
ejpam-4468	6	43	of	of	ADP
ejpam-4468	6	44	mathematical	mathematical	ADJ
ejpam-4468	6	45	models	model	NOUN
ejpam-4468	6	46	is	be	AUX
ejpam-4468	6	47	the	the	DET
ejpam-4468	6	48	burger	burger	NOUN
ejpam-4468	6	49	’s	’s	PART
ejpam-4468	6	50	equation	equation	NOUN
ejpam-4468	6	51	which	which	PRON
ejpam-4468	6	52	provides	provide	VERB
ejpam-4468	6	53	the	the	DET
ejpam-4468	6	54	simplest	simple	ADJ
ejpam-4468	6	55	nonlinear	nonlinear	ADJ
ejpam-4468	6	56	model	model	NOUN
ejpam-4468	6	57	of	of	ADP
ejpam-4468	6	58	turbulence	turbulence	NOUN
ejpam-4468	6	59	,	,	PUNCT
ejpam-4468	6	60	and	and	CCONJ
ejpam-4468	6	61	else	else	ADV
ejpam-4468	6	62	occurring	occur	VERB
ejpam-4468	6	63	in	in	ADP
ejpam-4468	6	64	various	various	ADJ
ejpam-4468	6	65	areas	area	NOUN
ejpam-4468	6	66	of	of	ADP
ejpam-4468	6	67	applied	apply	VERB
ejpam-4468	6	68	mathematics	mathematic	NOUN
ejpam-4468	6	69	such	such	ADJ
ejpam-4468	6	70	as	as	ADP
ejpam-4468	6	71	fluid	fluid	ADJ
ejpam-4468	6	72	mechanics	mechanic	NOUN
ejpam-4468	6	73	,	,	PUNCT
ejpam-4468	6	74	gas	gas	NOUN
ejpam-4468	6	75	dynamics	dynamic	NOUN
ejpam-4468	6	76	,	,	PUNCT
ejpam-4468	6	77	and	and	CCONJ
ejpam-4468	6	78	traffic	traffic	NOUN
ejpam-4468	6	79	flow	flow	NOUN
ejpam-4468	6	80	.	.	PUNCT
ejpam-4468	7	1	this	this	DET
ejpam-4468	7	2	equation	equation	NOUN
ejpam-4468	7	3	was	be	AUX
ejpam-4468	7	4	first	first	ADV
ejpam-4468	7	5	introduced	introduce	VERB
ejpam-4468	7	6	by	by	ADP
ejpam-4468	7	7	harry	harry	PROPN
ejpam-4468	7	8	bateman	bateman	PROPN
ejpam-4468	7	9	in	in	ADP
ejpam-4468	7	10	1915	1915	NUM
ejpam-4468	7	11	,	,	PUNCT
ejpam-4468	7	12	[	[	X
ejpam-4468	7	13	1	1	NUM
ejpam-4468	7	14	]	]	PUNCT
ejpam-4468	7	15	and	and	CCONJ
ejpam-4468	7	16	later	later	ADV
ejpam-4468	7	17	studied	study	VERB
ejpam-4468	7	18	by	by	ADP
ejpam-4468	7	19	johannes	johannes	PROPN
ejpam-4468	7	20	martinus	martinus	PROPN
ejpam-4468	7	21	burgers	burger	NOUN
ejpam-4468	7	22	,	,	PUNCT
ejpam-4468	7	23	[	[	X
ejpam-4468	7	24	4	4	X
ejpam-4468	7	25	]	]	PUNCT
ejpam-4468	7	26	in	in	ADP
ejpam-4468	7	27	1948	1948	NUM
ejpam-4468	7	28	.	.	PUNCT
ejpam-4468	8	1	in	in	ADP
ejpam-4468	8	2	this	this	DET
ejpam-4468	8	3	paper	paper	NOUN
ejpam-4468	8	4	,	,	PUNCT
ejpam-4468	8	5	we	we	PRON
ejpam-4468	8	6	present	present	VERB
ejpam-4468	8	7	a	a	DET
ejpam-4468	8	8	new	new	ADJ
ejpam-4468	8	9	way	way	NOUN
ejpam-4468	8	10	of	of	ADP
ejpam-4468	8	11	solving	solve	VERB
ejpam-4468	8	12	the	the	DET
ejpam-4468	8	13	nonlinear	nonlinear	ADJ
ejpam-4468	8	14	(	(	PUNCT
ejpam-4468	8	15	burger	burger	NOUN
ejpam-4468	8	16	equation	equation	NOUN
ejpam-4468	8	17	)	)	PUNCT
ejpam-4468	8	18	partial	partial	ADJ
ejpam-4468	8	19	differential	differential	NOUN
ejpam-4468	8	20	equation	equation	NOUN
ejpam-4468	8	21	ut	ut	PROPN
ejpam-4468	9	1	+	+	CCONJ
ejpam-4468	9	2	αuux	αuux	NOUN
ejpam-4468	9	3	=	=	SYM
ejpam-4468	9	4	υuxx	υuxx	NOUN
ejpam-4468	9	5	using	use	VERB
ejpam-4468	9	6	tensor	tensor	NOUN
ejpam-4468	9	7	product	product	NOUN
ejpam-4468	9	8	technique	technique	NOUN
ejpam-4468	9	9	.	.	PUNCT
ejpam-4468	10	1	general	general	ADJ
ejpam-4468	10	2	burger	burger	NOUN
ejpam-4468	10	3	’s	’s	PART
ejpam-4468	10	4	equation	equation	NOUN
ejpam-4468	10	5	:	:	PUNCT
ejpam-4468	10	6	consider	consider	VERB
ejpam-4468	10	7	the	the	DET
ejpam-4468	10	8	one	one	NUM
ejpam-4468	10	9	-	-	PUNCT
ejpam-4468	10	10	dimensional	dimensional	ADJ
ejpam-4468	10	11	quasi	quasi	ADJ
ejpam-4468	10	12	-	-	ADJ
ejpam-4468	10	13	linear	linear	ADJ
ejpam-4468	10	14	burger	burger	NOUN
ejpam-4468	10	15	’s	’s	PART
ejpam-4468	10	16	equation	equation	NOUN
ejpam-4468	10	17	with	with	ADP
ejpam-4468	10	18	the	the	DET
ejpam-4468	10	19	following	following	ADJ
ejpam-4468	10	20	initial	initial	ADJ
ejpam-4468	10	21	and	and	CCONJ
ejpam-4468	10	22	boundary	boundary	ADJ
ejpam-4468	10	23	conditions	condition	NOUN
ejpam-4468	10	24	:	:	PUNCT
ejpam-4468	10	25	ut	ut	PROPN
ejpam-4468	10	26	+	+	NUM
ejpam-4468	10	27	αuux	αuux	NOUN
ejpam-4468	10	28	=	=	PUNCT
ejpam-4468	10	29	υuxx	υuxx	ADJ
ejpam-4468	10	30	u(x	u(x	PROPN
ejpam-4468	10	31	,	,	PUNCT
ejpam-4468	10	32	0	0	NUM
ejpam-4468	10	33	)	)	PUNCT
ejpam-4468	10	34	=	=	SYM
ejpam-4468	10	35	f(x	f(x	PROPN
ejpam-4468	10	36	)	)	PUNCT
ejpam-4468	10	37	,	,	PUNCT
ejpam-4468	10	38	0	0	NUM
ejpam-4468	10	39	≤	≤	NUM
ejpam-4468	10	40	x	x	SYM
ejpam-4468	10	41	≤	≤	NUM
ejpam-4468	10	42	l	l	NOUN
ejpam-4468	10	43	∗corresponding	∗corresponding	NOUN
ejpam-4468	10	44	author	author	NOUN
ejpam-4468	10	45	.	.	PUNCT
ejpam-4468	11	1	doi	doi	NOUN
ejpam-4468	11	2	:	:	PUNCT
ejpam-4468	11	3	https://doi.org/10.29020/nybg.ejpam.v15i4.4468	https://doi.org/10.29020/nybg.ejpam.v15i4.4468	ADJ
ejpam-4468	11	4	email	email	NOUN
ejpam-4468	11	5	addresses	address	NOUN
ejpam-4468	11	6	:	:	PUNCT
ejpam-4468	11	7	amera.gassan@gmail.com	amera.gassan@gmail.com	X
ejpam-4468	11	8	(	(	PUNCT
ejpam-4468	11	9	a.	a.	PROPN
ejpam-4468	11	10	al	al	PROPN
ejpam-4468	11	11	-	-	PUNCT
ejpam-4468	11	12	jarrah	jarrah	PROPN
ejpam-4468	11	13	)	)	PUNCT
ejpam-4468	11	14	,	,	PUNCT
ejpam-4468	12	1	sharifa@yu.edu.jo	sharifa@yu.edu.jo	PROPN
ejpam-4468	12	2	(	(	PUNCT
ejpam-4468	12	3	sh	sh	PROPN
ejpam-4468	12	4	.	.	PROPN
ejpam-4468	12	5	alsharif	alsharif	PROPN
ejpam-4468	12	6	)	)	PUNCT
ejpam-4468	12	7	,	,	PUNCT
ejpam-4468	12	8	almefleh@yu.edu.jo	almefleh@yu.edu.jo	PROPN
ejpam-4468	12	9	(	(	PUNCT
ejpam-4468	12	10	h.	h.	PROPN
ejpam-4468	12	11	almefleh	almefleh	PROPN
ejpam-4468	12	12	)	)	PUNCT
ejpam-4468	12	13	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4468	12	14	1444	1444	NUM
ejpam-4468	12	15	©	©	PROPN
ejpam-4468	12	16	2022	2022	NUM
ejpam-4468	12	17	ejpam	ejpam	VERB
ejpam-4468	12	18	all	all	DET
ejpam-4468	12	19	rights	right	NOUN
ejpam-4468	12	20	reserved	reserve	VERB
ejpam-4468	12	21	.	.	PUNCT
ejpam-4468	13	1	a.	a.	PROPN
ejpam-4468	13	2	al	al	PROPN
ejpam-4468	13	3	-	-	PUNCT
ejpam-4468	13	4	jarrah	jarrah	PROPN
ejpam-4468	13	5	,	,	PUNCT
ejpam-4468	13	6	sh	sh	PROPN
ejpam-4468	13	7	.	.	PROPN
ejpam-4468	13	8	alsharif	alsharif	PROPN
ejpam-4468	13	9	,	,	PUNCT
ejpam-4468	13	10	h.	h.	PROPN
ejpam-4468	13	11	almefleh	almefleh	PROPN
ejpam-4468	13	12	/	/	SYM
ejpam-4468	13	13	eur	eur	PROPN
ejpam-4468	13	14	.	.	PUNCT
ejpam-4468	14	1	j.	j.	PROPN
ejpam-4468	14	2	pure	pure	PROPN
ejpam-4468	14	3	appl	appl	PROPN
ejpam-4468	14	4	.	.	PROPN
ejpam-4468	14	5	math	math	PROPN
ejpam-4468	14	6	,	,	PUNCT
ejpam-4468	14	7	15	15	NUM
ejpam-4468	14	8	(	(	PUNCT
ejpam-4468	14	9	4	4	NUM
ejpam-4468	14	10	)	)	PUNCT
ejpam-4468	14	11	(	(	PUNCT
ejpam-4468	14	12	2022	2022	NUM
ejpam-4468	14	13	)	)	PUNCT
ejpam-4468	14	14	,	,	PUNCT
ejpam-4468	14	15	1444	1444	NUM
ejpam-4468	14	16	-	-	SYM
ejpam-4468	14	17	1454	1454	NUM
ejpam-4468	14	18	1445	1445	NUM
ejpam-4468	14	19	u(0	u(0	PROPN
ejpam-4468	14	20	,	,	PUNCT
ejpam-4468	14	21	t	t	PROPN
ejpam-4468	14	22	)	)	PUNCT
ejpam-4468	14	23	=	=	SYM
ejpam-4468	14	24	f1(t	f1(t	PROPN
ejpam-4468	14	25	)	)	PUNCT
ejpam-4468	14	26	ux(0	ux(0	PROPN
ejpam-4468	14	27	,	,	PUNCT
ejpam-4468	14	28	t	t	PROPN
ejpam-4468	14	29	)	)	PUNCT
ejpam-4468	14	30	=	=	SYM
ejpam-4468	14	31	f2(t	f2(t	PROPN
ejpam-4468	14	32	)	)	PUNCT
ejpam-4468	14	33	,	,	PUNCT
ejpam-4468	14	34	t	t	PROPN
ejpam-4468	14	35	>	>	X
ejpam-4468	14	36	0	0	PROPN
ejpam-4468	14	37	,	,	PUNCT
ejpam-4468	14	38	where	where	SCONJ
ejpam-4468	14	39	u	u	NOUN
ejpam-4468	14	40	=	=	SYM
ejpam-4468	14	41	u(x	u(x	PROPN
ejpam-4468	14	42	,	,	PUNCT
ejpam-4468	14	43	t	t	PROPN
ejpam-4468	14	44	)	)	PUNCT
ejpam-4468	14	45	is	be	AUX
ejpam-4468	14	46	unknown	unknown	ADJ
ejpam-4468	14	47	function	function	NOUN
ejpam-4468	14	48	in	in	ADP
ejpam-4468	14	49	some	some	DET
ejpam-4468	14	50	domain	domain	NOUN
ejpam-4468	14	51	and	and	CCONJ
ejpam-4468	14	52	the	the	DET
ejpam-4468	14	53	nonlinear	nonlinear	ADJ
ejpam-4468	14	54	term	term	NOUN
ejpam-4468	14	55	coefficient	coefficient	NOUN
ejpam-4468	14	56	α	α	NOUN
ejpam-4468	14	57	is	be	AUX
ejpam-4468	14	58	an	an	DET
ejpam-4468	14	59	arbitrary	arbitrary	ADJ
ejpam-4468	14	60	constant	constant	ADJ
ejpam-4468	14	61	and	and	CCONJ
ejpam-4468	14	62	υ	υ	NOUN
ejpam-4468	14	63	is	be	AUX
ejpam-4468	14	64	the	the	DET
ejpam-4468	14	65	coefficient	coefficient	NOUN
ejpam-4468	14	66	of	of	ADP
ejpam-4468	14	67	the	the	DET
ejpam-4468	14	68	kinematics	kinematic	NOUN
ejpam-4468	14	69	viscosity	viscosity	NOUN
ejpam-4468	14	70	of	of	ADP
ejpam-4468	14	71	fluids	fluid	NOUN
ejpam-4468	14	72	which	which	PRON
ejpam-4468	14	73	is	be	AUX
ejpam-4468	14	74	equal	equal	ADJ
ejpam-4468	14	75	to	to	ADP
ejpam-4468	14	76	1	1	NUM
ejpam-4468	14	77	r	r	NOUN
ejpam-4468	14	78	.	.	PUNCT
ejpam-4468	15	1	further	far	ADV
ejpam-4468	15	2	,	,	PUNCT
ejpam-4468	15	3	r	r	NOUN
ejpam-4468	15	4	is	be	AUX
ejpam-4468	15	5	the	the	DET
ejpam-4468	15	6	reynolds	reynold	NOUN
ejpam-4468	15	7	number	number	NOUN
ejpam-4468	15	8	,	,	PUNCT
ejpam-4468	15	9	and	and	CCONJ
ejpam-4468	15	10	when	when	SCONJ
ejpam-4468	15	11	it	it	PRON
ejpam-4468	15	12	is	be	AUX
ejpam-4468	15	13	large	large	ADJ
ejpam-4468	15	14	the	the	DET
ejpam-4468	15	15	equation	equation	NOUN
ejpam-4468	15	16	describes	describe	VERB
ejpam-4468	15	17	shock	shock	NOUN
ejpam-4468	15	18	wave	wave	NOUN
ejpam-4468	15	19	behavior	behavior	NOUN
ejpam-4468	15	20	,	,	PUNCT
ejpam-4468	15	21	where	where	SCONJ
ejpam-4468	15	22	uux	uux	PROPN
ejpam-4468	15	23	is	be	AUX
ejpam-4468	15	24	the	the	DET
ejpam-4468	15	25	nonlinear	nonlinear	ADJ
ejpam-4468	15	26	term	term	NOUN
ejpam-4468	15	27	.	.	PUNCT
ejpam-4468	16	1	this	this	DET
ejpam-4468	16	2	equation	equation	NOUN
ejpam-4468	16	3	has	have	AUX
ejpam-4468	16	4	been	be	AUX
ejpam-4468	16	5	solved	solve	VERB
ejpam-4468	16	6	in	in	ADP
ejpam-4468	16	7	different	different	ADJ
ejpam-4468	16	8	methods	method	NOUN
ejpam-4468	16	9	,	,	PUNCT
ejpam-4468	16	10	such	such	ADJ
ejpam-4468	16	11	as	as	ADP
ejpam-4468	16	12	homotopy	homotopy	NOUN
ejpam-4468	16	13	perturbation	perturbation	NOUN
ejpam-4468	16	14	method	method	NOUN
ejpam-4468	16	15	[	[	X
ejpam-4468	16	16	2	2	NUM
ejpam-4468	16	17	]	]	PUNCT
ejpam-4468	16	18	,	,	PUNCT
ejpam-4468	16	19	linearized	linearize	VERB
ejpam-4468	16	20	solution	solution	NOUN
ejpam-4468	16	21	,	,	PUNCT
ejpam-4468	16	22	and	and	CCONJ
ejpam-4468	16	23	numerically	numerically	ADV
ejpam-4468	16	24	like	like	ADP
ejpam-4468	16	25	the	the	DET
ejpam-4468	16	26	least	least	ADJ
ejpam-4468	16	27	-	-	PUNCT
ejpam-4468	16	28	squares	square	NOUN
ejpam-4468	16	29	quadratic	quadratic	ADJ
ejpam-4468	16	30	b	b	NOUN
ejpam-4468	16	31	-	-	PUNCT
ejpam-4468	16	32	spline	spline	ADJ
ejpam-4468	16	33	finite	finite	PROPN
ejpam-4468	16	34	element	element	NOUN
ejpam-4468	16	35	method	method	NOUN
ejpam-4468	16	36	[	[	X
ejpam-4468	16	37	5	5	NUM
ejpam-4468	16	38	,	,	PUNCT
ejpam-4468	16	39	6	6	NUM
ejpam-4468	16	40	,	,	PUNCT
ejpam-4468	16	41	12–14	12–14	NUM
ejpam-4468	16	42	]	]	PUNCT
ejpam-4468	16	43	,	,	PUNCT
ejpam-4468	16	44	explicit	explicit	ADJ
ejpam-4468	16	45	and	and	CCONJ
ejpam-4468	16	46	exact	exact	ADJ
ejpam-4468	16	47	-	-	PUNCT
ejpam-4468	16	48	explicit	explicit	ADJ
ejpam-4468	16	49	finite	finite	ADJ
ejpam-4468	16	50	difference	difference	NOUN
ejpam-4468	16	51	methods	method	NOUN
ejpam-4468	16	52	,	,	PUNCT
ejpam-4468	16	53	variational	variational	ADJ
ejpam-4468	16	54	iteration	iteration	NOUN
ejpam-4468	16	55	method	method	NOUN
ejpam-4468	16	56	(	(	PUNCT
ejpam-4468	16	57	vim	vim	NOUN
ejpam-4468	16	58	)	)	PUNCT
ejpam-4468	17	1	[	[	X
ejpam-4468	17	2	3	3	NUM
ejpam-4468	17	3	]	]	PUNCT
ejpam-4468	17	4	.	.	PUNCT
ejpam-4468	18	1	as	as	ADV
ejpam-4468	18	2	well	well	ADV
ejpam-4468	18	3	,	,	PUNCT
ejpam-4468	18	4	tensor	tensor	NOUN
ejpam-4468	18	5	product	product	NOUN
ejpam-4468	18	6	used	use	VERB
ejpam-4468	18	7	to	to	PART
ejpam-4468	18	8	solve	solve	VERB
ejpam-4468	18	9	one	one	NUM
ejpam-4468	18	10	of	of	ADP
ejpam-4468	18	11	the	the	DET
ejpam-4468	18	12	classical	classical	ADJ
ejpam-4468	18	13	differential	differential	ADJ
ejpam-4468	18	14	equations	equation	NOUN
ejpam-4468	18	15	in	in	ADP
ejpam-4468	18	16	banach	banach	NOUN
ejpam-4468	18	17	spaces	space	NOUN
ejpam-4468	18	18	is	be	AUX
ejpam-4468	18	19	called	call	VERB
ejpam-4468	18	20	abstract	abstract	ADJ
ejpam-4468	18	21	cauchy	cauchy	ADJ
ejpam-4468	18	22	problem	problem	NOUN
ejpam-4468	18	23	by	by	ADP
ejpam-4468	18	24	ziqan	ziqan	PROPN
ejpam-4468	18	25	,	,	PUNCT
ejpam-4468	18	26	al	al	PROPN
ejpam-4468	18	27	-	-	PUNCT
ejpam-4468	18	28	horani	horani	PROPN
ejpam-4468	18	29	,	,	PUNCT
ejpam-4468	18	30	and	and	CCONJ
ejpam-4468	18	31	khalil	khalil	PROPN
ejpam-4468	19	1	[	[	X
ejpam-4468	19	2	15	15	NUM
ejpam-4468	19	3	]	]	PUNCT
ejpam-4468	19	4	,	,	PUNCT
ejpam-4468	19	5	and	and	CCONJ
ejpam-4468	19	6	also	also	ADV
ejpam-4468	19	7	abdullah	abdullah	PROPN
ejpam-4468	19	8	and	and	CCONJ
ejpam-4468	19	9	khalil	khalil	PROPN
ejpam-4468	20	1	[	[	X
ejpam-4468	20	2	7	7	X
ejpam-4468	20	3	]	]	PUNCT
ejpam-4468	20	4	in	in	ADP
ejpam-4468	20	5	a	a	DET
ejpam-4468	20	6	different	different	ADJ
ejpam-4468	20	7	conditions	condition	NOUN
ejpam-4468	20	8	.	.	PUNCT
ejpam-4468	21	1	also	also	ADV
ejpam-4468	21	2	,	,	PUNCT
ejpam-4468	21	3	many	many	ADJ
ejpam-4468	21	4	of	of	ADP
ejpam-4468	21	5	the	the	DET
ejpam-4468	21	6	non	non	ADJ
ejpam-4468	21	7	-	-	ADJ
ejpam-4468	21	8	homogeneous	homogeneous	ADJ
ejpam-4468	21	9	second	second	ADJ
ejpam-4468	21	10	order	order	NOUN
ejpam-4468	21	11	partial	partial	ADJ
ejpam-4468	21	12	differential	differential	NOUN
ejpam-4468	21	13	equations	equation	NOUN
ejpam-4468	21	14	has	have	AUX
ejpam-4468	21	15	been	be	AUX
ejpam-4468	21	16	solved	solve	VERB
ejpam-4468	21	17	by	by	ADP
ejpam-4468	21	18	finding	find	VERB
ejpam-4468	21	19	an	an	DET
ejpam-4468	21	20	atomic	atomic	ADJ
ejpam-4468	21	21	solution	solution	NOUN
ejpam-4468	21	22	u	u	NOUN
ejpam-4468	21	23	=	=	PROPN
ejpam-4468	21	24	u1	u1	PROPN
ejpam-4468	21	25	⊗	⊗	NOUN
ejpam-4468	21	26	x	x	PUNCT
ejpam-4468	22	1	[	[	X
ejpam-4468	22	2	10	10	NUM
ejpam-4468	22	3	,	,	PUNCT
ejpam-4468	22	4	11	11	NUM
ejpam-4468	22	5	]	]	PUNCT
ejpam-4468	22	6	.	.	PUNCT
ejpam-4468	23	1	2	2	X
ejpam-4468	23	2	.	.	NOUN
ejpam-4468	23	3	tensor	tensor	NOUN
ejpam-4468	23	4	product	product	NOUN
ejpam-4468	23	5	let	let	VERB
ejpam-4468	23	6	x	x	PRON
ejpam-4468	23	7	,	,	PUNCT
ejpam-4468	23	8	y	y	PROPN
ejpam-4468	23	9	be	be	VERB
ejpam-4468	23	10	two	two	NUM
ejpam-4468	23	11	banach	banach	NOUN
ejpam-4468	23	12	spaces	space	NOUN
ejpam-4468	23	13	and	and	CCONJ
ejpam-4468	23	14	x∗	x∗	PROPN
ejpam-4468	23	15	,	,	PUNCT
ejpam-4468	23	16	y	y	PROPN
ejpam-4468	23	17	∗	∗	NOUN
ejpam-4468	23	18	denote	denote	VERB
ejpam-4468	23	19	their	their	PRON
ejpam-4468	23	20	respective	respective	ADJ
ejpam-4468	23	21	duals	dual	NOUN
ejpam-4468	23	22	.	.	PUNCT
ejpam-4468	24	1	for	for	SCONJ
ejpam-4468	24	2	x	x	SYM
ejpam-4468	24	3	∈	∈	PROPN
ejpam-4468	24	4	x	x	X
ejpam-4468	24	5	and	and	CCONJ
ejpam-4468	24	6	y	y	PROPN
ejpam-4468	24	7	∈	∈	PROPN
ejpam-4468	24	8	y	y	PROPN
ejpam-4468	24	9	,	,	PUNCT
ejpam-4468	24	10	define	define	VERB
ejpam-4468	24	11	the	the	DET
ejpam-4468	24	12	linear	linear	ADJ
ejpam-4468	24	13	operator	operator	NOUN
ejpam-4468	24	14	x⊗	x⊗	VERB
ejpam-4468	24	15	y	y	PROPN
ejpam-4468	24	16	:	:	PUNCT
ejpam-4468	24	17	x∗	x∗	PROPN
ejpam-4468	24	18	−→	−→	ADJ
ejpam-4468	24	19	y	y	PROPN
ejpam-4468	24	20	x⊗	x⊗	PROPN
ejpam-4468	24	21	y(x∗	y(x∗	PROPN
ejpam-4468	24	22	)	)	PUNCT
ejpam-4468	24	23	=	=	PUNCT
ejpam-4468	24	24	⟨x	⟨x	VERB
ejpam-4468	24	25	,	,	PUNCT
ejpam-4468	24	26	x∗⟩y	x∗⟩y	PROPN
ejpam-4468	24	27	,	,	PUNCT
ejpam-4468	24	28	where	where	SCONJ
ejpam-4468	24	29	⟨x	⟨x	VERB
ejpam-4468	24	30	,	,	PUNCT
ejpam-4468	24	31	x∗⟩	x∗⟩	PROPN
ejpam-4468	24	32	is	be	AUX
ejpam-4468	24	33	the	the	DET
ejpam-4468	24	34	value	value	NOUN
ejpam-4468	24	35	of	of	ADP
ejpam-4468	24	36	x∗	x∗	PROPN
ejpam-4468	24	37	at	at	ADP
ejpam-4468	24	38	x	x	PROPN
ejpam-4468	24	39	,	,	PUNCT
ejpam-4468	24	40	x⊗	x⊗	PROPN
ejpam-4468	24	41	y	y	PROPN
ejpam-4468	24	42	is	be	AUX
ejpam-4468	24	43	called	call	VERB
ejpam-4468	24	44	an	an	DET
ejpam-4468	24	45	atom	atom	NOUN
ejpam-4468	24	46	.	.	PUNCT
ejpam-4468	25	1	it	it	PRON
ejpam-4468	25	2	is	be	AUX
ejpam-4468	25	3	easy	easy	ADJ
ejpam-4468	25	4	to	to	PART
ejpam-4468	25	5	see	see	VERB
ejpam-4468	25	6	that	that	DET
ejpam-4468	25	7	x⊗	x⊗	PROPN
ejpam-4468	25	8	y	y	PROPN
ejpam-4468	25	9	is	be	AUX
ejpam-4468	25	10	a	a	DET
ejpam-4468	25	11	bounded	bounded	ADJ
ejpam-4468	25	12	linear	linear	ADJ
ejpam-4468	25	13	operator	operator	NOUN
ejpam-4468	25	14	with	with	ADP
ejpam-4468	25	15	norm	norm	NOUN
ejpam-4468	25	16	∥x⊗	∥x⊗	NOUN
ejpam-4468	25	17	y∥	y∥	NOUN
ejpam-4468	25	18	=	=	VERB
ejpam-4468	25	19	∥x∥	∥x∥	NOUN
ejpam-4468	25	20	∥y∥.	∥y∥.	NOUN
ejpam-4468	25	21	the	the	DET
ejpam-4468	25	22	tensor	tensor	NOUN
ejpam-4468	25	23	product	product	NOUN
ejpam-4468	25	24	x	x	PROPN
ejpam-4468	25	25	⊗	⊗	NOUN
ejpam-4468	25	26	y	y	PROPN
ejpam-4468	25	27	:	:	PUNCT
ejpam-4468	25	28	=	=	PUNCT
ejpam-4468	25	29	span{x⊗	span{x⊗	ADP
ejpam-4468	25	30	y	y	NOUN
ejpam-4468	25	31	:	:	PUNCT
ejpam-4468	25	32	x	x	SYM
ejpam-4468	25	33	∈	∈	NOUN
ejpam-4468	25	34	x	x	NOUN
ejpam-4468	25	35	,	,	PUNCT
ejpam-4468	25	36	y	y	PROPN
ejpam-4468	25	37	∈	∈	PROPN
ejpam-4468	25	38	y	y	PROPN
ejpam-4468	25	39	}	}	PUNCT
ejpam-4468	25	40	,	,	PUNCT
ejpam-4468	25	41	where	where	SCONJ
ejpam-4468	25	42	x	x	PUNCT
ejpam-4468	25	43	⊗	⊗	PROPN
ejpam-4468	25	44	y	y	PROPN
ejpam-4468	25	45	⊆	⊆	NUM
ejpam-4468	25	46	l(x∗	l(x∗	NOUN
ejpam-4468	25	47	,	,	PUNCT
ejpam-4468	25	48	y	y	PROPN
ejpam-4468	25	49	)	)	PUNCT
ejpam-4468	25	50	;	;	PUNCT
ejpam-4468	25	51	l(x∗	l(x∗	PROPN
ejpam-4468	25	52	,	,	PUNCT
ejpam-4468	25	53	y	y	PROPN
ejpam-4468	25	54	)	)	PUNCT
ejpam-4468	25	55	is	be	AUX
ejpam-4468	25	56	the	the	DET
ejpam-4468	25	57	space	space	NOUN
ejpam-4468	25	58	of	of	ADP
ejpam-4468	25	59	bounded	bounded	ADJ
ejpam-4468	25	60	linear	linear	PROPN
ejpam-4468	25	61	operators	operator	NOUN
ejpam-4468	25	62	from	from	ADP
ejpam-4468	25	63	x∗	x∗	PROPN
ejpam-4468	25	64	into	into	ADP
ejpam-4468	25	65	y	y	PROPN
ejpam-4468	25	66	,	,	PUNCT
ejpam-4468	25	67	x	x	PROPN
ejpam-4468	25	68	⊗	⊗	PROPN
ejpam-4468	25	69	y	y	PROPN
ejpam-4468	25	70	is	be	AUX
ejpam-4468	25	71	a	a	DET
ejpam-4468	25	72	linear	linear	ADJ
ejpam-4468	25	73	subspace	subspace	NOUN
ejpam-4468	25	74	of	of	ADP
ejpam-4468	25	75	finite	finite	PROPN
ejpam-4468	25	76	rank	rank	PROPN
ejpam-4468	25	77	operators	operator	NOUN
ejpam-4468	25	78	in	in	ADP
ejpam-4468	25	79	l(x∗	l(x∗	PROPN
ejpam-4468	25	80	,	,	PUNCT
ejpam-4468	25	81	y	y	PROPN
ejpam-4468	25	82	)	)	PUNCT
ejpam-4468	26	1	[	[	X
ejpam-4468	26	2	8	8	NUM
ejpam-4468	26	3	]	]	PUNCT
ejpam-4468	26	4	.	.	PUNCT
ejpam-4468	27	1	lemma	lemma	PROPN
ejpam-4468	27	2	1	1	NUM
ejpam-4468	27	3	.	.	PUNCT
ejpam-4468	28	1	[	[	X
ejpam-4468	28	2	9	9	NUM
ejpam-4468	28	3	]	]	PUNCT
ejpam-4468	28	4	for	for	ADP
ejpam-4468	28	5	any	any	DET
ejpam-4468	28	6	x	x	NOUN
ejpam-4468	28	7	,	,	PUNCT
ejpam-4468	28	8	z	z	PROPN
ejpam-4468	28	9	∈	∈	PROPN
ejpam-4468	28	10	x	x	SYM
ejpam-4468	28	11	,	,	PUNCT
ejpam-4468	28	12	y	y	PROPN
ejpam-4468	28	13	,	,	PUNCT
ejpam-4468	28	14	t	t	PROPN
ejpam-4468	28	15	∈	∈	PROPN
ejpam-4468	28	16	y	y	PROPN
ejpam-4468	28	17	and	and	CCONJ
ejpam-4468	28	18	scaler	scaler	PROPN
ejpam-4468	28	19	β	β	PROPN
ejpam-4468	28	20	,	,	PUNCT
ejpam-4468	28	21	the	the	DET
ejpam-4468	28	22	following	follow	VERB
ejpam-4468	28	23	are	be	AUX
ejpam-4468	28	24	valid	valid	ADJ
ejpam-4468	28	25	:	:	PUNCT
ejpam-4468	28	26	1β(x⊗	1β(x⊗	NUM
ejpam-4468	28	27	y	y	NOUN
ejpam-4468	28	28	)	)	PUNCT
ejpam-4468	28	29	=	=	PUNCT
ejpam-4468	29	1	βx⊗	βx⊗	PUNCT
ejpam-4468	29	2	y	y	X
ejpam-4468	29	3	=	=	PUNCT
ejpam-4468	29	4	x⊗	x⊗	PROPN
ejpam-4468	29	5	βy	βy	PROPN
ejpam-4468	29	6	.	.	PUNCT
ejpam-4468	30	1	2(x+	2(x+	NUM
ejpam-4468	30	2	z)⊗	z)⊗	NOUN
ejpam-4468	30	3	y	y	PROPN
ejpam-4468	30	4	=	=	PRON
ejpam-4468	30	5	x⊗	x⊗	PROPN
ejpam-4468	30	6	y	y	PROPN
ejpam-4468	31	1	+	+	CCONJ
ejpam-4468	31	2	z	z	PROPN
ejpam-4468	32	1	⊗	⊗	PROPN
ejpam-4468	32	2	y.	y.	PROPN
ejpam-4468	32	3	3x⊗	3x⊗	NUM
ejpam-4468	33	1	(	(	PUNCT
ejpam-4468	33	2	y	y	PROPN
ejpam-4468	33	3	+	+	PROPN
ejpam-4468	33	4	t	t	PROPN
ejpam-4468	33	5	)	)	PUNCT
ejpam-4468	34	1	=	=	VERB
ejpam-4468	34	2	x⊗	x⊗	VERB
ejpam-4468	34	3	y	y	PROPN
ejpam-4468	34	4	+	+	PROPN
ejpam-4468	34	5	x⊗	x⊗	PROPN
ejpam-4468	34	6	t.	t.	PROPN
ejpam-4468	34	7	4x⊗	4x⊗	NUM
ejpam-4468	34	8	0	0	NUM
ejpam-4468	35	1	=	=	SYM
ejpam-4468	35	2	0⊗	0⊗	PUNCT
ejpam-4468	36	1	y	y	NOUN
ejpam-4468	36	2	=	=	SYM
ejpam-4468	36	3	0⊗	0⊗	NUM
ejpam-4468	36	4	0	0	NUM
ejpam-4468	36	5	.	.	PUNCT
ejpam-4468	37	1	5||x⊗	5||x⊗	NUM
ejpam-4468	37	2	y||	y||	NOUN
ejpam-4468	37	3	=	=	SYM
ejpam-4468	37	4	||x||	||x||	ADJ
ejpam-4468	37	5	||y||	||y||	X
ejpam-4468	37	6	.	.	PUNCT
ejpam-4468	38	1	6any	6any	NUM
ejpam-4468	38	2	t	t	NOUN
ejpam-4468	38	3	∈	∈	NOUN
ejpam-4468	39	1	x	x	X
ejpam-4468	39	2	⊗	⊗	PROPN
ejpam-4468	39	3	y	y	PROPN
ejpam-4468	39	4	can	can	AUX
ejpam-4468	39	5	be	be	AUX
ejpam-4468	39	6	written	write	VERB
ejpam-4468	39	7	as	as	ADP
ejpam-4468	39	8	∑n	∑n	PROPN
ejpam-4468	39	9	i=1	i=1	PROPN
ejpam-4468	39	10	λi(xi	λi(xi	X
ejpam-4468	39	11	⊗	⊗	NUM
ejpam-4468	39	12	yi	yi	NOUN
ejpam-4468	39	13	)	)	PUNCT
ejpam-4468	39	14	with	with	ADP
ejpam-4468	39	15	||xi||	||xi||	NOUN
ejpam-4468	39	16	=	=	SYM
ejpam-4468	39	17	||yi||	||yi||	ADJ
ejpam-4468	39	18	=	=	SYM
ejpam-4468	39	19	1	1	NUM
ejpam-4468	39	20	.	.	PUNCT
ejpam-4468	39	21	definition	definition	NOUN
ejpam-4468	39	22	1	1	NUM
ejpam-4468	39	23	.	.	PUNCT
ejpam-4468	40	1	[	[	X
ejpam-4468	40	2	9	9	NUM
ejpam-4468	40	3	]	]	PUNCT
ejpam-4468	40	4	let	let	VERB
ejpam-4468	40	5	t	t	NOUN
ejpam-4468	40	6	=	=	PUNCT
ejpam-4468	41	1	∑n	∑n	PROPN
ejpam-4468	41	2	i=1	i=1	X
ejpam-4468	41	3	xi	xi	PROPN
ejpam-4468	41	4	⊗	⊗	PROPN
ejpam-4468	41	5	yi	yi	PROPN
ejpam-4468	42	1	∈	∈	PROPN
ejpam-4468	42	2	x	x	PUNCT
ejpam-4468	42	3	⊗	⊗	PROPN
ejpam-4468	42	4	y	y	PROPN
ejpam-4468	42	5	,	,	PUNCT
ejpam-4468	42	6	define	define	VERB
ejpam-4468	42	7	the	the	DET
ejpam-4468	42	8	injective	injective	ADJ
ejpam-4468	42	9	norm	norm	NOUN
ejpam-4468	42	10	on	on	ADP
ejpam-4468	42	11	x	x	PROPN
ejpam-4468	42	12	⊗	⊗	PROPN
ejpam-4468	42	13	y	y	PROPN
ejpam-4468	42	14	as	as	ADP
ejpam-4468	42	15	||t	||t	PROPN
ejpam-4468	42	16	||∨	||∨	PROPN
ejpam-4468	42	17	=	=	SYM
ejpam-4468	42	18	sup	sup	NOUN
ejpam-4468	42	19	{	{	PUNCT
ejpam-4468	42	20	n∑	n∑	NOUN
ejpam-4468	42	21	i=1	i=1	PROPN
ejpam-4468	42	22	|⟨x	|⟨x	PROPN
ejpam-4468	42	23	,	,	PUNCT
ejpam-4468	42	24	x∗⟩⟨y	x∗⟩⟨y	PROPN
ejpam-4468	42	25	,	,	PUNCT
ejpam-4468	42	26	y∗⟩|	y∗⟩|	PRON
ejpam-4468	42	27	,	,	PUNCT
ejpam-4468	42	28	x∗	x∗	PROPN
ejpam-4468	43	1	⊗	⊗	PROPN
ejpam-4468	43	2	y∗	y∗	PROPN
ejpam-4468	44	1	∈	∈	PROPN
ejpam-4468	44	2	x∗	x∗	PROPN
ejpam-4468	44	3	⊗	⊗	PROPN
ejpam-4468	44	4	y	y	PROPN
ejpam-4468	44	5	∗	∗	NOUN
ejpam-4468	44	6	,	,	PUNCT
ejpam-4468	44	7	||x∗||	||x∗||	PROPN
ejpam-4468	44	8	=	=	SYM
ejpam-4468	44	9	||y∗||	||y∗||	NOUN
ejpam-4468	44	10	=	=	NOUN
ejpam-4468	44	11	1	1	X
ejpam-4468	44	12	}	}	PUNCT
ejpam-4468	44	13	.	.	PUNCT
ejpam-4468	45	1	a.	a.	PROPN
ejpam-4468	45	2	al	al	PROPN
ejpam-4468	45	3	-	-	PUNCT
ejpam-4468	45	4	jarrah	jarrah	PROPN
ejpam-4468	45	5	,	,	PUNCT
ejpam-4468	45	6	sh	sh	PROPN
ejpam-4468	45	7	.	.	PROPN
ejpam-4468	45	8	alsharif	alsharif	PROPN
ejpam-4468	45	9	,	,	PUNCT
ejpam-4468	45	10	h.	h.	PROPN
ejpam-4468	45	11	almefleh	almefleh	PROPN
ejpam-4468	45	12	/	/	SYM
ejpam-4468	45	13	eur	eur	PROPN
ejpam-4468	45	14	.	.	PUNCT
ejpam-4468	46	1	j.	j.	PROPN
ejpam-4468	46	2	pure	pure	PROPN
ejpam-4468	46	3	appl	appl	PROPN
ejpam-4468	46	4	.	.	PROPN
ejpam-4468	46	5	math	math	PROPN
ejpam-4468	46	6	,	,	PUNCT
ejpam-4468	46	7	15	15	NUM
ejpam-4468	46	8	(	(	PUNCT
ejpam-4468	46	9	4	4	NUM
ejpam-4468	46	10	)	)	PUNCT
ejpam-4468	46	11	(	(	PUNCT
ejpam-4468	46	12	2022	2022	NUM
ejpam-4468	46	13	)	)	PUNCT
ejpam-4468	46	14	,	,	PUNCT
ejpam-4468	46	15	1444	1444	NUM
ejpam-4468	46	16	-	-	SYM
ejpam-4468	46	17	1454	1454	NUM
ejpam-4468	46	18	1446	1446	NUM
ejpam-4468	46	19	the	the	DET
ejpam-4468	46	20	space	space	NOUN
ejpam-4468	46	21	(	(	PUNCT
ejpam-4468	46	22	x	x	PROPN
ejpam-4468	46	23	⊗	⊗	PROPN
ejpam-4468	46	24	y	y	PROPN
ejpam-4468	46	25	,	,	PUNCT
ejpam-4468	46	26	||.||∨	||.||∨	VERB
ejpam-4468	46	27	)	)	PUNCT
ejpam-4468	46	28	need	need	AUX
ejpam-4468	46	29	not	not	PART
ejpam-4468	46	30	be	be	AUX
ejpam-4468	46	31	complete	complete	ADJ
ejpam-4468	46	32	.	.	PUNCT
ejpam-4468	47	1	we	we	PRON
ejpam-4468	47	2	let	let	VERB
ejpam-4468	47	3	x	x	PUNCT
ejpam-4468	47	4	∨	∨	NUM
ejpam-4468	47	5	⊗	⊗	PROPN
ejpam-4468	47	6	y	y	PROPN
ejpam-4468	47	7	denote	denote	VERB
ejpam-4468	47	8	the	the	DET
ejpam-4468	47	9	completion	completion	NOUN
ejpam-4468	47	10	of	of	ADP
ejpam-4468	47	11	x	x	X
ejpam-4468	47	12	⊗	⊗	PROPN
ejpam-4468	47	13	y	y	PROPN
ejpam-4468	47	14	in	in	ADP
ejpam-4468	47	15	l	l	PROPN
ejpam-4468	47	16	(	(	PUNCT
ejpam-4468	47	17	x∗	x∗	PROPN
ejpam-4468	47	18	,	,	PUNCT
ejpam-4468	47	19	y	y	PROPN
ejpam-4468	47	20	)	)	PUNCT
ejpam-4468	47	21	with	with	ADP
ejpam-4468	47	22	respect	respect	NOUN
ejpam-4468	47	23	to	to	ADP
ejpam-4468	47	24	the	the	DET
ejpam-4468	47	25	injective	injective	ADJ
ejpam-4468	47	26	norm	norm	NOUN
ejpam-4468	47	27	.	.	PUNCT
ejpam-4468	48	1	theorem	theorem	NOUN
ejpam-4468	48	2	1	1	NUM
ejpam-4468	48	3	.	.	PUNCT
ejpam-4468	49	1	[	[	X
ejpam-4468	49	2	9]for	9]for	NUM
ejpam-4468	49	3	any	any	DET
ejpam-4468	49	4	compact	compact	ADJ
ejpam-4468	49	5	hausdorff	hausdorff	NOUN
ejpam-4468	49	6	space	space	NOUN
ejpam-4468	49	7	i	i	PRON
ejpam-4468	49	8	and	and	CCONJ
ejpam-4468	49	9	a	a	DET
ejpam-4468	49	10	banach	banach	NOUN
ejpam-4468	49	11	space	space	NOUN
ejpam-4468	49	12	x	x	NOUN
ejpam-4468	49	13	,	,	PUNCT
ejpam-4468	49	14	we	we	PRON
ejpam-4468	49	15	have	have	VERB
ejpam-4468	49	16	c(i	c(i	NOUN
ejpam-4468	49	17	,	,	PUNCT
ejpam-4468	49	18	x	x	X
ejpam-4468	49	19	)	)	PUNCT
ejpam-4468	49	20	is	be	AUX
ejpam-4468	49	21	isometrically	isometrically	PROPN
ejpam-4468	49	22	isomorphic	isomorphic	ADJ
ejpam-4468	49	23	to	to	ADP
ejpam-4468	49	24	c(i	c(i	NOUN
ejpam-4468	49	25	)	)	PUNCT
ejpam-4468	49	26	∨	∨	NUM
ejpam-4468	49	27	⊗x	⊗x	NOUN
ejpam-4468	49	28	.	.	PUNCT
ejpam-4468	50	1	for	for	ADP
ejpam-4468	50	2	more	more	ADJ
ejpam-4468	50	3	on	on	ADP
ejpam-4468	50	4	tensor	tensor	NOUN
ejpam-4468	50	5	product	product	NOUN
ejpam-4468	50	6	we	we	PRON
ejpam-4468	50	7	refer	refer	VERB
ejpam-4468	50	8	the	the	DET
ejpam-4468	50	9	reader	reader	NOUN
ejpam-4468	50	10	to	to	ADP
ejpam-4468	50	11	[	[	X
ejpam-4468	50	12	9	9	NUM
ejpam-4468	50	13	]	]	SYM
ejpam-4468	50	14	.	.	PUNCT
ejpam-4468	51	1	3	3	X
ejpam-4468	51	2	.	.	X
ejpam-4468	51	3	atomic	atomic	ADJ
ejpam-4468	51	4	solution	solution	NOUN
ejpam-4468	51	5	of	of	ADP
ejpam-4468	51	6	linear	linear	ADJ
ejpam-4468	51	7	partial	partial	ADJ
ejpam-4468	51	8	differential	differential	NOUN
ejpam-4468	51	9	equations	equation	NOUN
ejpam-4468	51	10	in	in	ADP
ejpam-4468	51	11	this	this	DET
ejpam-4468	51	12	section	section	NOUN
ejpam-4468	51	13	,	,	PUNCT
ejpam-4468	51	14	we	we	PRON
ejpam-4468	51	15	solve	solve	VERB
ejpam-4468	51	16	two	two	NUM
ejpam-4468	51	17	kinds	kind	NOUN
ejpam-4468	51	18	of	of	ADP
ejpam-4468	51	19	partial	partial	ADJ
ejpam-4468	51	20	differential	differential	NOUN
ejpam-4468	51	21	equations	equation	NOUN
ejpam-4468	51	22	by	by	ADP
ejpam-4468	51	23	using	use	VERB
ejpam-4468	51	24	tensor	tensor	NOUN
ejpam-4468	51	25	product	product	NOUN
ejpam-4468	51	26	technique	technique	NOUN
ejpam-4468	51	27	.	.	PUNCT
ejpam-4468	52	1	we	we	PRON
ejpam-4468	52	2	start	start	VERB
ejpam-4468	52	3	by	by	ADP
ejpam-4468	52	4	the	the	DET
ejpam-4468	52	5	following	follow	VERB
ejpam-4468	52	6	lemma	lemma	PROPN
ejpam-4468	52	7	:	:	PUNCT
ejpam-4468	52	8	lemma	lemma	PROPN
ejpam-4468	52	9	2	2	X
ejpam-4468	52	10	.	.	PUNCT
ejpam-4468	53	1	let	let	VERB
ejpam-4468	53	2	x1	x1	PROPN
ejpam-4468	53	3	⊗	⊗	PROPN
ejpam-4468	53	4	y1	y1	PROPN
ejpam-4468	54	1	and	and	CCONJ
ejpam-4468	55	1	x2	x2	PROPN
ejpam-4468	55	2	⊗	⊗	PROPN
ejpam-4468	55	3	y2	y2	INTJ
ejpam-4468	55	4	be	be	VERB
ejpam-4468	55	5	two	two	NUM
ejpam-4468	55	6	non	non	ADJ
ejpam-4468	55	7	zero	zero	NUM
ejpam-4468	55	8	atoms	atom	NOUN
ejpam-4468	55	9	in	in	ADP
ejpam-4468	55	10	x	x	PROPN
ejpam-4468	55	11	∨	∨	NUM
ejpam-4468	55	12	⊗	⊗	PROPN
ejpam-4468	55	13	y	y	PROPN
ejpam-4468	55	14	.	.	PUNCT
ejpam-4468	56	1	then	then	ADV
ejpam-4468	56	2	the	the	DET
ejpam-4468	56	3	following	follow	VERB
ejpam-4468	56	4	are	be	AUX
ejpam-4468	56	5	equivalent	equivalent	ADJ
ejpam-4468	56	6	:	:	PUNCT
ejpam-4468	56	7	(	(	PUNCT
ejpam-4468	56	8	i	i	NOUN
ejpam-4468	56	9	)	)	PUNCT
ejpam-4468	57	1	x1	x1	PROPN
ejpam-4468	57	2	⊗	⊗	PROPN
ejpam-4468	57	3	y1	y1	PROPN
ejpam-4468	58	1	+	+	CCONJ
ejpam-4468	59	1	x2	x2	PROPN
ejpam-4468	60	1	⊗	⊗	ADJ
ejpam-4468	60	2	y2	y2	PROPN
ejpam-4468	60	3	=	=	SYM
ejpam-4468	61	1	x3	x3	ADJ
ejpam-4468	61	2	⊗	⊗	PROPN
ejpam-4468	61	3	y3	y3	PROPN
ejpam-4468	61	4	a	a	DET
ejpam-4468	61	5	non	non	ADJ
ejpam-4468	61	6	zero	zero	NUM
ejpam-4468	61	7	atom	atom	NOUN
ejpam-4468	61	8	.	.	PUNCT
ejpam-4468	62	1	(	(	PUNCT
ejpam-4468	62	2	ii	ii	NOUN
ejpam-4468	62	3	)	)	PUNCT
ejpam-4468	62	4	x1	x1	PROPN
ejpam-4468	62	5	,	,	PUNCT
ejpam-4468	62	6	x2	x2	PROPN
ejpam-4468	62	7	or	or	CCONJ
ejpam-4468	62	8	y1	y1	NOUN
ejpam-4468	62	9	,	,	PUNCT
ejpam-4468	62	10	y2	y2	PROPN
ejpam-4468	62	11	are	be	AUX
ejpam-4468	62	12	linearly	linearly	ADV
ejpam-4468	62	13	dependent	dependent	ADJ
ejpam-4468	62	14	.	.	PUNCT
ejpam-4468	63	1	proof	proof	NOUN
ejpam-4468	63	2	.	.	PUNCT
ejpam-4468	64	1	(	(	PUNCT
ejpam-4468	64	2	i	i	NOUN
ejpam-4468	64	3	)	)	PUNCT
ejpam-4468	64	4	→	→	SYM
ejpam-4468	64	5	(	(	PUNCT
ejpam-4468	64	6	ii	ii	NOUN
ejpam-4468	64	7	)	)	PUNCT
ejpam-4468	64	8	if	if	SCONJ
ejpam-4468	64	9	x3	x3	ADJ
ejpam-4468	64	10	⊗	⊗	PROPN
ejpam-4468	64	11	y3	y3	NOUN
ejpam-4468	64	12	=	=	SYM
ejpam-4468	64	13	0	0	NUM
ejpam-4468	64	14	,	,	PUNCT
ejpam-4468	64	15	we	we	PRON
ejpam-4468	64	16	are	be	AUX
ejpam-4468	64	17	done	do	VERB
ejpam-4468	64	18	.	.	PUNCT
ejpam-4468	65	1	assume	assume	VERB
ejpam-4468	65	2	x3	x3	ADJ
ejpam-4468	65	3	⊗	⊗	PROPN
ejpam-4468	65	4	y3	y3	PROPN
ejpam-4468	65	5	̸=	̸=	PROPN
ejpam-4468	65	6	0	0	NUM
ejpam-4468	65	7	.	.	PUNCT
ejpam-4468	66	1	then	then	ADV
ejpam-4468	66	2	there	there	PRON
ejpam-4468	66	3	exists	exist	VERB
ejpam-4468	66	4	t0	t0	PROPN
ejpam-4468	66	5	∈	∈	PROPN
ejpam-4468	67	1	i	i	PRON
ejpam-4468	67	2	and	and	CCONJ
ejpam-4468	67	3	y∗	y∗	PROPN
ejpam-4468	67	4	∈	∈	PROPN
ejpam-4468	67	5	y	y	PROPN
ejpam-4468	67	6	∗	∗	NOUN
ejpam-4468	67	7	such	such	ADJ
ejpam-4468	67	8	that	that	DET
ejpam-4468	67	9	x3	x3	PROPN
ejpam-4468	67	10	(	(	PUNCT
ejpam-4468	67	11	t0	t0	NOUN
ejpam-4468	67	12	)	)	PUNCT
ejpam-4468	67	13	̸=	̸=	NOUN
ejpam-4468	67	14	0	0	NUM
ejpam-4468	67	15	and	and	CCONJ
ejpam-4468	67	16	y∗	y∗	PROPN
ejpam-4468	67	17	(	(	PUNCT
ejpam-4468	67	18	y3	y3	NOUN
ejpam-4468	67	19	)	)	PUNCT
ejpam-4468	67	20	̸=	̸=	PROPN
ejpam-4468	67	21	0	0	NUM
ejpam-4468	67	22	.	.	PUNCT
ejpam-4468	68	1	using	use	VERB
ejpam-4468	68	2	(	(	PUNCT
ejpam-4468	68	3	i	i	NOUN
ejpam-4468	68	4	)	)	PUNCT
ejpam-4468	68	5	we	we	PRON
ejpam-4468	68	6	have	have	VERB
ejpam-4468	68	7	x3	x3	NOUN
ejpam-4468	68	8	=	=	SYM
ejpam-4468	68	9	y∗	y∗	PROPN
ejpam-4468	68	10	(	(	PUNCT
ejpam-4468	68	11	y1	y1	NOUN
ejpam-4468	68	12	)	)	PUNCT
ejpam-4468	68	13	y∗	y∗	PROPN
ejpam-4468	68	14	(	(	PUNCT
ejpam-4468	68	15	y3	y3	PROPN
ejpam-4468	68	16	)	)	PUNCT
ejpam-4468	68	17	x1	x1	PROPN
ejpam-4468	69	1	+	+	CCONJ
ejpam-4468	69	2	y∗	y∗	PROPN
ejpam-4468	69	3	(	(	PUNCT
ejpam-4468	69	4	y2	y2	NOUN
ejpam-4468	69	5	)	)	PUNCT
ejpam-4468	69	6	y∗	y∗	PROPN
ejpam-4468	69	7	(	(	PUNCT
ejpam-4468	69	8	y3	y3	NOUN
ejpam-4468	69	9	)	)	PUNCT
ejpam-4468	69	10	x2	x2	NOUN
ejpam-4468	70	1	=	=	SYM
ejpam-4468	70	2	c1x1	c1x1	PROPN
ejpam-4468	70	3	+	+	CCONJ
ejpam-4468	70	4	c2x2	c2x2	NOUN
ejpam-4468	70	5	,	,	PUNCT
ejpam-4468	70	6	y3	y3	NOUN
ejpam-4468	70	7	=	=	SYM
ejpam-4468	70	8	x1	x1	PROPN
ejpam-4468	70	9	(	(	PUNCT
ejpam-4468	70	10	t0	t0	NOUN
ejpam-4468	70	11	)	)	PUNCT
ejpam-4468	70	12	x3	x3	PROPN
ejpam-4468	70	13	(	(	PUNCT
ejpam-4468	70	14	t0	t0	NOUN
ejpam-4468	70	15	)	)	PUNCT
ejpam-4468	71	1	y1	y1	NOUN
ejpam-4468	72	1	+	+	CCONJ
ejpam-4468	72	2	x2	x2	PROPN
ejpam-4468	72	3	(	(	PUNCT
ejpam-4468	72	4	t0	t0	NOUN
ejpam-4468	72	5	)	)	PUNCT
ejpam-4468	72	6	x3	x3	PROPN
ejpam-4468	72	7	(	(	PUNCT
ejpam-4468	72	8	t0	t0	NOUN
ejpam-4468	72	9	)	)	PUNCT
ejpam-4468	72	10	y2	y2	NOUN
ejpam-4468	72	11	=	=	PUNCT
ejpam-4468	73	1	b1y1	b1y1	PUNCT
ejpam-4468	73	2	+	+	CCONJ
ejpam-4468	73	3	b2y2	b2y2	X
ejpam-4468	73	4	.	.	PUNCT
ejpam-4468	74	1	consequently	consequently	ADV
ejpam-4468	74	2	x3	x3	ADJ
ejpam-4468	74	3	⊗	⊗	PROPN
ejpam-4468	74	4	y3	y3	NOUN
ejpam-4468	74	5	=	=	PUNCT
ejpam-4468	74	6	c1b1x1	c1b1x1	NOUN
ejpam-4468	74	7	⊗	⊗	PROPN
ejpam-4468	74	8	y1	y1	PROPN
ejpam-4468	74	9	+	+	CCONJ
ejpam-4468	74	10	c1b2x1	c1b2x1	PROPN
ejpam-4468	74	11	⊗	⊗	PROPN
ejpam-4468	74	12	y2	y2	PROPN
ejpam-4468	75	1	+	+	CCONJ
ejpam-4468	75	2	c2b1x2	c2b1x2	PROPN
ejpam-4468	75	3	⊗	⊗	PROPN
ejpam-4468	75	4	y1	y1	PROPN
ejpam-4468	76	1	+	+	CCONJ
ejpam-4468	76	2	b2c2x2	b2c2x2	CCONJ
ejpam-4468	77	1	⊗	⊗	ADJ
ejpam-4468	77	2	y2	y2	PROPN
ejpam-4468	77	3	=	=	SYM
ejpam-4468	78	1	x1	x1	PROPN
ejpam-4468	78	2	⊗	⊗	PROPN
ejpam-4468	78	3	y1	y1	PROPN
ejpam-4468	79	1	+	+	CCONJ
ejpam-4468	79	2	x2	x2	PROPN
ejpam-4468	79	3	⊗	⊗	PROPN
ejpam-4468	79	4	y2	y2	PROPN
ejpam-4468	79	5	.	.	PUNCT
ejpam-4468	80	1	hence	hence	ADV
ejpam-4468	80	2	x1	x1	PROPN
ejpam-4468	80	3	⊗	⊗	PROPN
ejpam-4468	80	4	y1	y1	PROPN
ejpam-4468	80	5	(	(	PUNCT
ejpam-4468	80	6	1−	1−	NUM
ejpam-4468	80	7	c1b1	c1b1	PUNCT
ejpam-4468	80	8	)	)	PUNCT
ejpam-4468	80	9	+	+	CCONJ
ejpam-4468	80	10	x2	x2	PROPN
ejpam-4468	80	11	⊗	⊗	ADJ
ejpam-4468	80	12	y2	y2	PROPN
ejpam-4468	80	13	(	(	PUNCT
ejpam-4468	80	14	1−	1−	NUM
ejpam-4468	80	15	c2b2	c2b2	NOUN
ejpam-4468	80	16	)	)	PUNCT
ejpam-4468	80	17	+	+	CCONJ
ejpam-4468	80	18	c1b2x1	c1b2x1	PROPN
ejpam-4468	80	19	⊗	⊗	PROPN
ejpam-4468	80	20	y2	y2	PROPN
ejpam-4468	80	21	+	+	CCONJ
ejpam-4468	80	22	c2b1x2	c2b1x2	PROPN
ejpam-4468	80	23	⊗	⊗	PROPN
ejpam-4468	80	24	y1	y1	PROPN
ejpam-4468	80	25	=	=	PUNCT
ejpam-4468	80	26	0	0	X
ejpam-4468	80	27	.	.	PUNCT
ejpam-4468	81	1	if	if	SCONJ
ejpam-4468	81	2	x1	x1	PROPN
ejpam-4468	81	3	,	,	PUNCT
ejpam-4468	81	4	x2	x2	PROPN
ejpam-4468	81	5	and	and	CCONJ
ejpam-4468	81	6	y1	y1	PROPN
ejpam-4468	81	7	,	,	PUNCT
ejpam-4468	81	8	y2	y2	PROPN
ejpam-4468	81	9	are	be	AUX
ejpam-4468	81	10	linearly	linearly	ADV
ejpam-4468	81	11	independent	independent	ADJ
ejpam-4468	81	12	,	,	PUNCT
ejpam-4468	81	13	it	it	PRON
ejpam-4468	81	14	follows	follow	VERB
ejpam-4468	81	15	that	that	SCONJ
ejpam-4468	81	16	1−	1−	NUM
ejpam-4468	82	1	b1c1	b1c1	NOUN
ejpam-4468	83	1	=	=	SYM
ejpam-4468	84	1	1−	1−	NUM
ejpam-4468	84	2	b2c2	b2c2	ADP
ejpam-4468	84	3	=	=	PUNCT
ejpam-4468	84	4	b2c1	b2c1	PROPN
ejpam-4468	84	5	=	=	PUNCT
ejpam-4468	84	6	b1c2	b1c2	PROPN
ejpam-4468	84	7	=	=	SYM
ejpam-4468	84	8	0	0	PROPN
ejpam-4468	84	9	,	,	PUNCT
ejpam-4468	84	10	which	which	PRON
ejpam-4468	84	11	turns	turn	VERB
ejpam-4468	84	12	out	out	ADP
ejpam-4468	84	13	to	to	ADP
ejpam-4468	84	14	a	a	DET
ejpam-4468	84	15	contradiction	contradiction	NOUN
ejpam-4468	84	16	1	1	NUM
ejpam-4468	84	17	=	=	SYM
ejpam-4468	84	18	b1c1	b1c1	NOUN
ejpam-4468	84	19	,	,	PUNCT
ejpam-4468	84	20	1−	1−	NUM
ejpam-4468	84	21	b2c2	b2c2	NOUN
ejpam-4468	84	22	,	,	PUNCT
ejpam-4468	84	23	b2c1	b2c1	ADP
ejpam-4468	84	24	=	=	SYM
ejpam-4468	84	25	0	0	PROPN
ejpam-4468	84	26	,	,	PUNCT
ejpam-4468	84	27	b1c2	b1c2	NOUN
ejpam-4468	84	28	=	=	NOUN
ejpam-4468	84	29	0	0	X
ejpam-4468	84	30	.	.	PUNCT
ejpam-4468	85	1	hence	hence	ADV
ejpam-4468	85	2	the	the	DET
ejpam-4468	85	3	result	result	NOUN
ejpam-4468	85	4	.	.	PUNCT
ejpam-4468	86	1	(	(	PUNCT
ejpam-4468	86	2	ii	ii	NOUN
ejpam-4468	86	3	)	)	PUNCT
ejpam-4468	86	4	→	→	SYM
ejpam-4468	86	5	(	(	PUNCT
ejpam-4468	86	6	i	i	NOUN
ejpam-4468	86	7	)	)	PUNCT
ejpam-4468	86	8	if	if	SCONJ
ejpam-4468	86	9	x1	x1	PROPN
ejpam-4468	86	10	,	,	PUNCT
ejpam-4468	86	11	x2	x2	PRON
ejpam-4468	86	12	are	be	AUX
ejpam-4468	86	13	linearly	linearly	ADV
ejpam-4468	86	14	dependent	dependent	ADJ
ejpam-4468	86	15	,	,	PUNCT
ejpam-4468	86	16	then	then	ADV
ejpam-4468	86	17	x1	x1	PROPN
ejpam-4468	86	18	=	=	PUNCT
ejpam-4468	86	19	λx2	λx2	NOUN
ejpam-4468	86	20	.	.	PUNCT
ejpam-4468	87	1	using	use	VERB
ejpam-4468	87	2	(	(	PUNCT
ejpam-4468	87	3	ii	ii	NOUN
ejpam-4468	87	4	)	)	PUNCT
ejpam-4468	87	5	x3	x3	ADJ
ejpam-4468	87	6	⊗	⊗	PROPN
ejpam-4468	87	7	y3	y3	NOUN
ejpam-4468	87	8	=	=	PUNCT
ejpam-4468	87	9	λx2	λx2	NOUN
ejpam-4468	87	10	⊗	⊗	PROPN
ejpam-4468	87	11	y1	y1	PROPN
ejpam-4468	88	1	+	+	CCONJ
ejpam-4468	88	2	x2	x2	PROPN
ejpam-4468	89	1	⊗	⊗	NUM
ejpam-4468	89	2	y2	y2	PROPN
ejpam-4468	90	1	=	=	SYM
ejpam-4468	91	1	x2	x2	PROPN
ejpam-4468	91	2	⊗	⊗	PROPN
ejpam-4468	91	3	(	(	PUNCT
ejpam-4468	91	4	λy1	λy1	VERB
ejpam-4468	91	5	+	+	CCONJ
ejpam-4468	91	6	y2	y2	NOUN
ejpam-4468	91	7	)	)	PUNCT
ejpam-4468	91	8	which	which	PRON
ejpam-4468	91	9	completes	complete	VERB
ejpam-4468	91	10	the	the	DET
ejpam-4468	91	11	proof	proof	NOUN
ejpam-4468	91	12	.	.	PUNCT
ejpam-4468	92	1	a.	a.	PROPN
ejpam-4468	92	2	al	al	PROPN
ejpam-4468	92	3	-	-	PUNCT
ejpam-4468	92	4	jarrah	jarrah	PROPN
ejpam-4468	92	5	,	,	PUNCT
ejpam-4468	92	6	sh	sh	PROPN
ejpam-4468	92	7	.	.	PROPN
ejpam-4468	92	8	alsharif	alsharif	PROPN
ejpam-4468	92	9	,	,	PUNCT
ejpam-4468	92	10	h.	h.	PROPN
ejpam-4468	92	11	almefleh	almefleh	PROPN
ejpam-4468	92	12	/	/	SYM
ejpam-4468	92	13	eur	eur	PROPN
ejpam-4468	92	14	.	.	PUNCT
ejpam-4468	93	1	j.	j.	PROPN
ejpam-4468	93	2	pure	pure	PROPN
ejpam-4468	93	3	appl	appl	PROPN
ejpam-4468	93	4	.	.	PROPN
ejpam-4468	93	5	math	math	PROPN
ejpam-4468	93	6	,	,	PUNCT
ejpam-4468	93	7	15	15	NUM
ejpam-4468	93	8	(	(	PUNCT
ejpam-4468	93	9	4	4	NUM
ejpam-4468	93	10	)	)	PUNCT
ejpam-4468	93	11	(	(	PUNCT
ejpam-4468	93	12	2022	2022	NUM
ejpam-4468	93	13	)	)	PUNCT
ejpam-4468	93	14	,	,	PUNCT
ejpam-4468	93	15	1444	1444	NUM
ejpam-4468	93	16	-	-	SYM
ejpam-4468	93	17	1454	1454	NUM
ejpam-4468	93	18	1447	1447	NUM
ejpam-4468	93	19	theorem	theorem	NOUN
ejpam-4468	93	20	2	2	NUM
ejpam-4468	93	21	.	.	PUNCT
ejpam-4468	94	1	let	let	VERB
ejpam-4468	94	2	u(x	u(x	NOUN
ejpam-4468	94	3	,	,	PUNCT
ejpam-4468	94	4	t	t	PROPN
ejpam-4468	94	5	)	)	PUNCT
ejpam-4468	94	6	∈	∈	PROPN
ejpam-4468	94	7	c(i	c(i	VERB
ejpam-4468	94	8	×	×	PROPN
ejpam-4468	94	9	j	j	PROPN
ejpam-4468	94	10	)	)	PUNCT
ejpam-4468	94	11	,	,	PUNCT
ejpam-4468	94	12	where	where	SCONJ
ejpam-4468	94	13	i	i	PRON
ejpam-4468	94	14	,	,	PUNCT
ejpam-4468	94	15	j	j	PROPN
ejpam-4468	95	1	=	=	PUNCT
ejpam-4468	96	1	[	[	X
ejpam-4468	96	2	0	0	NUM
ejpam-4468	96	3	,	,	PUNCT
ejpam-4468	96	4	1	1	NUM
ejpam-4468	96	5	]	]	PUNCT
ejpam-4468	96	6	or	or	CCONJ
ejpam-4468	96	7	[	[	X
ejpam-4468	96	8	0,∞	0,∞	NUM
ejpam-4468	96	9	)	)	PUNCT
ejpam-4468	96	10	.	.	PUNCT
ejpam-4468	97	1	if	if	SCONJ
ejpam-4468	97	2	u	u	NOUN
ejpam-4468	97	3	has	have	VERB
ejpam-4468	97	4	continuous	continuous	ADJ
ejpam-4468	97	5	second	second	ADJ
ejpam-4468	97	6	partial	partial	ADJ
ejpam-4468	97	7	derivatives	derivative	NOUN
ejpam-4468	97	8	,	,	PUNCT
ejpam-4468	97	9	then	then	ADV
ejpam-4468	97	10	the	the	DET
ejpam-4468	97	11	linear	linear	ADJ
ejpam-4468	97	12	differential	differential	NOUN
ejpam-4468	97	13	equation	equation	NOUN
ejpam-4468	97	14	ut	ut	PROPN
ejpam-4468	98	1	+	+	CCONJ
ejpam-4468	98	2	ux	ux	PROPN
ejpam-4468	98	3	=	=	SYM
ejpam-4468	98	4	uxx	uxx	X
ejpam-4468	98	5	(	(	PUNCT
ejpam-4468	98	6	1	1	X
ejpam-4468	98	7	)	)	PUNCT
ejpam-4468	98	8	has	have	VERB
ejpam-4468	98	9	an	an	DET
ejpam-4468	98	10	atomic	atomic	ADJ
ejpam-4468	98	11	solution	solution	NOUN
ejpam-4468	98	12	.	.	PUNCT
ejpam-4468	99	1	proof	proof	NOUN
ejpam-4468	99	2	.	.	PUNCT
ejpam-4468	100	1	let	let	VERB
ejpam-4468	100	2	u(x	u(x	NOUN
ejpam-4468	100	3	,	,	PUNCT
ejpam-4468	100	4	t	t	PROPN
ejpam-4468	100	5	)	)	PUNCT
ejpam-4468	100	6	=	=	PUNCT
ejpam-4468	101	1	φ	φ	PROPN
ejpam-4468	101	2	⊗	⊗	PROPN
ejpam-4468	101	3	ψ	ψ	PROPN
ejpam-4468	101	4	,	,	PUNCT
ejpam-4468	101	5	where	where	SCONJ
ejpam-4468	101	6	φ	φ	PROPN
ejpam-4468	101	7	is	be	AUX
ejpam-4468	101	8	a	a	DET
ejpam-4468	101	9	function	function	NOUN
ejpam-4468	101	10	of	of	ADP
ejpam-4468	101	11	x	x	PUNCT
ejpam-4468	101	12	and	and	CCONJ
ejpam-4468	101	13	ψ	ψ	NOUN
ejpam-4468	101	14	is	be	AUX
ejpam-4468	101	15	a	a	DET
ejpam-4468	101	16	function	function	NOUN
ejpam-4468	101	17	of	of	ADP
ejpam-4468	101	18	t	t	PROPN
ejpam-4468	101	19	with	with	ADP
ejpam-4468	101	20	φ(0	φ(0	ADJ
ejpam-4468	101	21	)	)	PUNCT
ejpam-4468	101	22	=	=	SYM
ejpam-4468	101	23	1	1	NUM
ejpam-4468	101	24	,	,	PUNCT
ejpam-4468	101	25	φ′(0	φ′(0	X
ejpam-4468	101	26	)	)	PUNCT
ejpam-4468	101	27	=	=	SYM
ejpam-4468	101	28	1	1	NUM
ejpam-4468	101	29	and	and	CCONJ
ejpam-4468	101	30	ψ(0	ψ(0	PROPN
ejpam-4468	101	31	)	)	PUNCT
ejpam-4468	101	32	=	=	SYM
ejpam-4468	102	1	1	1	X
ejpam-4468	102	2	.	.	PUNCT
ejpam-4468	102	3	then	then	ADV
ejpam-4468	102	4	ux	ux	ADV
ejpam-4468	102	5	=	=	SYM
ejpam-4468	102	6	φ′	φ′	NUM
ejpam-4468	102	7	⊗	⊗	NUM
ejpam-4468	102	8	ψ	ψ	PROPN
ejpam-4468	102	9	,	,	PUNCT
ejpam-4468	102	10	ut	ut	PROPN
ejpam-4468	102	11	=	=	PROPN
ejpam-4468	102	12	φ	φ	PROPN
ejpam-4468	102	13	⊗	⊗	PROPN
ejpam-4468	102	14	ψ′	ψ′	PROPN
ejpam-4468	102	15	and	and	CCONJ
ejpam-4468	102	16	uxx	uxx	X
ejpam-4468	102	17	=	=	SYM
ejpam-4468	102	18	φ′′	φ′′	PROPN
ejpam-4468	102	19	⊗	⊗	PROPN
ejpam-4468	102	20	ψ	ψ	PROPN
ejpam-4468	102	21	.	.	PUNCT
ejpam-4468	103	1	this	this	PRON
ejpam-4468	103	2	implies	imply	VERB
ejpam-4468	103	3	that	that	SCONJ
ejpam-4468	103	4	φ⊗ψ′	φ⊗ψ′	PROPN
ejpam-4468	103	5	+	+	NOUN
ejpam-4468	103	6	φ′	φ′	NUM
ejpam-4468	103	7	⊗ψ	⊗ψ	NOUN
ejpam-4468	103	8	=	=	SYM
ejpam-4468	103	9	φ′′	φ′′	PROPN
ejpam-4468	103	10	⊗ψ	⊗ψ	NOUN
ejpam-4468	103	11	.	.	PUNCT
ejpam-4468	104	1	(	(	PUNCT
ejpam-4468	104	2	2	2	NUM
ejpam-4468	104	3	)	)	PUNCT
ejpam-4468	104	4	by	by	ADP
ejpam-4468	104	5	using	use	VERB
ejpam-4468	104	6	lemma	lemma	PROPN
ejpam-4468	104	7	(	(	PUNCT
ejpam-4468	104	8	2	2	NUM
ejpam-4468	104	9	)	)	PUNCT
ejpam-4468	104	10	either	either	CCONJ
ejpam-4468	104	11	φ′	φ′	NUM
ejpam-4468	104	12	=	=	SYM
ejpam-4468	104	13	λφ	λφ	ADP
ejpam-4468	104	14	or	or	CCONJ
ejpam-4468	104	15	ψ́	ψ́	NOUN
ejpam-4468	104	16	=	=	SYM
ejpam-4468	104	17	µψ	µψ	PROPN
ejpam-4468	104	18	.	.	PUNCT
ejpam-4468	105	1	without	without	ADP
ejpam-4468	105	2	loss	loss	NOUN
ejpam-4468	105	3	of	of	ADP
ejpam-4468	105	4	generality	generality	NOUN
ejpam-4468	105	5	we	we	PRON
ejpam-4468	105	6	can	can	AUX
ejpam-4468	105	7	assume	assume	VERB
ejpam-4468	105	8	λ	λ	X
ejpam-4468	105	9	=	=	SYM
ejpam-4468	105	10	µ	µ	X
ejpam-4468	105	11	=	=	SYM
ejpam-4468	105	12	1	1	NUM
ejpam-4468	105	13	.	.	PUNCT
ejpam-4468	105	14	case	case	NOUN
ejpam-4468	105	15	(	(	PUNCT
ejpam-4468	105	16	1	1	X
ejpam-4468	105	17	)	)	PUNCT
ejpam-4468	105	18	if	if	SCONJ
ejpam-4468	105	19	φ′	φ′	NUM
ejpam-4468	105	20	=	=	SYM
ejpam-4468	105	21	φ	φ	PROPN
ejpam-4468	105	22	=	=	SYM
ejpam-4468	105	23	φ′′	φ′′	PROPN
ejpam-4468	105	24	,	,	PUNCT
ejpam-4468	105	25	then	then	ADV
ejpam-4468	105	26	φ′	φ′	NUM
ejpam-4468	105	27	φ	φ	NOUN
ejpam-4468	105	28	=	=	SYM
ejpam-4468	105	29	1	1	X
ejpam-4468	105	30	.	.	X
ejpam-4468	105	31	integrating	integrate	VERB
ejpam-4468	105	32	both	both	DET
ejpam-4468	105	33	sides	side	NOUN
ejpam-4468	105	34	,	,	PUNCT
ejpam-4468	105	35	we	we	PRON
ejpam-4468	105	36	get	get	VERB
ejpam-4468	105	37	∫	∫	PROPN
ejpam-4468	105	38	dφ	dφ	ADP
ejpam-4468	105	39	φ	φ	PROPN
ejpam-4468	105	40	=	=	SYM
ejpam-4468	105	41	∫	∫	PROPN
ejpam-4468	105	42	dx	dx	PROPN
ejpam-4468	105	43	ln	ln	PROPN
ejpam-4468	105	44	|φ|	|φ|	PROPN
ejpam-4468	105	45	=	=	PUNCT
ejpam-4468	106	1	x+	x+	PROPN
ejpam-4468	106	2	c	c	PROPN
ejpam-4468	106	3	φ	φ	PROPN
ejpam-4468	106	4	=	=	SYM
ejpam-4468	106	5	cex	cex	PROPN
ejpam-4468	106	6	since	since	SCONJ
ejpam-4468	106	7	φ(0	φ(0	PROPN
ejpam-4468	106	8	)	)	PUNCT
ejpam-4468	106	9	=	=	SYM
ejpam-4468	107	1	1	1	NUM
ejpam-4468	107	2	=	=	NOUN
ejpam-4468	107	3	⇒	⇒	X
ejpam-4468	107	4	φ	φ	X
ejpam-4468	107	5	=	=	SYM
ejpam-4468	107	6	ex	ex	PROPN
ejpam-4468	107	7	.	.	PUNCT
ejpam-4468	108	1	now	now	ADV
ejpam-4468	108	2	,	,	PUNCT
ejpam-4468	108	3	since	since	SCONJ
ejpam-4468	108	4	the	the	DET
ejpam-4468	108	5	first	first	ADJ
ejpam-4468	108	6	and	and	CCONJ
ejpam-4468	108	7	the	the	DET
ejpam-4468	108	8	second	second	ADJ
ejpam-4468	108	9	derivatives	derivative	NOUN
ejpam-4468	108	10	of	of	ADP
ejpam-4468	108	11	φ	φ	PROPN
ejpam-4468	108	12	are	be	AUX
ejpam-4468	108	13	equal	equal	ADJ
ejpam-4468	108	14	,	,	PUNCT
ejpam-4468	108	15	then	then	ADV
ejpam-4468	108	16	equation	equation	NOUN
ejpam-4468	108	17	(	(	PUNCT
ejpam-4468	108	18	2	2	X
ejpam-4468	108	19	)	)	PUNCT
ejpam-4468	108	20	becomes	become	VERB
ejpam-4468	108	21	φ⊗ψ′	φ⊗ψ′	PROPN
ejpam-4468	108	22	+	+	ADJ
ejpam-4468	108	23	φ⊗ψ	φ⊗ψ	NOUN
ejpam-4468	108	24	=	=	SYM
ejpam-4468	108	25	φ⊗ψ	φ⊗ψ	PROPN
ejpam-4468	108	26	.	.	PUNCT
ejpam-4468	109	1	(	(	PUNCT
ejpam-4468	109	2	ψ′	ψ′	PUNCT
ejpam-4468	109	3	+	+	ADV
ejpam-4468	109	4	ψ−ψ)⊗	ψ−ψ)⊗	X
ejpam-4468	109	5	φ	φ	NOUN
ejpam-4468	109	6	=	=	SYM
ejpam-4468	109	7	0	0	PROPN
ejpam-4468	109	8	.	.	PUNCT
ejpam-4468	109	9	ψ′	ψ′	PUNCT
ejpam-4468	110	1	⊗	⊗	PROPN
ejpam-4468	110	2	φ	φ	PROPN
ejpam-4468	110	3	=	=	SYM
ejpam-4468	110	4	0	0	PROPN
ejpam-4468	110	5	.	.	PUNCT
ejpam-4468	111	1	here	here	ADV
ejpam-4468	111	2	φ	φ	PROPN
ejpam-4468	111	3	=	=	SYM
ejpam-4468	111	4	0	0	PROPN
ejpam-4468	111	5	or	or	CCONJ
ejpam-4468	111	6	ψ′	ψ′	PROPN
ejpam-4468	111	7	=	=	NOUN
ejpam-4468	111	8	0	0	PROPN
ejpam-4468	111	9	.	.	PUNCT
ejpam-4468	112	1	if	if	SCONJ
ejpam-4468	112	2	φ	φ	PROPN
ejpam-4468	112	3	=	=	SYM
ejpam-4468	112	4	0	0	PROPN
ejpam-4468	112	5	,	,	PUNCT
ejpam-4468	112	6	then	then	ADV
ejpam-4468	112	7	we	we	PRON
ejpam-4468	112	8	have	have	VERB
ejpam-4468	112	9	a	a	DET
ejpam-4468	112	10	contradiction	contradiction	NOUN
ejpam-4468	112	11	since	since	SCONJ
ejpam-4468	112	12	φ	φ	PROPN
ejpam-4468	112	13	̸=	̸=	PROPN
ejpam-4468	112	14	0	0	NUM
ejpam-4468	112	15	.	.	PUNCT
ejpam-4468	113	1	so	so	ADV
ejpam-4468	113	2	ψ′	ψ′	PUNCT
ejpam-4468	113	3	=	=	SYM
ejpam-4468	113	4	0	0	NUM
ejpam-4468	113	5	,	,	PUNCT
ejpam-4468	113	6	this	this	PRON
ejpam-4468	113	7	implies	imply	VERB
ejpam-4468	113	8	ψ	ψ	X
ejpam-4468	113	9	=	=	SYM
ejpam-4468	113	10	k	k	X
ejpam-4468	113	11	,	,	PUNCT
ejpam-4468	113	12	where	where	SCONJ
ejpam-4468	113	13	k	k	PROPN
ejpam-4468	113	14	is	be	AUX
ejpam-4468	113	15	a	a	DET
ejpam-4468	113	16	constant	constant	ADJ
ejpam-4468	113	17	.	.	PUNCT
ejpam-4468	114	1	to	to	PART
ejpam-4468	114	2	verify	verify	VERB
ejpam-4468	114	3	equation	equation	NOUN
ejpam-4468	114	4	(	(	PUNCT
ejpam-4468	114	5	2	2	NUM
ejpam-4468	114	6	)	)	PUNCT
ejpam-4468	114	7	,	,	PUNCT
ejpam-4468	114	8	set	set	VERB
ejpam-4468	114	9	u	u	NOUN
ejpam-4468	114	10	=	=	PUNCT
ejpam-4468	114	11	φ⊗ψ	φ⊗ψ	PROPN
ejpam-4468	114	12	,	,	PUNCT
ejpam-4468	114	13	ux	ux	PROPN
ejpam-4468	114	14	=	=	SYM
ejpam-4468	114	15	φ′	φ′	NUM
ejpam-4468	114	16	⊗ψ	⊗ψ	NOUN
ejpam-4468	114	17	=	=	SYM
ejpam-4468	114	18	φ⊗ψ	φ⊗ψ	PROPN
ejpam-4468	114	19	,	,	PUNCT
ejpam-4468	114	20	uxx	uxx	X
ejpam-4468	115	1	=	=	SYM
ejpam-4468	115	2	φ′′	φ′′	ADJ
ejpam-4468	115	3	⊗ψ	⊗ψ	NOUN
ejpam-4468	115	4	=	=	SYM
ejpam-4468	115	5	φ⊗ψ	φ⊗ψ	PROPN
ejpam-4468	115	6	,	,	PUNCT
ejpam-4468	115	7	ut	ut	X
ejpam-4468	115	8	=	=	SYM
ejpam-4468	115	9	φ⊗ψ′	φ⊗ψ′	PROPN
ejpam-4468	115	10	=	=	NOUN
ejpam-4468	115	11	φ⊗	φ⊗	NOUN
ejpam-4468	115	12	0	0	PUNCT
ejpam-4468	116	1	=	=	SYM
ejpam-4468	116	2	0	0	PROPN
ejpam-4468	116	3	.	.	PUNCT
ejpam-4468	117	1	then	then	ADV
ejpam-4468	117	2	ut	ut	PROPN
ejpam-4468	117	3	+	+	CCONJ
ejpam-4468	117	4	ux	ux	X
ejpam-4468	117	5	=	=	NOUN
ejpam-4468	117	6	φ⊗	φ⊗	VERB
ejpam-4468	117	7	0	0	PUNCT
ejpam-4468	118	1	+	+	CCONJ
ejpam-4468	118	2	φ⊗ψ	φ⊗ψ	NOUN
ejpam-4468	118	3	=	=	SYM
ejpam-4468	118	4	0	0	PUNCT
ejpam-4468	118	5	+	+	NUM
ejpam-4468	118	6	φ⊗ψ	φ⊗ψ	NOUN
ejpam-4468	118	7	=	=	PUNCT
ejpam-4468	118	8	φ⊗ψ	φ⊗ψ	PROPN
ejpam-4468	118	9	=	=	SYM
ejpam-4468	118	10	uxx	uxx	PROPN
ejpam-4468	118	11	.	.	PUNCT
ejpam-4468	119	1	a.	a.	PROPN
ejpam-4468	119	2	al	al	PROPN
ejpam-4468	119	3	-	-	PUNCT
ejpam-4468	119	4	jarrah	jarrah	PROPN
ejpam-4468	119	5	,	,	PUNCT
ejpam-4468	119	6	sh	sh	PROPN
ejpam-4468	119	7	.	.	PROPN
ejpam-4468	119	8	alsharif	alsharif	PROPN
ejpam-4468	119	9	,	,	PUNCT
ejpam-4468	119	10	h.	h.	PROPN
ejpam-4468	119	11	almefleh	almefleh	PROPN
ejpam-4468	119	12	/	/	SYM
ejpam-4468	119	13	eur	eur	PROPN
ejpam-4468	119	14	.	.	PUNCT
ejpam-4468	120	1	j.	j.	PROPN
ejpam-4468	120	2	pure	pure	PROPN
ejpam-4468	120	3	appl	appl	PROPN
ejpam-4468	120	4	.	.	PROPN
ejpam-4468	120	5	math	math	PROPN
ejpam-4468	120	6	,	,	PUNCT
ejpam-4468	120	7	15	15	NUM
ejpam-4468	120	8	(	(	PUNCT
ejpam-4468	120	9	4	4	NUM
ejpam-4468	120	10	)	)	PUNCT
ejpam-4468	120	11	(	(	PUNCT
ejpam-4468	120	12	2022	2022	NUM
ejpam-4468	120	13	)	)	PUNCT
ejpam-4468	120	14	,	,	PUNCT
ejpam-4468	120	15	1444	1444	NUM
ejpam-4468	120	16	-	-	SYM
ejpam-4468	120	17	1454	1454	NUM
ejpam-4468	120	18	1448	1448	NUM
ejpam-4468	120	19	this	this	PRON
ejpam-4468	120	20	implies	imply	VERB
ejpam-4468	120	21	u	u	NOUN
ejpam-4468	120	22	=	=	PUNCT
ejpam-4468	120	23	φ⊗ψ	φ⊗ψ	PROPN
ejpam-4468	120	24	,	,	PUNCT
ejpam-4468	120	25	where	where	SCONJ
ejpam-4468	120	26	φ	φ	PROPN
ejpam-4468	120	27	=	=	SYM
ejpam-4468	120	28	ex	ex	X
ejpam-4468	120	29	and	and	CCONJ
ejpam-4468	120	30	ψ	ψ	X
ejpam-4468	120	31	=	=	PROPN
ejpam-4468	120	32	k.	k.	PROPN
ejpam-4468	120	33	case	case	NOUN
ejpam-4468	120	34	(	(	PUNCT
ejpam-4468	120	35	2	2	X
ejpam-4468	120	36	)	)	PUNCT
ejpam-4468	120	37	if	if	SCONJ
ejpam-4468	120	38	ψ′	ψ′	NUM
ejpam-4468	120	39	=	=	SYM
ejpam-4468	120	40	ψ	ψ	NOUN
ejpam-4468	120	41	,	,	PUNCT
ejpam-4468	120	42	then	then	ADV
ejpam-4468	120	43	ψ′	ψ′	PUNCT
ejpam-4468	120	44	ψ	ψ	NOUN
ejpam-4468	120	45	=	=	NOUN
ejpam-4468	120	46	1	1	X
ejpam-4468	120	47	.	.	X
ejpam-4468	120	48	integrating	integrate	VERB
ejpam-4468	120	49	both	both	DET
ejpam-4468	120	50	sides	side	NOUN
ejpam-4468	120	51	,	,	PUNCT
ejpam-4468	120	52	we	we	PRON
ejpam-4468	120	53	get	get	VERB
ejpam-4468	120	54	∫	∫	PROPN
ejpam-4468	120	55	dψ	dψ	NOUN
ejpam-4468	120	56	ψ	ψ	NOUN
ejpam-4468	120	57	=	=	SYM
ejpam-4468	120	58	∫	∫	PROPN
ejpam-4468	120	59	dt	dt	X
ejpam-4468	120	60	ln	ln	PROPN
ejpam-4468	120	61	|ψ|	|ψ|	PROPN
ejpam-4468	120	62	=	=	SYM
ejpam-4468	120	63	t+	t+	PUNCT
ejpam-4468	120	64	a	a	DET
ejpam-4468	120	65	ψ	ψ	X
ejpam-4468	120	66	=	=	SYM
ejpam-4468	120	67	aet	aet	PROPN
ejpam-4468	120	68	.	.	PUNCT
ejpam-4468	121	1	since	since	SCONJ
ejpam-4468	121	2	ψ(0	ψ(0	PROPN
ejpam-4468	121	3	)	)	PUNCT
ejpam-4468	121	4	=	=	SYM
ejpam-4468	121	5	1	1	NUM
ejpam-4468	121	6	=	=	AUX
ejpam-4468	121	7	⇒	⇒	NOUN
ejpam-4468	121	8	ψ	ψ	X
ejpam-4468	121	9	=	=	NOUN
ejpam-4468	121	10	et	et	PROPN
ejpam-4468	121	11	.	.	PUNCT
ejpam-4468	121	12	now	now	ADV
ejpam-4468	121	13	,	,	PUNCT
ejpam-4468	121	14	ψ′	ψ′	PUNCT
ejpam-4468	121	15	=	=	SYM
ejpam-4468	121	16	et	et	NOUN
ejpam-4468	121	17	=	=	SYM
ejpam-4468	121	18	ψ	ψ	PROPN
ejpam-4468	121	19	,	,	PUNCT
ejpam-4468	121	20	then	then	ADV
ejpam-4468	121	21	equation	equation	NOUN
ejpam-4468	121	22	(	(	PUNCT
ejpam-4468	121	23	2	2	X
ejpam-4468	121	24	)	)	PUNCT
ejpam-4468	121	25	becomes	become	VERB
ejpam-4468	121	26	φ⊗ψ+φ′	φ⊗ψ+φ′	ADJ
ejpam-4468	121	27	⊗ψ	⊗ψ	NOUN
ejpam-4468	121	28	=	=	SYM
ejpam-4468	121	29	φ′′	φ′′	PROPN
ejpam-4468	121	30	⊗ψ	⊗ψ	NOUN
ejpam-4468	122	1	[	[	X
ejpam-4468	122	2	φ	φ	X
ejpam-4468	122	3	+	+	NOUN
ejpam-4468	122	4	φ′	φ′	NUM
ejpam-4468	122	5	−	−	NOUN
ejpam-4468	122	6	φ′′]⊗ψ	φ′′]⊗ψ	NOUN
ejpam-4468	122	7	=	=	SYM
ejpam-4468	122	8	0	0	X
ejpam-4468	122	9	.	.	PUNCT
ejpam-4468	123	1	using	use	VERB
ejpam-4468	123	2	lemma	lemma	PROPN
ejpam-4468	123	3	(	(	PUNCT
ejpam-4468	123	4	1	1	X
ejpam-4468	123	5	)	)	PUNCT
ejpam-4468	123	6	φ′′	φ′′	PROPN
ejpam-4468	123	7	−φ′	−φ′	PROPN
ejpam-4468	123	8	−φ	−φ	VERB
ejpam-4468	123	9	=	=	SYM
ejpam-4468	123	10	0	0	NUM
ejpam-4468	123	11	or	or	CCONJ
ejpam-4468	123	12	ψ	ψ	X
ejpam-4468	123	13	=	=	NOUN
ejpam-4468	123	14	0	0	X
ejpam-4468	123	15	.	.	PUNCT
ejpam-4468	124	1	if	if	SCONJ
ejpam-4468	124	2	ψ	ψ	X
ejpam-4468	124	3	=	=	SYM
ejpam-4468	124	4	0	0	NUM
ejpam-4468	124	5	,	,	PUNCT
ejpam-4468	124	6	then	then	ADV
ejpam-4468	124	7	we	we	PRON
ejpam-4468	124	8	have	have	VERB
ejpam-4468	124	9	a	a	DET
ejpam-4468	124	10	contradiction	contradiction	NOUN
ejpam-4468	124	11	since	since	SCONJ
ejpam-4468	124	12	ψ	ψ	VERB
ejpam-4468	124	13	̸=	̸=	PROPN
ejpam-4468	124	14	0	0	NUM
ejpam-4468	124	15	.	.	PUNCT
ejpam-4468	125	1	so	so	ADV
ejpam-4468	125	2	φ′′	φ′′	PROPN
ejpam-4468	125	3	−	−	PROPN
ejpam-4468	125	4	φ′	φ′	NUM
ejpam-4468	125	5	−	−	PROPN
ejpam-4468	125	6	φ	φ	PROPN
ejpam-4468	125	7	=	=	SYM
ejpam-4468	125	8	0	0	PROPN
ejpam-4468	125	9	.	.	PUNCT
ejpam-4468	126	1	(	(	PUNCT
ejpam-4468	126	2	3	3	X
ejpam-4468	126	3	)	)	PUNCT
ejpam-4468	126	4	the	the	DET
ejpam-4468	126	5	characteristic	characteristic	ADJ
ejpam-4468	126	6	equation	equation	NOUN
ejpam-4468	126	7	of	of	ADP
ejpam-4468	126	8	equation	equation	NOUN
ejpam-4468	126	9	(	(	PUNCT
ejpam-4468	126	10	3	3	X
ejpam-4468	126	11	)	)	PUNCT
ejpam-4468	126	12	is	be	AUX
ejpam-4468	126	13	λ2	λ2	PROPN
ejpam-4468	126	14	−	−	PROPN
ejpam-4468	126	15	λ−	λ−	PROPN
ejpam-4468	126	16	1	1	NUM
ejpam-4468	126	17	=	=	SYM
ejpam-4468	126	18	0	0	NUM
ejpam-4468	126	19	,	,	PUNCT
ejpam-4468	126	20	with	with	ADP
ejpam-4468	126	21	roots	root	NOUN
ejpam-4468	126	22	λ1	λ1	ADJ
ejpam-4468	126	23	=	=	SYM
ejpam-4468	126	24	1	1	NUM
ejpam-4468	126	25	+	+	NUM
ejpam-4468	126	26	√	√	NUM
ejpam-4468	126	27	5	5	NUM
ejpam-4468	126	28	2	2	NUM
ejpam-4468	126	29	and	and	CCONJ
ejpam-4468	126	30	λ2	λ2	NOUN
ejpam-4468	126	31	=	=	SYM
ejpam-4468	126	32	1−	1−	NUM
ejpam-4468	126	33	√	√	NUM
ejpam-4468	126	34	5	5	NUM
ejpam-4468	126	35	2	2	NUM
ejpam-4468	126	36	.	.	PUNCT
ejpam-4468	127	1	hence	hence	ADV
ejpam-4468	127	2	φ	φ	PROPN
ejpam-4468	127	3	=	=	SYM
ejpam-4468	127	4	geλ1x	geλ1x	PROPN
ejpam-4468	127	5	+	+	CCONJ
ejpam-4468	127	6	feλ2x	feλ2x	PROPN
ejpam-4468	127	7	,	,	PUNCT
ejpam-4468	127	8	since	since	SCONJ
ejpam-4468	127	9	φ(0	φ(0	ADJ
ejpam-4468	127	10	)	)	PUNCT
ejpam-4468	127	11	=	=	SYM
ejpam-4468	127	12	1	1	NUM
ejpam-4468	127	13	and	and	CCONJ
ejpam-4468	127	14	φ′(0	φ′(0	NOUN
ejpam-4468	127	15	)	)	PUNCT
ejpam-4468	127	16	=	=	SYM
ejpam-4468	127	17	1	1	NUM
ejpam-4468	127	18	,	,	PUNCT
ejpam-4468	127	19	then	then	ADV
ejpam-4468	127	20	f	f	PROPN
ejpam-4468	127	21	=	=	PUNCT
ejpam-4468	128	1	λ1−1	λ1−1	NOUN
ejpam-4468	128	2	λ1−λ2	λ1−λ2	NOUN
ejpam-4468	128	3	and	and	CCONJ
ejpam-4468	128	4	g	g	NOUN
ejpam-4468	128	5	=	=	PROPN
ejpam-4468	128	6	λ2−1	λ2−1	PRON
ejpam-4468	128	7	λ2−λ1	λ2−λ1	ADJ
ejpam-4468	128	8	.	.	PUNCT
ejpam-4468	129	1	to	to	PART
ejpam-4468	129	2	verify	verify	VERB
ejpam-4468	129	3	equation	equation	NOUN
ejpam-4468	129	4	(	(	PUNCT
ejpam-4468	129	5	2	2	NUM
ejpam-4468	129	6	)	)	PUNCT
ejpam-4468	129	7	,	,	PUNCT
ejpam-4468	129	8	set	set	VERB
ejpam-4468	129	9	u	u	NOUN
ejpam-4468	129	10	=	=	PUNCT
ejpam-4468	129	11	φ⊗ψ	φ⊗ψ	PROPN
ejpam-4468	129	12	,	,	PUNCT
ejpam-4468	129	13	ux	ux	PROPN
ejpam-4468	129	14	=	=	SYM
ejpam-4468	129	15	φ′⊗ψ	φ′⊗ψ	PROPN
ejpam-4468	129	16	,	,	PUNCT
ejpam-4468	129	17	uxx	uxx	X
ejpam-4468	129	18	=	=	SYM
ejpam-4468	129	19	φ′′⊗ψ	φ′′⊗ψ	PROPN
ejpam-4468	129	20	,	,	PUNCT
ejpam-4468	129	21	ut	ut	PROPN
ejpam-4468	129	22	=	=	SYM
ejpam-4468	129	23	φ⊗ψ′	φ⊗ψ′	PROPN
ejpam-4468	129	24	,	,	PUNCT
ejpam-4468	129	25	where	where	SCONJ
ejpam-4468	129	26	φ	φ	PROPN
ejpam-4468	129	27	=	=	PUNCT
ejpam-4468	130	1	λ2−1	λ2−1	PRON
ejpam-4468	130	2	λ2−λ1	λ2−λ1	ADJ
ejpam-4468	130	3	eλ1x+	eλ1x+	X
ejpam-4468	130	4	λ1−1	λ1−1	VERB
ejpam-4468	130	5	λ1−λ2	λ1−λ2	PUNCT
ejpam-4468	130	6	eλ2x	eλ2x	NOUN
ejpam-4468	130	7	,	,	PUNCT
ejpam-4468	130	8	φ′	φ′	NUM
ejpam-4468	130	9	=	=	SYM
ejpam-4468	130	10	λ1	λ1	PROPN
ejpam-4468	130	11	λ2−1	λ2−1	DET
ejpam-4468	130	12	λ2−λ1	λ2−λ1	ADJ
ejpam-4468	130	13	eλ1x+λ2	eλ1x+λ2	ADV
ejpam-4468	130	14	λ1−1	λ1−1	ADV
ejpam-4468	130	15	λ1−λ2	λ1−λ2	VERB
ejpam-4468	130	16	eλ2x	eλ2x	PROPN
ejpam-4468	130	17	,	,	PUNCT
ejpam-4468	130	18	φ′′	φ′′	PROPN
ejpam-4468	130	19	=	=	SYM
ejpam-4468	130	20	λ2	λ2	PROPN
ejpam-4468	130	21	1	1	NUM
ejpam-4468	130	22	λ2−1	λ2−1	PRON
ejpam-4468	130	23	λ2−λ1	λ2−λ1	ADJ
ejpam-4468	130	24	eλ1x+λ2	eλ1x+λ2	NOUN
ejpam-4468	130	25	2	2	NUM
ejpam-4468	130	26	λ1−1	λ1−1	PRON
ejpam-4468	130	27	λ1−λ2	λ1−λ2	PUNCT
ejpam-4468	130	28	eλ2x	eλ2x	PROPN
ejpam-4468	130	29	,	,	PUNCT
ejpam-4468	130	30	ψ	ψ	X
ejpam-4468	130	31	=	=	SYM
ejpam-4468	130	32	et	et	NOUN
ejpam-4468	130	33	,	,	PUNCT
ejpam-4468	130	34	and	and	CCONJ
ejpam-4468	130	35	ψ′	ψ′	PUNCT
ejpam-4468	130	36	=	=	ADJ
ejpam-4468	130	37	et	et	PROPN
ejpam-4468	130	38	.	.	PUNCT
ejpam-4468	131	1	then	then	ADV
ejpam-4468	131	2	ut	ut	PROPN
ejpam-4468	131	3	+	+	CCONJ
ejpam-4468	131	4	ux	ux	PROPN
ejpam-4468	131	5	=	=	SYM
ejpam-4468	132	1	φ⊗ψ′	φ⊗ψ′	PROPN
ejpam-4468	132	2	+	+	NOUN
ejpam-4468	132	3	φ′	φ′	NUM
ejpam-4468	132	4	⊗ψ	⊗ψ	ADJ
ejpam-4468	132	5	=	=	PUNCT
ejpam-4468	132	6	φ⊗ψ+φ′	φ⊗ψ+φ′	ADJ
ejpam-4468	132	7	⊗ψ	⊗ψ	NOUN
ejpam-4468	132	8	=	=	PUNCT
ejpam-4468	133	1	[	[	X
ejpam-4468	133	2	φ	φ	X
ejpam-4468	133	3	+	+	X
ejpam-4468	133	4	φ′]⊗ψ	φ′]⊗ψ	PROPN
ejpam-4468	133	5	,	,	PUNCT
ejpam-4468	133	6	and	and	CCONJ
ejpam-4468	133	7	so	so	ADV
ejpam-4468	133	8	φ	φ	PROPN
ejpam-4468	133	9	+	+	PROPN
ejpam-4468	133	10	φ′	φ′	NUM
ejpam-4468	133	11	=	=	SYM
ejpam-4468	133	12	(	(	PUNCT
ejpam-4468	133	13	λ2	λ2	NOUN
ejpam-4468	133	14	−	−	PROPN
ejpam-4468	133	15	1	1	NUM
ejpam-4468	133	16	λ2	λ2	NOUN
ejpam-4468	133	17	−	−	PROPN
ejpam-4468	133	18	λ1	λ1	PROPN
ejpam-4468	133	19	eλ1x	eλ1x	PROPN
ejpam-4468	133	20	+	+	CCONJ
ejpam-4468	134	1	λ1	λ1	PROPN
ejpam-4468	134	2	−	−	PROPN
ejpam-4468	134	3	1	1	NUM
ejpam-4468	134	4	λ1	λ1	PROPN
ejpam-4468	134	5	−	−	PROPN
ejpam-4468	134	6	λ2	λ2	PROPN
ejpam-4468	134	7	eλ2x	eλ2x	PROPN
ejpam-4468	134	8	+	+	CCONJ
ejpam-4468	134	9	λ1	λ1	ADJ
ejpam-4468	134	10	λ2	λ2	NOUN
ejpam-4468	134	11	−	−	PROPN
ejpam-4468	134	12	1	1	NUM
ejpam-4468	134	13	λ2	λ2	NOUN
ejpam-4468	134	14	−	−	PROPN
ejpam-4468	134	15	λ1	λ1	PROPN
ejpam-4468	134	16	eλ1x	eλ1x	PROPN
ejpam-4468	134	17	+	+	CCONJ
ejpam-4468	134	18	λ2	λ2	NOUN
ejpam-4468	134	19	λ1	λ1	ADJ
ejpam-4468	134	20	−	−	PROPN
ejpam-4468	134	21	1	1	NUM
ejpam-4468	134	22	λ1	λ1	PROPN
ejpam-4468	134	23	−	−	PROPN
ejpam-4468	134	24	λ2	λ2	PROPN
ejpam-4468	134	25	eλ2x	eλ2x	PROPN
ejpam-4468	134	26	)	)	PUNCT
ejpam-4468	134	27	a.	a.	NOUN
ejpam-4468	134	28	al	al	PROPN
ejpam-4468	134	29	-	-	PUNCT
ejpam-4468	134	30	jarrah	jarrah	PROPN
ejpam-4468	134	31	,	,	PUNCT
ejpam-4468	134	32	sh	sh	PROPN
ejpam-4468	134	33	.	.	PROPN
ejpam-4468	134	34	alsharif	alsharif	PROPN
ejpam-4468	134	35	,	,	PUNCT
ejpam-4468	134	36	h.	h.	PROPN
ejpam-4468	134	37	almefleh	almefleh	PROPN
ejpam-4468	134	38	/	/	SYM
ejpam-4468	134	39	eur	eur	PROPN
ejpam-4468	134	40	.	.	PUNCT
ejpam-4468	135	1	j.	j.	PROPN
ejpam-4468	135	2	pure	pure	PROPN
ejpam-4468	135	3	appl	appl	PROPN
ejpam-4468	135	4	.	.	PROPN
ejpam-4468	135	5	math	math	PROPN
ejpam-4468	135	6	,	,	PUNCT
ejpam-4468	135	7	15	15	NUM
ejpam-4468	135	8	(	(	PUNCT
ejpam-4468	135	9	4	4	NUM
ejpam-4468	135	10	)	)	PUNCT
ejpam-4468	135	11	(	(	PUNCT
ejpam-4468	135	12	2022	2022	NUM
ejpam-4468	135	13	)	)	PUNCT
ejpam-4468	135	14	,	,	PUNCT
ejpam-4468	135	15	1444	1444	NUM
ejpam-4468	135	16	-	-	SYM
ejpam-4468	135	17	1454	1454	NUM
ejpam-4468	135	18	1449	1449	NUM
ejpam-4468	135	19	=	=	SYM
ejpam-4468	135	20	(	(	PUNCT
ejpam-4468	135	21	1	1	NUM
ejpam-4468	135	22	+	+	SYM
ejpam-4468	135	23	λ1	λ1	ADJ
ejpam-4468	135	24	)	)	PUNCT
ejpam-4468	135	25	(	(	PUNCT
ejpam-4468	135	26	λ2	λ2	NOUN
ejpam-4468	135	27	−	−	PROPN
ejpam-4468	135	28	1	1	NUM
ejpam-4468	135	29	λ2	λ2	NOUN
ejpam-4468	135	30	−	−	NOUN
ejpam-4468	135	31	λ1	λ1	PROPN
ejpam-4468	135	32	)	)	PUNCT
ejpam-4468	135	33	eλ1x	eλ1x	VERB
ejpam-4468	135	34	+	+	CCONJ
ejpam-4468	135	35	(	(	PUNCT
ejpam-4468	135	36	1	1	NUM
ejpam-4468	135	37	+	+	NUM
ejpam-4468	135	38	λ2	λ2	NOUN
ejpam-4468	135	39	)	)	PUNCT
ejpam-4468	135	40	(	(	PUNCT
ejpam-4468	135	41	λ1	λ1	PROPN
ejpam-4468	135	42	−	−	PROPN
ejpam-4468	135	43	1	1	NUM
ejpam-4468	135	44	λ1	λ1	PROPN
ejpam-4468	135	45	−	−	PROPN
ejpam-4468	135	46	λ2	λ2	NOUN
ejpam-4468	135	47	)	)	PUNCT
ejpam-4468	135	48	eλ2x	eλ2x	PROPN
ejpam-4468	135	49	.	.	PUNCT
ejpam-4468	136	1	now	now	ADV
ejpam-4468	136	2	,	,	PUNCT
ejpam-4468	136	3	1	1	NUM
ejpam-4468	136	4	+	+	NUM
ejpam-4468	136	5	λ1	λ1	ADJ
ejpam-4468	136	6	=	=	SYM
ejpam-4468	136	7	1	1	NUM
ejpam-4468	136	8	+	+	NUM
ejpam-4468	136	9	1	1	NUM
ejpam-4468	136	10	+	+	NUM
ejpam-4468	136	11	√	√	NUM
ejpam-4468	136	12	5	5	NUM
ejpam-4468	136	13	2	2	NUM
ejpam-4468	136	14	=	=	SYM
ejpam-4468	136	15	3	3	NUM
ejpam-4468	136	16	+	+	NUM
ejpam-4468	136	17	√	√	NUM
ejpam-4468	136	18	5	5	NUM
ejpam-4468	136	19	2	2	NUM
ejpam-4468	136	20	and	and	CCONJ
ejpam-4468	136	21	1	1	NUM
ejpam-4468	136	22	+	+	NUM
ejpam-4468	136	23	λ2	λ2	NOUN
ejpam-4468	136	24	=	=	SYM
ejpam-4468	136	25	1	1	NUM
ejpam-4468	136	26	+	+	NUM
ejpam-4468	136	27	1−	1−	NUM
ejpam-4468	136	28	√	√	NUM
ejpam-4468	136	29	5	5	NUM
ejpam-4468	136	30	2	2	NUM
ejpam-4468	136	31	=	=	SYM
ejpam-4468	136	32	3−	3−	NUM
ejpam-4468	136	33	√	√	NUM
ejpam-4468	136	34	5	5	NUM
ejpam-4468	136	35	2	2	NUM
ejpam-4468	136	36	,	,	PUNCT
ejpam-4468	136	37	but	but	CCONJ
ejpam-4468	136	38	λ2	λ2	NOUN
ejpam-4468	136	39	1	1	NUM
ejpam-4468	136	40	=	=	SYM
ejpam-4468	136	41	(	(	PUNCT
ejpam-4468	136	42	1	1	NUM
ejpam-4468	136	43	+	+	NUM
ejpam-4468	136	44	√	√	NUM
ejpam-4468	136	45	5	5	NUM
ejpam-4468	136	46	2	2	NUM
ejpam-4468	136	47	)	)	PUNCT
ejpam-4468	136	48	2	2	NUM
ejpam-4468	136	49	=	=	SYM
ejpam-4468	136	50	3	3	NUM
ejpam-4468	136	51	+	+	NUM
ejpam-4468	136	52	√	√	NUM
ejpam-4468	136	53	5	5	NUM
ejpam-4468	136	54	2	2	NUM
ejpam-4468	136	55	and	and	CCONJ
ejpam-4468	136	56	λ2	λ2	NOUN
ejpam-4468	136	57	2	2	NUM
ejpam-4468	136	58	=	=	SYM
ejpam-4468	136	59	(	(	PUNCT
ejpam-4468	136	60	1−	1−	NUM
ejpam-4468	136	61	√	√	NUM
ejpam-4468	136	62	5	5	NUM
ejpam-4468	136	63	2	2	NUM
ejpam-4468	136	64	)	)	PUNCT
ejpam-4468	136	65	2	2	NUM
ejpam-4468	136	66	=	=	SYM
ejpam-4468	136	67	3−	3−	NUM
ejpam-4468	136	68	√	√	NUM
ejpam-4468	136	69	5	5	NUM
ejpam-4468	136	70	2	2	NUM
ejpam-4468	136	71	so	so	ADV
ejpam-4468	136	72	1	1	NUM
ejpam-4468	136	73	+	+	NUM
ejpam-4468	136	74	λ1	λ1	ADJ
ejpam-4468	136	75	=	=	SYM
ejpam-4468	136	76	λ2	λ2	NOUN
ejpam-4468	136	77	1	1	NUM
ejpam-4468	136	78	and	and	CCONJ
ejpam-4468	136	79	1	1	NUM
ejpam-4468	136	80	+	+	NUM
ejpam-4468	136	81	λ2	λ2	NOUN
ejpam-4468	136	82	=	=	SYM
ejpam-4468	136	83	λ2	λ2	NOUN
ejpam-4468	136	84	2	2	NUM
ejpam-4468	136	85	,	,	PUNCT
ejpam-4468	136	86	then	then	ADV
ejpam-4468	136	87	φ	φ	PROPN
ejpam-4468	136	88	+	+	CCONJ
ejpam-4468	136	89	φ′	φ′	NUM
ejpam-4468	136	90	=	=	SYM
ejpam-4468	136	91	(	(	PUNCT
ejpam-4468	136	92	1	1	NUM
ejpam-4468	136	93	+	+	CCONJ
ejpam-4468	136	94	λ1)e	λ1)e	NOUN
ejpam-4468	136	95	λ1x	λ1x	X
ejpam-4468	136	96	+	+	CCONJ
ejpam-4468	136	97	(	(	PUNCT
ejpam-4468	136	98	1	1	NUM
ejpam-4468	136	99	+	+	CCONJ
ejpam-4468	136	100	λ2)e	λ2)e	NOUN
ejpam-4468	136	101	λ2x	λ2x	ADP
ejpam-4468	136	102	=	=	SYM
ejpam-4468	136	103	λ2	λ2	NOUN
ejpam-4468	136	104	1e	1e	NOUN
ejpam-4468	136	105	λ1x	λ1x	X
ejpam-4468	136	106	+	+	NUM
ejpam-4468	136	107	λ2	λ2	NOUN
ejpam-4468	136	108	2e	2e	NOUN
ejpam-4468	136	109	λ2x	λ2x	PUNCT
ejpam-4468	136	110	=	=	PUNCT
ejpam-4468	137	1	φ′′.	φ′′.	PROPN
ejpam-4468	137	2	ut	ut	PROPN
ejpam-4468	138	1	+	+	NUM
ejpam-4468	138	2	ux	ux	NOUN
ejpam-4468	138	3	=	=	SYM
ejpam-4468	139	1	[	[	X
ejpam-4468	139	2	φ	φ	X
ejpam-4468	139	3	+	+	NUM
ejpam-4468	139	4	φ′]⊗ψ	φ′]⊗ψ	X
ejpam-4468	139	5	=	=	PUNCT
ejpam-4468	139	6	φ′′	φ′′	PROPN
ejpam-4468	139	7	⊗ψ	⊗ψ	NOUN
ejpam-4468	139	8	=	=	SYM
ejpam-4468	139	9	uxx	uxx	PROPN
ejpam-4468	139	10	.	.	PUNCT
ejpam-4468	140	1	this	this	PRON
ejpam-4468	140	2	implies	imply	VERB
ejpam-4468	140	3	that	that	SCONJ
ejpam-4468	140	4	u	u	NOUN
ejpam-4468	140	5	=	=	PROPN
ejpam-4468	140	6	φ	φ	PROPN
ejpam-4468	140	7	⊗	⊗	PROPN
ejpam-4468	140	8	ψ	ψ	PROPN
ejpam-4468	140	9	is	be	AUX
ejpam-4468	140	10	a	a	DET
ejpam-4468	140	11	solution	solution	NOUN
ejpam-4468	140	12	of	of	ADP
ejpam-4468	140	13	equation	equation	NOUN
ejpam-4468	140	14	(	(	PUNCT
ejpam-4468	140	15	1	1	NUM
ejpam-4468	140	16	)	)	PUNCT
ejpam-4468	140	17	,	,	PUNCT
ejpam-4468	140	18	where	where	SCONJ
ejpam-4468	140	19	φ	φ	PROPN
ejpam-4468	140	20	=	=	SYM
ejpam-4468	140	21	(	(	PUNCT
ejpam-4468	140	22	λ2−1	λ2−1	PRON
ejpam-4468	140	23	λ2−λ1	λ2−λ1	ADJ
ejpam-4468	140	24	)	)	PUNCT
ejpam-4468	140	25	eλ1x	eλ1x	VERB
ejpam-4468	140	26	+	+	CCONJ
ejpam-4468	140	27	(	(	PUNCT
ejpam-4468	140	28	λ1−1	λ1−1	PUNCT
ejpam-4468	140	29	λ1−λ2	λ1−λ2	NOUN
ejpam-4468	140	30	)	)	PUNCT
ejpam-4468	140	31	eλ2x	eλ2x	PROPN
ejpam-4468	140	32	and	and	CCONJ
ejpam-4468	140	33	ψ	ψ	X
ejpam-4468	140	34	=	=	ADJ
ejpam-4468	140	35	et	et	NOUN
ejpam-4468	140	36	.	.	PUNCT
ejpam-4468	141	1	in	in	ADP
ejpam-4468	141	2	the	the	DET
ejpam-4468	141	3	following	follow	VERB
ejpam-4468	141	4	theorem	theorem	NOUN
ejpam-4468	141	5	we	we	PRON
ejpam-4468	141	6	use	use	VERB
ejpam-4468	141	7	tensor	tensor	NOUN
ejpam-4468	141	8	product	product	NOUN
ejpam-4468	141	9	technique	technique	NOUN
ejpam-4468	141	10	to	to	PART
ejpam-4468	141	11	find	find	VERB
ejpam-4468	141	12	an	an	DET
ejpam-4468	141	13	exact	exact	ADJ
ejpam-4468	141	14	solution	solution	NOUN
ejpam-4468	141	15	of	of	ADP
ejpam-4468	141	16	a	a	DET
ejpam-4468	141	17	general	general	ADJ
ejpam-4468	141	18	form	form	NOUN
ejpam-4468	141	19	of	of	ADP
ejpam-4468	141	20	equation	equation	NOUN
ejpam-4468	141	21	(	(	PUNCT
ejpam-4468	141	22	1	1	NUM
ejpam-4468	141	23	)	)	PUNCT
ejpam-4468	141	24	.	.	PUNCT
ejpam-4468	142	1	theorem	theorem	NOUN
ejpam-4468	142	2	3	3	X
ejpam-4468	142	3	.	.	PUNCT
ejpam-4468	143	1	let	let	VERB
ejpam-4468	143	2	u(x	u(x	NOUN
ejpam-4468	143	3	,	,	PUNCT
ejpam-4468	143	4	t	t	PROPN
ejpam-4468	143	5	)	)	PUNCT
ejpam-4468	143	6	∈	∈	PROPN
ejpam-4468	143	7	c(i	c(i	VERB
ejpam-4468	143	8	×	×	PROPN
ejpam-4468	143	9	j	j	PROPN
ejpam-4468	143	10	)	)	PUNCT
ejpam-4468	143	11	,	,	PUNCT
ejpam-4468	143	12	where	where	SCONJ
ejpam-4468	143	13	i	i	PRON
ejpam-4468	143	14	,	,	PUNCT
ejpam-4468	143	15	j	j	PROPN
ejpam-4468	144	1	=	=	PUNCT
ejpam-4468	145	1	[	[	X
ejpam-4468	145	2	0	0	NUM
ejpam-4468	145	3	,	,	PUNCT
ejpam-4468	145	4	1	1	NUM
ejpam-4468	145	5	]	]	PUNCT
ejpam-4468	145	6	or	or	CCONJ
ejpam-4468	145	7	[	[	X
ejpam-4468	145	8	0,∞	0,∞	NUM
ejpam-4468	145	9	)	)	PUNCT
ejpam-4468	145	10	.	.	PUNCT
ejpam-4468	146	1	if	if	SCONJ
ejpam-4468	146	2	u	u	NOUN
ejpam-4468	146	3	has	have	VERB
ejpam-4468	146	4	continuous	continuous	ADJ
ejpam-4468	146	5	second	second	ADJ
ejpam-4468	146	6	partial	partial	ADJ
ejpam-4468	146	7	derivatives	derivative	NOUN
ejpam-4468	146	8	and	and	CCONJ
ejpam-4468	146	9	f	f	NOUN
ejpam-4468	146	10	any	any	DET
ejpam-4468	146	11	continuous	continuous	ADJ
ejpam-4468	146	12	function	function	NOUN
ejpam-4468	146	13	of	of	ADP
ejpam-4468	146	14	t	t	PROPN
ejpam-4468	146	15	,	,	PUNCT
ejpam-4468	146	16	then	then	ADV
ejpam-4468	146	17	the	the	DET
ejpam-4468	146	18	differential	differential	ADJ
ejpam-4468	146	19	equation	equation	NOUN
ejpam-4468	146	20	ut	ut	PROPN
ejpam-4468	147	1	+	+	CCONJ
ejpam-4468	147	2	fux	fux	PROPN
ejpam-4468	147	3	=	=	PROPN
ejpam-4468	147	4	uxx	uxx	PROPN
ejpam-4468	147	5	(	(	PUNCT
ejpam-4468	147	6	4	4	X
ejpam-4468	147	7	)	)	PUNCT
ejpam-4468	147	8	can	can	AUX
ejpam-4468	147	9	be	be	AUX
ejpam-4468	147	10	solved	solve	VERB
ejpam-4468	147	11	by	by	ADP
ejpam-4468	147	12	tensor	tensor	NOUN
ejpam-4468	147	13	product	product	NOUN
ejpam-4468	147	14	.	.	PUNCT
ejpam-4468	148	1	proof	proof	NOUN
ejpam-4468	148	2	.	.	PUNCT
ejpam-4468	149	1	put	put	VERB
ejpam-4468	149	2	u	u	NOUN
ejpam-4468	149	3	=	=	PUNCT
ejpam-4468	149	4	φ⊗ψ	φ⊗ψ	PROPN
ejpam-4468	149	5	,	,	PUNCT
ejpam-4468	149	6	with	with	ADP
ejpam-4468	149	7	φ(0	φ(0	ADJ
ejpam-4468	149	8	)	)	PUNCT
ejpam-4468	149	9	=	=	SYM
ejpam-4468	149	10	1	1	NUM
ejpam-4468	149	11	and	and	CCONJ
ejpam-4468	149	12	ψ(0	ψ(0	PROPN
ejpam-4468	149	13	)	)	PUNCT
ejpam-4468	149	14	=	=	SYM
ejpam-4468	149	15	1	1	NUM
ejpam-4468	149	16	φ⊗ψ	φ⊗ψ	NOUN
ejpam-4468	149	17	′	′	NUM
ejpam-4468	150	1	+	+	NOUN
ejpam-4468	150	2	φ′	φ′	NOUN
ejpam-4468	150	3	⊗	⊗	ADJ
ejpam-4468	150	4	fψ	fψ	NOUN
ejpam-4468	150	5	=	=	PUNCT
ejpam-4468	150	6	φ′′	φ′′	PROPN
ejpam-4468	150	7	⊗ψ	⊗ψ	NOUN
ejpam-4468	150	8	.	.	PUNCT
ejpam-4468	151	1	(	(	PUNCT
ejpam-4468	151	2	5	5	NUM
ejpam-4468	151	3	)	)	PUNCT
ejpam-4468	151	4	since	since	SCONJ
ejpam-4468	151	5	the	the	DET
ejpam-4468	151	6	sum	sum	NOUN
ejpam-4468	151	7	of	of	ADP
ejpam-4468	151	8	two	two	NUM
ejpam-4468	151	9	atoms	atom	NOUN
ejpam-4468	151	10	is	be	AUX
ejpam-4468	151	11	an	an	DET
ejpam-4468	151	12	atom	atom	NOUN
ejpam-4468	151	13	using	use	VERB
ejpam-4468	151	14	lemma	lemma	PROPN
ejpam-4468	151	15	(	(	PUNCT
ejpam-4468	151	16	2	2	NUM
ejpam-4468	151	17	)	)	PUNCT
ejpam-4468	151	18	,	,	PUNCT
ejpam-4468	151	19	we	we	PRON
ejpam-4468	151	20	have	have	VERB
ejpam-4468	151	21	φ′	φ′	NUM
ejpam-4468	151	22	=	=	SYM
ejpam-4468	151	23	φ	φ	PROPN
ejpam-4468	151	24	or	or	CCONJ
ejpam-4468	151	25	ψ′	ψ′	PROPN
ejpam-4468	151	26	=	=	SYM
ejpam-4468	151	27	fψ	fψ	PROPN
ejpam-4468	151	28	.	.	PUNCT
ejpam-4468	151	29	case	case	NOUN
ejpam-4468	151	30	(	(	PUNCT
ejpam-4468	151	31	1	1	X
ejpam-4468	151	32	)	)	PUNCT
ejpam-4468	151	33	if	if	SCONJ
ejpam-4468	151	34	ψ′	ψ′	NUM
ejpam-4468	151	35	=	=	SYM
ejpam-4468	151	36	fψ	fψ	NOUN
ejpam-4468	151	37	,	,	PUNCT
ejpam-4468	151	38	then	then	ADV
ejpam-4468	151	39	ψ′	ψ′	PUNCT
ejpam-4468	151	40	ψ	ψ	PROPN
ejpam-4468	151	41	=	=	SYM
ejpam-4468	152	1	f.	f.	PROPN
ejpam-4468	152	2	integrating	integrate	VERB
ejpam-4468	152	3	both	both	DET
ejpam-4468	152	4	sides	side	NOUN
ejpam-4468	152	5	,	,	PUNCT
ejpam-4468	152	6	we	we	PRON
ejpam-4468	152	7	get	get	VERB
ejpam-4468	152	8	∫	∫	PROPN
ejpam-4468	152	9	t	t	PROPN
ejpam-4468	152	10	0	0	NUM
ejpam-4468	152	11	dψ	dψ	PROPN
ejpam-4468	152	12	ψ	ψ	X
ejpam-4468	152	13	=	=	SYM
ejpam-4468	152	14	∫	∫	PROPN
ejpam-4468	152	15	t	t	PROPN
ejpam-4468	152	16	0	0	NUM
ejpam-4468	152	17	fdu	fdu	PROPN
ejpam-4468	152	18	lnψ	lnψ	PROPN
ejpam-4468	152	19	∣∣∣∣t	∣∣∣∣t	NOUN
ejpam-4468	152	20	0	0	PUNCT
ejpam-4468	153	1	=	=	SYM
ejpam-4468	153	2	∫	∫	PROPN
ejpam-4468	153	3	t	t	PROPN
ejpam-4468	153	4	0	0	NUM
ejpam-4468	153	5	fdu	fdu	PROPN
ejpam-4468	153	6	lnψ−	lnψ−	PROPN
ejpam-4468	153	7	lnψ(0	lnψ(0	NOUN
ejpam-4468	153	8	)	)	PUNCT
ejpam-4468	154	1	=	=	SYM
ejpam-4468	155	1	∫	∫	PROPN
ejpam-4468	155	2	t	t	PROPN
ejpam-4468	155	3	0	0	NUM
ejpam-4468	155	4	fdu	fdu	PROPN
ejpam-4468	155	5	a.	a.	PROPN
ejpam-4468	155	6	al	al	PROPN
ejpam-4468	155	7	-	-	PUNCT
ejpam-4468	155	8	jarrah	jarrah	PROPN
ejpam-4468	155	9	,	,	PUNCT
ejpam-4468	155	10	sh	sh	PROPN
ejpam-4468	155	11	.	.	PROPN
ejpam-4468	155	12	alsharif	alsharif	PROPN
ejpam-4468	155	13	,	,	PUNCT
ejpam-4468	155	14	h.	h.	PROPN
ejpam-4468	155	15	almefleh	almefleh	PROPN
ejpam-4468	155	16	/	/	SYM
ejpam-4468	155	17	eur	eur	PROPN
ejpam-4468	155	18	.	.	PUNCT
ejpam-4468	156	1	j.	j.	PROPN
ejpam-4468	156	2	pure	pure	PROPN
ejpam-4468	156	3	appl	appl	PROPN
ejpam-4468	156	4	.	.	PROPN
ejpam-4468	156	5	math	math	PROPN
ejpam-4468	156	6	,	,	PUNCT
ejpam-4468	156	7	15	15	NUM
ejpam-4468	156	8	(	(	PUNCT
ejpam-4468	156	9	4	4	NUM
ejpam-4468	156	10	)	)	PUNCT
ejpam-4468	156	11	(	(	PUNCT
ejpam-4468	156	12	2022	2022	NUM
ejpam-4468	156	13	)	)	PUNCT
ejpam-4468	156	14	,	,	PUNCT
ejpam-4468	156	15	1444	1444	NUM
ejpam-4468	156	16	-	-	SYM
ejpam-4468	156	17	1454	1454	NUM
ejpam-4468	156	18	1450	1450	NUM
ejpam-4468	157	1	lnψ−	lnψ−	ADP
ejpam-4468	157	2	ln	ln	NOUN
ejpam-4468	157	3	1	1	NUM
ejpam-4468	157	4	=	=	SYM
ejpam-4468	157	5	∫	∫	PROPN
ejpam-4468	157	6	t	t	PROPN
ejpam-4468	157	7	0	0	NUM
ejpam-4468	157	8	fdu	fdu	PROPN
ejpam-4468	157	9	lnψ	lnψ	NOUN
ejpam-4468	157	10	=	=	SYM
ejpam-4468	157	11	∫	∫	PROPN
ejpam-4468	157	12	t	t	PROPN
ejpam-4468	157	13	0	0	NUM
ejpam-4468	157	14	fdu	fdu	PROPN
ejpam-4468	157	15	ψ	ψ	NOUN
ejpam-4468	157	16	=	=	SYM
ejpam-4468	157	17	e	e	PROPN
ejpam-4468	157	18	∫	∫	PROPN
ejpam-4468	157	19	t	t	PROPN
ejpam-4468	157	20	0	0	NUM
ejpam-4468	157	21	fdu	fdu	PROPN
ejpam-4468	157	22	.	.	PUNCT
ejpam-4468	158	1	since	since	SCONJ
ejpam-4468	158	2	ψ′	ψ′	PROPN
ejpam-4468	158	3	=	=	SYM
ejpam-4468	158	4	fψ	fψ	NOUN
ejpam-4468	158	5	,	,	PUNCT
ejpam-4468	158	6	then	then	ADV
ejpam-4468	158	7	equation	equation	NOUN
ejpam-4468	158	8	(	(	PUNCT
ejpam-4468	158	9	5	5	NUM
ejpam-4468	158	10	)	)	PUNCT
ejpam-4468	158	11	becomes	become	VERB
ejpam-4468	158	12	φ⊗	φ⊗	ADJ
ejpam-4468	158	13	fψ+φ′	fψ+φ′	NOUN
ejpam-4468	158	14	⊗	⊗	PROPN
ejpam-4468	158	15	fψ	fψ	PROPN
ejpam-4468	158	16	=	=	PUNCT
ejpam-4468	158	17	φ′′	φ′′	PROPN
ejpam-4468	158	18	⊗ψ	⊗ψ	NOUN
ejpam-4468	159	1	[	[	X
ejpam-4468	159	2	φ	φ	X
ejpam-4468	159	3	+	+	X
ejpam-4468	159	4	φ′]⊗	φ′]⊗	ADJ
ejpam-4468	159	5	fψ	fψ	NOUN
ejpam-4468	159	6	=	=	PUNCT
ejpam-4468	159	7	φ′′	φ′′	PROPN
ejpam-4468	159	8	⊗ψ	⊗ψ	NOUN
ejpam-4468	160	1	[	[	X
ejpam-4468	160	2	φ	φ	X
ejpam-4468	160	3	+	+	X
ejpam-4468	160	4	φ′]⊗	φ′]⊗	PROPN
ejpam-4468	160	5	[	[	X
ejpam-4468	160	6	fψ]−	fψ]−	NOUN
ejpam-4468	160	7	φ′′	φ′′	PROPN
ejpam-4468	160	8	⊗ψ	⊗ψ	NOUN
ejpam-4468	160	9	=	=	SYM
ejpam-4468	160	10	0	0	PUNCT
ejpam-4468	160	11	(	(	PUNCT
ejpam-4468	160	12	[	[	X
ejpam-4468	160	13	φ	φ	X
ejpam-4468	160	14	+	+	X
ejpam-4468	160	15	φ′]f	φ′]f	ADP
ejpam-4468	160	16	−	−	PROPN
ejpam-4468	160	17	φ′′)⊗ψ	φ′′)⊗ψ	PROPN
ejpam-4468	160	18	=	=	NOUN
ejpam-4468	160	19	0	0	PROPN
ejpam-4468	160	20	.	.	PUNCT
ejpam-4468	161	1	using	use	VERB
ejpam-4468	161	2	lemma	lemma	PROPN
ejpam-4468	161	3	(	(	PUNCT
ejpam-4468	161	4	1	1	NUM
ejpam-4468	161	5	)	)	PUNCT
ejpam-4468	161	6	,	,	PUNCT
ejpam-4468	161	7	we	we	PRON
ejpam-4468	161	8	have	have	VERB
ejpam-4468	161	9	[	[	X
ejpam-4468	161	10	φ	φ	X
ejpam-4468	161	11	+	+	SYM
ejpam-4468	161	12	φ′]f	φ′]f	ADP
ejpam-4468	161	13	−	−	PROPN
ejpam-4468	161	14	φ′′	φ′′	PROPN
ejpam-4468	161	15	=	=	SYM
ejpam-4468	161	16	0	0	NUM
ejpam-4468	161	17	or	or	CCONJ
ejpam-4468	161	18	ψ	ψ	X
ejpam-4468	161	19	=	=	NOUN
ejpam-4468	161	20	0	0	X
ejpam-4468	161	21	.	.	PUNCT
ejpam-4468	162	1	if	if	SCONJ
ejpam-4468	162	2	ψ	ψ	X
ejpam-4468	162	3	=	=	SYM
ejpam-4468	162	4	0	0	NUM
ejpam-4468	162	5	,	,	PUNCT
ejpam-4468	162	6	then	then	ADV
ejpam-4468	162	7	we	we	PRON
ejpam-4468	162	8	have	have	VERB
ejpam-4468	162	9	a	a	DET
ejpam-4468	162	10	contradiction	contradiction	NOUN
ejpam-4468	162	11	since	since	SCONJ
ejpam-4468	162	12	ψ	ψ	VERB
ejpam-4468	162	13	̸=	̸=	PROPN
ejpam-4468	162	14	0	0	NUM
ejpam-4468	162	15	.	.	PUNCT
ejpam-4468	163	1	so	so	ADV
ejpam-4468	164	1	[	[	X
ejpam-4468	164	2	φ	φ	X
ejpam-4468	164	3	+	+	SYM
ejpam-4468	164	4	φ′]f	φ′]f	ADP
ejpam-4468	164	5	−	−	PROPN
ejpam-4468	164	6	φ′′	φ′′	PROPN
ejpam-4468	164	7	=	=	SYM
ejpam-4468	164	8	0	0	NUM
ejpam-4468	165	1	φ′′	φ′′	PROPN
ejpam-4468	165	2	φ′	φ′	NUM
ejpam-4468	165	3	+	+	NOUN
ejpam-4468	165	4	φ	φ	NOUN
ejpam-4468	165	5	=	=	SYM
ejpam-4468	165	6	f.	f.	PROPN
ejpam-4468	165	7	contradiction	contradiction	PROPN
ejpam-4468	165	8	,	,	PUNCT
ejpam-4468	165	9	since	since	SCONJ
ejpam-4468	165	10	φ	φ	PROPN
ejpam-4468	165	11	is	be	AUX
ejpam-4468	165	12	a	a	DET
ejpam-4468	165	13	function	function	NOUN
ejpam-4468	165	14	depends	depend	VERB
ejpam-4468	165	15	only	only	ADV
ejpam-4468	165	16	on	on	ADP
ejpam-4468	165	17	x	x	X
ejpam-4468	165	18	,	,	PUNCT
ejpam-4468	165	19	which	which	PRON
ejpam-4468	165	20	means	mean	VERB
ejpam-4468	165	21	that	that	SCONJ
ejpam-4468	165	22	this	this	DET
ejpam-4468	165	23	case	case	NOUN
ejpam-4468	165	24	does	do	AUX
ejpam-4468	165	25	not	not	PART
ejpam-4468	165	26	hold	hold	VERB
ejpam-4468	165	27	.	.	PUNCT
ejpam-4468	166	1	case(2	case(2	NOUN
ejpam-4468	166	2	)	)	PUNCT
ejpam-4468	167	1	if	if	SCONJ
ejpam-4468	167	2	φ′	φ′	NUM
ejpam-4468	167	3	=	=	SYM
ejpam-4468	167	4	φ	φ	PROPN
ejpam-4468	167	5	=	=	SYM
ejpam-4468	167	6	φ′′	φ′′	PROPN
ejpam-4468	167	7	,	,	PUNCT
ejpam-4468	167	8	then	then	ADV
ejpam-4468	167	9	φ′	φ′	NUM
ejpam-4468	167	10	φ	φ	NOUN
ejpam-4468	167	11	=	=	SYM
ejpam-4468	167	12	1	1	X
ejpam-4468	167	13	.	.	X
ejpam-4468	167	14	integrating	integrate	VERB
ejpam-4468	167	15	both	both	DET
ejpam-4468	167	16	sides	side	NOUN
ejpam-4468	167	17	,	,	PUNCT
ejpam-4468	167	18	we	we	PRON
ejpam-4468	167	19	get	get	VERB
ejpam-4468	167	20	:	:	PUNCT
ejpam-4468	167	21	∫	∫	PROPN
ejpam-4468	167	22	dφ	dφ	ADP
ejpam-4468	167	23	φ	φ	PROPN
ejpam-4468	167	24	=	=	SYM
ejpam-4468	167	25	∫	∫	PROPN
ejpam-4468	167	26	dx	dx	PROPN
ejpam-4468	167	27	ln	ln	PROPN
ejpam-4468	167	28	|φ|	|φ|	PROPN
ejpam-4468	167	29	=	=	PUNCT
ejpam-4468	167	30	x+	x+	PROPN
ejpam-4468	167	31	w	w	PROPN
ejpam-4468	167	32	φ	φ	PROPN
ejpam-4468	167	33	=	=	PUNCT
ejpam-4468	167	34	w1e	w1e	PROPN
ejpam-4468	167	35	x	x	X
ejpam-4468	167	36	,	,	PUNCT
ejpam-4468	167	37	since	since	SCONJ
ejpam-4468	167	38	φ(0	φ(0	ADJ
ejpam-4468	167	39	)	)	PUNCT
ejpam-4468	167	40	=	=	SYM
ejpam-4468	168	1	1	1	NUM
ejpam-4468	168	2	=	=	NOUN
ejpam-4468	168	3	⇒	⇒	X
ejpam-4468	168	4	φ	φ	X
ejpam-4468	168	5	=	=	SYM
ejpam-4468	168	6	ex	ex	PROPN
ejpam-4468	168	7	.	.	PUNCT
ejpam-4468	169	1	now	now	ADV
ejpam-4468	169	2	,	,	PUNCT
ejpam-4468	169	3	since	since	SCONJ
ejpam-4468	169	4	the	the	DET
ejpam-4468	169	5	first	first	ADJ
ejpam-4468	169	6	and	and	CCONJ
ejpam-4468	169	7	the	the	DET
ejpam-4468	169	8	second	second	ADJ
ejpam-4468	169	9	derivative	derivative	NOUN
ejpam-4468	169	10	of	of	ADP
ejpam-4468	169	11	φ	φ	PROPN
ejpam-4468	169	12	are	be	AUX
ejpam-4468	169	13	equal	equal	ADJ
ejpam-4468	169	14	then	then	ADV
ejpam-4468	169	15	equation	equation	NOUN
ejpam-4468	169	16	(	(	PUNCT
ejpam-4468	169	17	5	5	X
ejpam-4468	169	18	)	)	PUNCT
ejpam-4468	169	19	become	become	VERB
ejpam-4468	169	20	φ⊗ψ	φ⊗ψ	NOUN
ejpam-4468	169	21	′	′	NUM
ejpam-4468	170	1	+	+	SYM
ejpam-4468	170	2	φ⊗	φ⊗	ADJ
ejpam-4468	170	3	fψ	fψ	NOUN
ejpam-4468	170	4	=	=	SYM
ejpam-4468	170	5	φ⊗ψ	φ⊗ψ	NOUN
ejpam-4468	170	6	φ⊗	φ⊗	NOUN
ejpam-4468	171	1	[	[	X
ejpam-4468	171	2	ψ	ψ	X
ejpam-4468	171	3	′	′	NOUN
ejpam-4468	172	1	+	+	PUNCT
ejpam-4468	172	2	fψ−ψ	fψ−ψ	NOUN
ejpam-4468	172	3	]	]	X
ejpam-4468	172	4	=	=	SYM
ejpam-4468	172	5	0	0	NUM
ejpam-4468	172	6	φ⊗	φ⊗	VERB
ejpam-4468	173	1	[	[	X
ejpam-4468	173	2	ψ	ψ	X
ejpam-4468	173	3	′	′	NOUN
ejpam-4468	174	1	+	+	CCONJ
ejpam-4468	174	2	(	(	PUNCT
ejpam-4468	174	3	f	f	PROPN
ejpam-4468	174	4	−	−	PROPN
ejpam-4468	174	5	1)ψ	1)ψ	NUM
ejpam-4468	174	6	]	]	X
ejpam-4468	174	7	=	=	PUNCT
ejpam-4468	174	8	0	0	X
ejpam-4468	174	9	.	.	PUNCT
ejpam-4468	174	10	thus	thus	ADV
ejpam-4468	174	11	using	use	VERB
ejpam-4468	174	12	lemma	lemma	PROPN
ejpam-4468	174	13	(	(	PUNCT
ejpam-4468	174	14	1	1	X
ejpam-4468	174	15	)	)	PUNCT
ejpam-4468	174	16	either	either	CCONJ
ejpam-4468	174	17	φ	φ	PROPN
ejpam-4468	174	18	=	=	SYM
ejpam-4468	174	19	0	0	NUM
ejpam-4468	174	20	or	or	CCONJ
ejpam-4468	174	21	ψ	ψ	NOUN
ejpam-4468	174	22	′	′	NUM
ejpam-4468	175	1	+	+	CCONJ
ejpam-4468	175	2	(	(	PUNCT
ejpam-4468	175	3	f	f	X
ejpam-4468	175	4	−	−	PROPN
ejpam-4468	175	5	1)ψ	1)ψ	NUM
ejpam-4468	175	6	=	=	SYM
ejpam-4468	175	7	0	0	X
ejpam-4468	175	8	.	.	PUNCT
ejpam-4468	176	1	if	if	SCONJ
ejpam-4468	176	2	φ	φ	PROPN
ejpam-4468	176	3	=	=	SYM
ejpam-4468	176	4	0	0	PROPN
ejpam-4468	176	5	,	,	PUNCT
ejpam-4468	176	6	then	then	ADV
ejpam-4468	176	7	we	we	PRON
ejpam-4468	176	8	have	have	VERB
ejpam-4468	176	9	a	a	DET
ejpam-4468	176	10	contradiction	contradiction	NOUN
ejpam-4468	176	11	since	since	SCONJ
ejpam-4468	176	12	φ	φ	PROPN
ejpam-4468	176	13	̸=	̸=	PROPN
ejpam-4468	176	14	0	0	NUM
ejpam-4468	176	15	.	.	PUNCT
ejpam-4468	177	1	so	so	ADV
ejpam-4468	177	2	ψ	ψ	ADP
ejpam-4468	177	3	′	′	NOUN
ejpam-4468	178	1	+	+	CCONJ
ejpam-4468	178	2	(	(	PUNCT
ejpam-4468	178	3	f	f	X
ejpam-4468	178	4	−	−	PROPN
ejpam-4468	178	5	1)ψ	1)ψ	NUM
ejpam-4468	178	6	=	=	SYM
ejpam-4468	178	7	0	0	NUM
ejpam-4468	178	8	a.	a.	PROPN
ejpam-4468	178	9	al	al	PROPN
ejpam-4468	178	10	-	-	PUNCT
ejpam-4468	178	11	jarrah	jarrah	PROPN
ejpam-4468	178	12	,	,	PUNCT
ejpam-4468	178	13	sh	sh	PROPN
ejpam-4468	178	14	.	.	PROPN
ejpam-4468	178	15	alsharif	alsharif	PROPN
ejpam-4468	178	16	,	,	PUNCT
ejpam-4468	178	17	h.	h.	PROPN
ejpam-4468	178	18	almefleh	almefleh	PROPN
ejpam-4468	178	19	/	/	SYM
ejpam-4468	178	20	eur	eur	PROPN
ejpam-4468	178	21	.	.	PUNCT
ejpam-4468	179	1	j.	j.	PROPN
ejpam-4468	179	2	pure	pure	PROPN
ejpam-4468	179	3	appl	appl	PROPN
ejpam-4468	179	4	.	.	PROPN
ejpam-4468	179	5	math	math	PROPN
ejpam-4468	179	6	,	,	PUNCT
ejpam-4468	179	7	15	15	NUM
ejpam-4468	179	8	(	(	PUNCT
ejpam-4468	179	9	4	4	NUM
ejpam-4468	179	10	)	)	PUNCT
ejpam-4468	179	11	(	(	PUNCT
ejpam-4468	179	12	2022	2022	NUM
ejpam-4468	179	13	)	)	PUNCT
ejpam-4468	179	14	,	,	PUNCT
ejpam-4468	179	15	1444	1444	NUM
ejpam-4468	179	16	-	-	SYM
ejpam-4468	179	17	1454	1454	NUM
ejpam-4468	179	18	1451	1451	NUM
ejpam-4468	179	19	ψ	ψ	NOUN
ejpam-4468	179	20	′	′	NUM
ejpam-4468	179	21	ψ	ψ	NOUN
ejpam-4468	179	22	=	=	SYM
ejpam-4468	179	23	1−	1−	NUM
ejpam-4468	179	24	f∫	f∫	PROPN
ejpam-4468	179	25	dψ	dψ	X
ejpam-4468	179	26	ψ	ψ	NOUN
ejpam-4468	179	27	=	=	SYM
ejpam-4468	179	28	∫	∫	PROPN
ejpam-4468	179	29	(	(	PUNCT
ejpam-4468	179	30	1−	1−	NUM
ejpam-4468	179	31	f)dt	f)dt	PROPN
ejpam-4468	179	32	ln	ln	NOUN
ejpam-4468	179	33	|ψ|	|ψ|	PROPN
ejpam-4468	179	34	=	=	SYM
ejpam-4468	179	35	∫	∫	PROPN
ejpam-4468	179	36	(	(	PUNCT
ejpam-4468	179	37	1−	1−	NUM
ejpam-4468	179	38	f)dt	f)dt	PROPN
ejpam-4468	179	39	ψ	ψ	NOUN
ejpam-4468	179	40	=	=	SYM
ejpam-4468	179	41	e	e	X
ejpam-4468	179	42	∫	∫	PROPN
ejpam-4468	179	43	(	(	PUNCT
ejpam-4468	179	44	1−f)dt	1−f)dt	NOUN
ejpam-4468	179	45	.	.	PUNCT
ejpam-4468	179	46	to	to	PART
ejpam-4468	179	47	verify	verify	VERB
ejpam-4468	179	48	equation	equation	NOUN
ejpam-4468	179	49	(	(	PUNCT
ejpam-4468	179	50	5	5	NUM
ejpam-4468	179	51	)	)	PUNCT
ejpam-4468	179	52	,	,	PUNCT
ejpam-4468	179	53	set	set	VERB
ejpam-4468	179	54	φ	φ	NOUN
ejpam-4468	179	55	=	=	SYM
ejpam-4468	179	56	ex	ex	X
ejpam-4468	179	57	=	=	NOUN
ejpam-4468	179	58	φ′	φ′	NUM
ejpam-4468	179	59	=	=	SYM
ejpam-4468	179	60	φ′′	φ′′	PROPN
ejpam-4468	179	61	and	and	CCONJ
ejpam-4468	179	62	ψ	ψ	X
ejpam-4468	179	63	=	=	SYM
ejpam-4468	179	64	e	e	X
ejpam-4468	179	65	∫	∫	PROPN
ejpam-4468	179	66	(	(	PUNCT
ejpam-4468	179	67	1−f)dt	1−f)dt	NUM
ejpam-4468	179	68	and	and	CCONJ
ejpam-4468	179	69	ψ′	ψ′	PROPN
ejpam-4468	180	1	=	=	PUNCT
ejpam-4468	180	2	(	(	PUNCT
ejpam-4468	180	3	1−f)e	1−f)e	NUM
ejpam-4468	180	4	∫	∫	PROPN
ejpam-4468	180	5	(	(	PUNCT
ejpam-4468	180	6	1−f)dt	1−f)dt	NUM
ejpam-4468	180	7	=	=	SYM
ejpam-4468	180	8	(	(	PUNCT
ejpam-4468	180	9	1	1	NUM
ejpam-4468	180	10	−	−	NOUN
ejpam-4468	180	11	f)ψ	f)ψ	ADJ
ejpam-4468	180	12	,	,	PUNCT
ejpam-4468	180	13	then	then	ADV
ejpam-4468	180	14	u	u	X
ejpam-4468	180	15	=	=	PROPN
ejpam-4468	180	16	φ	φ	PROPN
ejpam-4468	180	17	⊗	⊗	PROPN
ejpam-4468	180	18	ψ	ψ	PROPN
ejpam-4468	180	19	,	,	PUNCT
ejpam-4468	180	20	ux	ux	PROPN
ejpam-4468	180	21	=	=	SYM
ejpam-4468	180	22	φ′	φ′	NUM
ejpam-4468	180	23	⊗	⊗	NOUN
ejpam-4468	180	24	ψ	ψ	X
ejpam-4468	180	25	=	=	SYM
ejpam-4468	180	26	φ	φ	PROPN
ejpam-4468	180	27	⊗	⊗	PROPN
ejpam-4468	180	28	ψ	ψ	PROPN
ejpam-4468	180	29	,	,	PUNCT
ejpam-4468	180	30	uxx	uxx	X
ejpam-4468	180	31	=	=	SYM
ejpam-4468	181	1	φ′′	φ′′	PROPN
ejpam-4468	181	2	⊗	⊗	PROPN
ejpam-4468	181	3	ψ	ψ	X
ejpam-4468	181	4	=	=	SYM
ejpam-4468	181	5	φ	φ	PROPN
ejpam-4468	181	6	⊗	⊗	PROPN
ejpam-4468	181	7	ψ	ψ	PROPN
ejpam-4468	181	8	,	,	PUNCT
ejpam-4468	181	9	and	and	CCONJ
ejpam-4468	181	10	ut	ut	PROPN
ejpam-4468	181	11	=	=	SYM
ejpam-4468	182	1	φ⊗ψ′	φ⊗ψ′	PROPN
ejpam-4468	182	2	=	=	NOUN
ejpam-4468	182	3	φ⊗	φ⊗	NOUN
ejpam-4468	182	4	(	(	PUNCT
ejpam-4468	182	5	1−	1−	NUM
ejpam-4468	182	6	f)ψ	f)ψ	X
ejpam-4468	182	7	.	.	PUNCT
ejpam-4468	183	1	then	then	ADV
ejpam-4468	183	2	ut	ut	PROPN
ejpam-4468	183	3	+	+	CCONJ
ejpam-4468	183	4	fux	fux	PROPN
ejpam-4468	183	5	=	=	PUNCT
ejpam-4468	183	6	φ⊗	φ⊗	PROPN
ejpam-4468	183	7	(	(	PUNCT
ejpam-4468	183	8	1−	1−	NUM
ejpam-4468	183	9	f)ψ	f)ψ	X
ejpam-4468	183	10	+	+	SYM
ejpam-4468	183	11	f(φ⊗ψ	f(φ⊗ψ	X
ejpam-4468	183	12	)	)	PUNCT
ejpam-4468	183	13	=	=	SYM
ejpam-4468	183	14	(	(	PUNCT
ejpam-4468	183	15	1−	1−	NUM
ejpam-4468	183	16	f)(φ⊗ψ	f)(φ⊗ψ	PROPN
ejpam-4468	183	17	)	)	PUNCT
ejpam-4468	184	1	+	+	SYM
ejpam-4468	184	2	f(φ⊗ψ	f(φ⊗ψ	X
ejpam-4468	184	3	)	)	PUNCT
ejpam-4468	184	4	=	=	SYM
ejpam-4468	184	5	(	(	PUNCT
ejpam-4468	184	6	φ⊗ψ)−	φ⊗ψ)−	X
ejpam-4468	184	7	f(φ⊗ψ	f(φ⊗ψ	X
ejpam-4468	184	8	)	)	PUNCT
ejpam-4468	184	9	+	+	CCONJ
ejpam-4468	184	10	f(φ⊗ψ	f(φ⊗ψ	X
ejpam-4468	184	11	)	)	PUNCT
ejpam-4468	184	12	=	=	SYM
ejpam-4468	184	13	φ⊗ψ	φ⊗ψ	PROPN
ejpam-4468	184	14	=	=	SYM
ejpam-4468	184	15	uxx	uxx	PROPN
ejpam-4468	184	16	,	,	PUNCT
ejpam-4468	184	17	this	this	PRON
ejpam-4468	184	18	implies	imply	VERB
ejpam-4468	184	19	u	u	NOUN
ejpam-4468	184	20	=	=	PRON
ejpam-4468	184	21	φ⊗ψ	φ⊗ψ	PROPN
ejpam-4468	184	22	is	be	AUX
ejpam-4468	184	23	a	a	DET
ejpam-4468	184	24	solution	solution	NOUN
ejpam-4468	184	25	of	of	ADP
ejpam-4468	184	26	equation	equation	NOUN
ejpam-4468	184	27	(	(	PUNCT
ejpam-4468	184	28	4	4	NUM
ejpam-4468	184	29	)	)	PUNCT
ejpam-4468	184	30	,	,	PUNCT
ejpam-4468	184	31	where	where	SCONJ
ejpam-4468	184	32	φ	φ	PROPN
ejpam-4468	184	33	=	=	SYM
ejpam-4468	184	34	ex	ex	X
ejpam-4468	184	35	and	and	CCONJ
ejpam-4468	184	36	ψ	ψ	X
ejpam-4468	184	37	=	=	SYM
ejpam-4468	184	38	e	e	X
ejpam-4468	184	39	∫	∫	PROPN
ejpam-4468	184	40	(	(	PUNCT
ejpam-4468	184	41	1−f)dt	1−f)dt	NUM
ejpam-4468	184	42	.	.	PUNCT
ejpam-4468	185	1	now	now	ADV
ejpam-4468	185	2	,	,	PUNCT
ejpam-4468	185	3	if	if	SCONJ
ejpam-4468	185	4	f(t	f(t	NOUN
ejpam-4468	185	5	)	)	PUNCT
ejpam-4468	185	6	=	=	SYM
ejpam-4468	185	7	t2	t2	NOUN
ejpam-4468	185	8	,	,	PUNCT
ejpam-4468	185	9	then	then	ADV
ejpam-4468	185	10	equation	equation	NOUN
ejpam-4468	185	11	(	(	PUNCT
ejpam-4468	185	12	4	4	X
ejpam-4468	185	13	)	)	PUNCT
ejpam-4468	185	14	becomes	become	VERB
ejpam-4468	185	15	ut	ut	PROPN
ejpam-4468	185	16	+	+	NUM
ejpam-4468	185	17	t2ux	t2ux	SYM
ejpam-4468	185	18	=	=	SYM
ejpam-4468	185	19	uxx	uxx	NOUN
ejpam-4468	185	20	,	,	PUNCT
ejpam-4468	185	21	which	which	PRON
ejpam-4468	185	22	has	have	VERB
ejpam-4468	185	23	the	the	DET
ejpam-4468	185	24	solution	solution	NOUN
ejpam-4468	185	25	u	u	NOUN
ejpam-4468	185	26	=	=	PUNCT
ejpam-4468	185	27	φ⊗ψ	φ⊗ψ	PROPN
ejpam-4468	185	28	,	,	PUNCT
ejpam-4468	185	29	where	where	SCONJ
ejpam-4468	185	30	φ	φ	PROPN
ejpam-4468	185	31	=	=	SYM
ejpam-4468	185	32	ex	ex	X
ejpam-4468	185	33	and	and	CCONJ
ejpam-4468	185	34	ψ	ψ	X
ejpam-4468	185	35	=	=	SYM
ejpam-4468	185	36	e	e	X
ejpam-4468	185	37	∫	∫	PROPN
ejpam-4468	185	38	(	(	PUNCT
ejpam-4468	185	39	1−t2)dt	1−t2)dt	NOUN
ejpam-4468	185	40	=	=	SYM
ejpam-4468	185	41	et−	et−	NUM
ejpam-4468	185	42	t3	t3	NOUN
ejpam-4468	185	43	3	3	NUM
ejpam-4468	185	44	.	.	PUNCT
ejpam-4468	186	1	4	4	X
ejpam-4468	186	2	.	.	X
ejpam-4468	186	3	atomic	atomic	ADJ
ejpam-4468	186	4	solution	solution	NOUN
ejpam-4468	186	5	of	of	ADP
ejpam-4468	186	6	burger	burger	NOUN
ejpam-4468	186	7	equation	equation	NOUN
ejpam-4468	186	8	theorem	theorem	VERB
ejpam-4468	186	9	4	4	NUM
ejpam-4468	186	10	.	.	PUNCT
ejpam-4468	187	1	let	let	VERB
ejpam-4468	187	2	u(x	u(x	NOUN
ejpam-4468	187	3	,	,	PUNCT
ejpam-4468	187	4	t	t	PROPN
ejpam-4468	187	5	)	)	PUNCT
ejpam-4468	187	6	∈	∈	PROPN
ejpam-4468	187	7	c(i	c(i	VERB
ejpam-4468	187	8	×	×	PROPN
ejpam-4468	187	9	j	j	PROPN
ejpam-4468	187	10	)	)	PUNCT
ejpam-4468	187	11	,	,	PUNCT
ejpam-4468	187	12	where	where	SCONJ
ejpam-4468	187	13	i	i	PRON
ejpam-4468	187	14	,	,	PUNCT
ejpam-4468	187	15	j	j	PROPN
ejpam-4468	188	1	=	=	PUNCT
ejpam-4468	189	1	[	[	X
ejpam-4468	189	2	0	0	NUM
ejpam-4468	189	3	,	,	PUNCT
ejpam-4468	189	4	1	1	NUM
ejpam-4468	189	5	]	]	PUNCT
ejpam-4468	189	6	or	or	CCONJ
ejpam-4468	189	7	[	[	X
ejpam-4468	189	8	0,∞	0,∞	NUM
ejpam-4468	189	9	)	)	PUNCT
ejpam-4468	189	10	.	.	PUNCT
ejpam-4468	190	1	if	if	SCONJ
ejpam-4468	190	2	u	u	NOUN
ejpam-4468	190	3	has	have	VERB
ejpam-4468	190	4	continuous	continuous	ADJ
ejpam-4468	190	5	second	second	ADJ
ejpam-4468	190	6	partial	partial	ADJ
ejpam-4468	190	7	derivatives	derivative	NOUN
ejpam-4468	190	8	,	,	PUNCT
ejpam-4468	190	9	then	then	ADV
ejpam-4468	190	10	the	the	DET
ejpam-4468	190	11	differential	differential	ADJ
ejpam-4468	190	12	equation	equation	NOUN
ejpam-4468	190	13	ut	ut	PROPN
ejpam-4468	191	1	+	+	CCONJ
ejpam-4468	191	2	αuux	αuux	NOUN
ejpam-4468	191	3	=	=	SYM
ejpam-4468	191	4	υuxx	υuxx	NOUN
ejpam-4468	191	5	(	(	PUNCT
ejpam-4468	191	6	6	6	NUM
ejpam-4468	191	7	)	)	PUNCT
ejpam-4468	191	8	has	have	VERB
ejpam-4468	191	9	an	an	DET
ejpam-4468	191	10	atomic	atomic	ADJ
ejpam-4468	191	11	solution	solution	NOUN
ejpam-4468	191	12	.	.	PUNCT
ejpam-4468	192	1	proof	proof	NOUN
ejpam-4468	192	2	.	.	PUNCT
ejpam-4468	193	1	put	put	VERB
ejpam-4468	193	2	u	u	NOUN
ejpam-4468	193	3	=	=	PUNCT
ejpam-4468	193	4	φ⊗ψ	φ⊗ψ	NOUN
ejpam-4468	193	5	where	where	SCONJ
ejpam-4468	193	6	φ(0	φ(0	ADJ
ejpam-4468	193	7	)	)	PUNCT
ejpam-4468	193	8	=	=	SYM
ejpam-4468	193	9	0	0	NUM
ejpam-4468	193	10	and	and	CCONJ
ejpam-4468	193	11	ψ(1	ψ(1	PRON
ejpam-4468	193	12	)	)	PUNCT
ejpam-4468	193	13	=	=	SYM
ejpam-4468	193	14	1	1	NUM
ejpam-4468	193	15	,	,	PUNCT
ejpam-4468	193	16	to	to	PART
ejpam-4468	193	17	get	get	VERB
ejpam-4468	193	18	φ⊗ψ′	φ⊗ψ′	PROPN
ejpam-4468	193	19	+	+	NUM
ejpam-4468	193	20	α[φ⊗ψ][φ′	α[φ⊗ψ][φ′	NUM
ejpam-4468	193	21	⊗ψ	⊗ψ	VERB
ejpam-4468	193	22	]	]	PUNCT
ejpam-4468	194	1	=	=	SYM
ejpam-4468	194	2	υφ′′	υφ′′	INTJ
ejpam-4468	194	3	⊗ψ	⊗ψ	NOUN
ejpam-4468	194	4	.	.	PUNCT
ejpam-4468	195	1	(	(	PUNCT
ejpam-4468	195	2	7	7	X
ejpam-4468	195	3	)	)	PUNCT
ejpam-4468	195	4	the	the	DET
ejpam-4468	195	5	product	product	NOUN
ejpam-4468	195	6	of	of	ADP
ejpam-4468	195	7	two	two	NUM
ejpam-4468	195	8	atoms	atom	NOUN
ejpam-4468	195	9	is	be	AUX
ejpam-4468	195	10	one	one	NUM
ejpam-4468	195	11	atom	atom	NOUN
ejpam-4468	195	12	(	(	PUNCT
ejpam-4468	195	13	φ⊗ψ)(φ′⊗ψ	φ⊗ψ)(φ′⊗ψ	NOUN
ejpam-4468	195	14	)	)	PUNCT
ejpam-4468	195	15	=	=	SYM
ejpam-4468	195	16	(	(	PUNCT
ejpam-4468	195	17	φφ′⊗ψψ	φφ′⊗ψψ	NOUN
ejpam-4468	195	18	)	)	PUNCT
ejpam-4468	195	19	,	,	PUNCT
ejpam-4468	195	20	so	so	SCONJ
ejpam-4468	195	21	that	that	SCONJ
ejpam-4468	195	22	equation	equation	NOUN
ejpam-4468	195	23	(	(	PUNCT
ejpam-4468	195	24	6	6	NUM
ejpam-4468	195	25	)	)	PUNCT
ejpam-4468	195	26	becomes	become	VERB
ejpam-4468	196	1	φ⊗ψ′	φ⊗ψ′	PROPN
ejpam-4468	196	2	+	+	NUM
ejpam-4468	196	3	αφφ′	αφφ′	PROPN
ejpam-4468	196	4	⊗ψ2	⊗ψ2	NOUN
ejpam-4468	196	5	=	=	PUNCT
ejpam-4468	196	6	υφ′′	υφ′′	NUM
ejpam-4468	196	7	⊗ψ	⊗ψ	NOUN
ejpam-4468	196	8	,	,	PUNCT
ejpam-4468	196	9	(	(	PUNCT
ejpam-4468	196	10	8)	8)	NUM
ejpam-4468	196	11	a.	a.	NOUN
ejpam-4468	196	12	al	al	PROPN
ejpam-4468	196	13	-	-	PUNCT
ejpam-4468	196	14	jarrah	jarrah	PROPN
ejpam-4468	196	15	,	,	PUNCT
ejpam-4468	196	16	sh	sh	PROPN
ejpam-4468	196	17	.	.	PROPN
ejpam-4468	196	18	alsharif	alsharif	PROPN
ejpam-4468	196	19	,	,	PUNCT
ejpam-4468	196	20	h.	h.	PROPN
ejpam-4468	196	21	almefleh	almefleh	PROPN
ejpam-4468	196	22	/	/	SYM
ejpam-4468	196	23	eur	eur	PROPN
ejpam-4468	196	24	.	.	PUNCT
ejpam-4468	197	1	j.	j.	PROPN
ejpam-4468	197	2	pure	pure	PROPN
ejpam-4468	197	3	appl	appl	PROPN
ejpam-4468	197	4	.	.	PROPN
ejpam-4468	197	5	math	math	PROPN
ejpam-4468	197	6	,	,	PUNCT
ejpam-4468	197	7	15	15	NUM
ejpam-4468	197	8	(	(	PUNCT
ejpam-4468	197	9	4	4	NUM
ejpam-4468	197	10	)	)	PUNCT
ejpam-4468	197	11	(	(	PUNCT
ejpam-4468	197	12	2022	2022	NUM
ejpam-4468	197	13	)	)	PUNCT
ejpam-4468	197	14	,	,	PUNCT
ejpam-4468	197	15	1444	1444	NUM
ejpam-4468	197	16	-	-	SYM
ejpam-4468	197	17	1454	1454	NUM
ejpam-4468	197	18	1452	1452	NUM
ejpam-4468	197	19	and	and	CCONJ
ejpam-4468	197	20	the	the	DET
ejpam-4468	197	21	sum	sum	NOUN
ejpam-4468	197	22	of	of	ADP
ejpam-4468	197	23	two	two	NUM
ejpam-4468	197	24	atoms	atom	NOUN
ejpam-4468	197	25	is	be	AUX
ejpam-4468	197	26	an	an	DET
ejpam-4468	197	27	atom	atom	NOUN
ejpam-4468	197	28	using	use	VERB
ejpam-4468	197	29	lemma	lemma	PROPN
ejpam-4468	197	30	1	1	NUM
ejpam-4468	197	31	,	,	PUNCT
ejpam-4468	197	32	we	we	PRON
ejpam-4468	197	33	have	have	VERB
ejpam-4468	197	34	αφ′φ	αφ′φ	NOUN
ejpam-4468	197	35	=	=	SYM
ejpam-4468	197	36	φ	φ	PROPN
ejpam-4468	197	37	or	or	CCONJ
ejpam-4468	197	38	ψ′	ψ′	PROPN
ejpam-4468	197	39	=	=	PUNCT
ejpam-4468	197	40	ψ2	ψ2	NOUN
ejpam-4468	197	41	.	.	PUNCT
ejpam-4468	198	1	case	case	NOUN
ejpam-4468	198	2	(	(	PUNCT
ejpam-4468	198	3	1	1	X
ejpam-4468	198	4	)	)	PUNCT
ejpam-4468	198	5	if	if	SCONJ
ejpam-4468	198	6	ψ′	ψ′	PUNCT
ejpam-4468	198	7	=	=	PUNCT
ejpam-4468	198	8	ψ2	ψ2	NOUN
ejpam-4468	198	9	,	,	PUNCT
ejpam-4468	198	10	then	then	ADV
ejpam-4468	198	11	ψ′	ψ′	VERB
ejpam-4468	198	12	ψ2	ψ2	NOUN
ejpam-4468	198	13	=	=	SYM
ejpam-4468	198	14	1	1	X
ejpam-4468	198	15	.	.	X
ejpam-4468	198	16	integrating	integrate	VERB
ejpam-4468	198	17	both	both	DET
ejpam-4468	198	18	sides	side	NOUN
ejpam-4468	198	19	,	,	PUNCT
ejpam-4468	198	20	we	we	PRON
ejpam-4468	198	21	get	get	VERB
ejpam-4468	198	22	∫	∫	PROPN
ejpam-4468	198	23	dψ	dψ	NOUN
ejpam-4468	198	24	ψ2	ψ2	NOUN
ejpam-4468	198	25	=	=	SYM
ejpam-4468	199	1	∫	∫	PROPN
ejpam-4468	199	2	dt	dt	X
ejpam-4468	199	3	1	1	NUM
ejpam-4468	199	4	ψ	ψ	NOUN
ejpam-4468	199	5	=	=	X
ejpam-4468	199	6	−t+	−t+	ADJ
ejpam-4468	199	7	g	g	NOUN
ejpam-4468	199	8	ψ	ψ	NOUN
ejpam-4468	199	9	=	=	X
ejpam-4468	199	10	−1	−1	NOUN
ejpam-4468	199	11	t	t	NOUN
ejpam-4468	199	12	+	+	CCONJ
ejpam-4468	199	13	g1	g1	NOUN
ejpam-4468	199	14	,	,	PUNCT
ejpam-4468	199	15	since	since	SCONJ
ejpam-4468	199	16	ψ(1	ψ(1	PRON
ejpam-4468	199	17	)	)	PUNCT
ejpam-4468	199	18	=	=	SYM
ejpam-4468	199	19	1	1	NUM
ejpam-4468	199	20	=	=	AUX
ejpam-4468	199	21	⇒	⇒	NOUN
ejpam-4468	199	22	ψ	ψ	X
ejpam-4468	199	23	=	=	X
ejpam-4468	199	24	−1	−1	NOUN
ejpam-4468	199	25	t	t	NOUN
ejpam-4468	199	26	+	+	CCONJ
ejpam-4468	199	27	2	2	X
ejpam-4468	199	28	.	.	PUNCT
ejpam-4468	199	29	now	now	ADV
ejpam-4468	199	30	,	,	PUNCT
ejpam-4468	199	31	ψ2	ψ2	NOUN
ejpam-4468	199	32	=	=	SYM
ejpam-4468	199	33	1	1	NUM
ejpam-4468	199	34	t2	t2	NOUN
ejpam-4468	199	35	−	−	PROPN
ejpam-4468	199	36	4(1	4(1	NOUN
ejpam-4468	199	37	t	t	NOUN
ejpam-4468	199	38	−	−	NOUN
ejpam-4468	199	39	1	1	X
ejpam-4468	199	40	)	)	PUNCT
ejpam-4468	199	41	̸=	̸=	PROPN
ejpam-4468	199	42	1	1	NUM
ejpam-4468	199	43	t2	t2	NOUN
ejpam-4468	199	44	=	=	SYM
ejpam-4468	199	45	ψ′	ψ′	PROPN
ejpam-4468	199	46	,	,	PUNCT
ejpam-4468	199	47	which	which	PRON
ejpam-4468	199	48	means	mean	VERB
ejpam-4468	199	49	this	this	DET
ejpam-4468	199	50	case	case	NOUN
ejpam-4468	199	51	dose	dose	VERB
ejpam-4468	199	52	not	not	PART
ejpam-4468	199	53	hold	hold	VERB
ejpam-4468	199	54	.	.	PUNCT
ejpam-4468	200	1	but	but	CCONJ
ejpam-4468	200	2	,	,	PUNCT
ejpam-4468	200	3	if	if	SCONJ
ejpam-4468	200	4	we	we	PRON
ejpam-4468	200	5	take	take	VERB
ejpam-4468	200	6	g	g	NOUN
ejpam-4468	200	7	=	=	NOUN
ejpam-4468	200	8	0	0	NUM
ejpam-4468	200	9	to	to	PART
ejpam-4468	200	10	hold	hold	VERB
ejpam-4468	200	11	this	this	DET
ejpam-4468	200	12	case	case	NOUN
ejpam-4468	200	13	we	we	PRON
ejpam-4468	200	14	get	get	VERB
ejpam-4468	200	15	ψ	ψ	X
ejpam-4468	200	16	=	=	X
ejpam-4468	200	17	−1	−1	NOUN
ejpam-4468	200	18	t	t	NOUN
ejpam-4468	200	19	,	,	PUNCT
ejpam-4468	200	20	so	so	ADV
ejpam-4468	200	21	ψ′	ψ′	PUNCT
ejpam-4468	200	22	=	=	SYM
ejpam-4468	200	23	1	1	NUM
ejpam-4468	200	24	t2	t2	NOUN
ejpam-4468	200	25	=	=	PUNCT
ejpam-4468	200	26	ψ2	ψ2	NOUN
ejpam-4468	200	27	,	,	PUNCT
ejpam-4468	200	28	then	then	ADV
ejpam-4468	200	29	equation	equation	NOUN
ejpam-4468	200	30	(	(	PUNCT
ejpam-4468	200	31	8)	8)	NUM
ejpam-4468	200	32	becomes	become	VERB
ejpam-4468	200	33	φ⊗ψ2	φ⊗ψ2	PROPN
ejpam-4468	200	34	+	+	CCONJ
ejpam-4468	201	1	αφφ′	αφφ′	PROPN
ejpam-4468	201	2	⊗ψ2	⊗ψ2	NOUN
ejpam-4468	201	3	=	=	PUNCT
ejpam-4468	202	1	υφ′′	υφ′′	INTJ
ejpam-4468	202	2	⊗ψ	⊗ψ	NOUN
ejpam-4468	203	1	[	[	X
ejpam-4468	203	2	φ	φ	X
ejpam-4468	203	3	+	+	PROPN
ejpam-4468	203	4	αφφ′]⊗ψ2	αφφ′]⊗ψ2	NOUN
ejpam-4468	203	5	=	=	SYM
ejpam-4468	203	6	υφ′′	υφ′′	NOUN
ejpam-4468	203	7	⊗ψ	⊗ψ	NOUN
ejpam-4468	203	8	.	.	PUNCT
ejpam-4468	204	1	thus	thus	ADV
ejpam-4468	204	2	φ	φ	PROPN
ejpam-4468	204	3	+	+	CCONJ
ejpam-4468	204	4	αφφ′	αφφ′	PROPN
ejpam-4468	204	5	=	=	PUNCT
ejpam-4468	204	6	υφ′′	υφ′′	INTJ
ejpam-4468	204	7	and	and	CCONJ
ejpam-4468	204	8	ψ2	ψ2	NOUN
ejpam-4468	204	9	=	=	SYM
ejpam-4468	204	10	ψ	ψ	NOUN
ejpam-4468	204	11	,	,	PUNCT
ejpam-4468	204	12	when	when	SCONJ
ejpam-4468	204	13	ψ2	ψ2	NOUN
ejpam-4468	204	14	=	=	SYM
ejpam-4468	204	15	ψ	ψ	NOUN
ejpam-4468	204	16	implies	imply	VERB
ejpam-4468	204	17	ψ	ψ	X
ejpam-4468	204	18	=	=	SYM
ejpam-4468	204	19	1	1	X
ejpam-4468	204	20	.	.	PUNCT
ejpam-4468	205	1	contradiction	contradiction	NOUN
ejpam-4468	205	2	,	,	PUNCT
ejpam-4468	205	3	since	since	SCONJ
ejpam-4468	205	4	ψ	ψ	X
ejpam-4468	205	5	=	=	X
ejpam-4468	205	6	−1	−1	NOUN
ejpam-4468	205	7	t	t	PROPN
ejpam-4468	205	8	,	,	PUNCT
ejpam-4468	205	9	which	which	PRON
ejpam-4468	205	10	means	mean	VERB
ejpam-4468	205	11	that	that	SCONJ
ejpam-4468	205	12	this	this	DET
ejpam-4468	205	13	case	case	NOUN
ejpam-4468	205	14	does	do	AUX
ejpam-4468	205	15	not	not	PART
ejpam-4468	205	16	hold	hold	VERB
ejpam-4468	205	17	.	.	PUNCT
ejpam-4468	206	1	case	case	NOUN
ejpam-4468	206	2	(	(	PUNCT
ejpam-4468	206	3	2	2	NUM
ejpam-4468	206	4	)	)	PUNCT
ejpam-4468	207	1	if	if	SCONJ
ejpam-4468	207	2	αφφ′	αφφ′	PROPN
ejpam-4468	207	3	=	=	SYM
ejpam-4468	207	4	φ	φ	PROPN
ejpam-4468	207	5	,	,	PUNCT
ejpam-4468	207	6	then	then	ADV
ejpam-4468	207	7	φ′	φ′	NUM
ejpam-4468	207	8	=	=	SYM
ejpam-4468	207	9	1	1	NUM
ejpam-4468	207	10	α∫	α∫	NUM
ejpam-4468	207	11	dφ	dφ	ADP
ejpam-4468	207	12	=	=	PUNCT
ejpam-4468	207	13	∫	∫	PROPN
ejpam-4468	207	14	1	1	NUM
ejpam-4468	207	15	α	α	PROPN
ejpam-4468	207	16	dx	dx	PROPN
ejpam-4468	207	17	φ	φ	PROPN
ejpam-4468	207	18	=	=	PROPN
ejpam-4468	207	19	x	x	SYM
ejpam-4468	207	20	α	α	PROPN
ejpam-4468	207	21	+	+	CCONJ
ejpam-4468	207	22	q	q	ADJ
ejpam-4468	207	23	,	,	PUNCT
ejpam-4468	207	24	since	since	SCONJ
ejpam-4468	207	25	φ(0	φ(0	ADJ
ejpam-4468	207	26	)	)	PUNCT
ejpam-4468	207	27	=	=	SYM
ejpam-4468	207	28	0	0	PUNCT
ejpam-4468	208	1	=	=	NOUN
ejpam-4468	208	2	⇒	⇒	X
ejpam-4468	208	3	φ	φ	NOUN
ejpam-4468	208	4	=	=	SYM
ejpam-4468	208	5	x	x	SYM
ejpam-4468	208	6	α	α	NOUN
ejpam-4468	208	7	.	.	PUNCT
ejpam-4468	209	1	now	now	ADV
ejpam-4468	209	2	,	,	PUNCT
ejpam-4468	209	3	φ′	φ′	NUM
ejpam-4468	209	4	=	=	SYM
ejpam-4468	209	5	1	1	NUM
ejpam-4468	209	6	α	α	NOUN
ejpam-4468	209	7	and	and	CCONJ
ejpam-4468	209	8	φ′′	φ′′	PROPN
ejpam-4468	209	9	=	=	PROPN
ejpam-4468	209	10	0	0	PROPN
ejpam-4468	209	11	,	,	PUNCT
ejpam-4468	209	12	then	then	ADV
ejpam-4468	209	13	equation	equation	NOUN
ejpam-4468	209	14	(	(	PUNCT
ejpam-4468	209	15	8)	8)	NUM
ejpam-4468	209	16	becomes	become	VERB
ejpam-4468	209	17	φ⊗ψ	φ⊗ψ	NOUN
ejpam-4468	209	18	′	′	NUM
ejpam-4468	210	1	+	+	CCONJ
ejpam-4468	210	2	α	α	NOUN
ejpam-4468	210	3	1	1	NUM
ejpam-4468	210	4	α	α	NOUN
ejpam-4468	210	5	φ⊗ψ2	φ⊗ψ2	NOUN
ejpam-4468	210	6	=	=	PUNCT
ejpam-4468	210	7	0⊗	0⊗	NUM
ejpam-4468	210	8	υψ	υψ	X
ejpam-4468	211	1	[	[	X
ejpam-4468	211	2	ψ	ψ	X
ejpam-4468	211	3	′	′	NUM
ejpam-4468	212	1	+	+	NOUN
ejpam-4468	212	2	ψ2]⊗	ψ2]⊗	X
ejpam-4468	212	3	φ	φ	X
ejpam-4468	212	4	=	=	SYM
ejpam-4468	212	5	0	0	PROPN
ejpam-4468	212	6	.	.	PUNCT
ejpam-4468	212	7	references	reference	NOUN
ejpam-4468	212	8	1453	1453	NUM
ejpam-4468	212	9	so	so	ADV
ejpam-4468	212	10	,	,	PUNCT
ejpam-4468	212	11	φ	φ	PROPN
ejpam-4468	212	12	=	=	SYM
ejpam-4468	212	13	0	0	NUM
ejpam-4468	212	14	or	or	CCONJ
ejpam-4468	212	15	ψ	ψ	NOUN
ejpam-4468	212	16	′	′	NUM
ejpam-4468	213	1	+	+	ADJ
ejpam-4468	213	2	ψ2	ψ2	NOUN
ejpam-4468	213	3	=	=	SYM
ejpam-4468	213	4	0	0	X
ejpam-4468	213	5	.	.	PUNCT
ejpam-4468	214	1	if	if	SCONJ
ejpam-4468	214	2	φ	φ	PROPN
ejpam-4468	214	3	=	=	SYM
ejpam-4468	214	4	0	0	PROPN
ejpam-4468	214	5	,	,	PUNCT
ejpam-4468	214	6	it	it	PRON
ejpam-4468	214	7	is	be	AUX
ejpam-4468	214	8	a	a	DET
ejpam-4468	214	9	contradiction	contradiction	NOUN
ejpam-4468	214	10	since	since	SCONJ
ejpam-4468	214	11	φ	φ	PROPN
ejpam-4468	214	12	̸=	̸=	PROPN
ejpam-4468	214	13	0	0	NUM
ejpam-4468	214	14	.	.	PUNCT
ejpam-4468	215	1	hence	hence	ADV
ejpam-4468	215	2	ψ	ψ	ADP
ejpam-4468	215	3	′	′	NUM
ejpam-4468	216	1	+	+	ADJ
ejpam-4468	216	2	ψ2	ψ2	NOUN
ejpam-4468	216	3	=	=	SYM
ejpam-4468	216	4	0∫	0∫	NUM
ejpam-4468	216	5	−dψ	−dψ	PROPN
ejpam-4468	216	6	ψ2	ψ2	NOUN
ejpam-4468	216	7	=	=	SYM
ejpam-4468	217	1	∫	∫	PROPN
ejpam-4468	217	2	dt	dt	X
ejpam-4468	217	3	1	1	NUM
ejpam-4468	217	4	ψ	ψ	NOUN
ejpam-4468	217	5	=	=	PUNCT
ejpam-4468	217	6	t+	t+	PUNCT
ejpam-4468	217	7	c	c	X
ejpam-4468	217	8	,	,	PUNCT
ejpam-4468	217	9	since	since	SCONJ
ejpam-4468	217	10	ψ(1	ψ(1	PRON
ejpam-4468	217	11	)	)	PUNCT
ejpam-4468	217	12	=	=	SYM
ejpam-4468	217	13	1	1	NUM
ejpam-4468	217	14	=	=	NOUN
ejpam-4468	217	15	⇒	⇒	NOUN
ejpam-4468	217	16	ψ	ψ	X
ejpam-4468	217	17	=	=	SYM
ejpam-4468	217	18	1	1	NUM
ejpam-4468	217	19	t	t	NOUN
ejpam-4468	217	20	.	.	PUNCT
ejpam-4468	218	1	to	to	PART
ejpam-4468	218	2	verify	verify	VERB
ejpam-4468	218	3	equation	equation	NOUN
ejpam-4468	218	4	(	(	PUNCT
ejpam-4468	218	5	6	6	NUM
ejpam-4468	218	6	)	)	PUNCT
ejpam-4468	218	7	,	,	PUNCT
ejpam-4468	218	8	set	set	VERB
ejpam-4468	218	9	φ	φ	PROPN
ejpam-4468	218	10	=	=	SYM
ejpam-4468	218	11	x	x	SYM
ejpam-4468	218	12	α	α	PROPN
ejpam-4468	218	13	,	,	PUNCT
ejpam-4468	218	14	φ	φ	PROPN
ejpam-4468	218	15	′	′	NUM
ejpam-4468	219	1	=	=	SYM
ejpam-4468	219	2	1	1	NUM
ejpam-4468	219	3	α	α	NOUN
ejpam-4468	219	4	,	,	PUNCT
ejpam-4468	219	5	φ	φ	NUM
ejpam-4468	219	6	′′	′′	PROPN
ejpam-4468	219	7	=	=	SYM
ejpam-4468	219	8	0	0	NUM
ejpam-4468	219	9	,	,	PUNCT
ejpam-4468	219	10	and	and	CCONJ
ejpam-4468	219	11	ψ	ψ	X
ejpam-4468	219	12	=	=	SYM
ejpam-4468	219	13	1	1	NUM
ejpam-4468	219	14	t	t	NOUN
ejpam-4468	219	15	,	,	PUNCT
ejpam-4468	219	16	ψ	ψ	VERB
ejpam-4468	219	17	′	′	NOUN
ejpam-4468	219	18	=	=	SYM
ejpam-4468	219	19	−1	−1	NOUN
ejpam-4468	219	20	t2	t2	NOUN
ejpam-4468	219	21	=	=	PUNCT
ejpam-4468	220	1	−	−	NOUN
ejpam-4468	220	2	ψ2	ψ2	NOUN
ejpam-4468	220	3	,	,	PUNCT
ejpam-4468	220	4	then	then	ADV
ejpam-4468	220	5	u	u	NOUN
ejpam-4468	220	6	=	=	PUNCT
ejpam-4468	220	7	φ⊗ψ	φ⊗ψ	PROPN
ejpam-4468	220	8	,	,	PUNCT
ejpam-4468	220	9	ux	ux	PROPN
ejpam-4468	220	10	=	=	SYM
ejpam-4468	220	11	φ′⊗ψ	φ′⊗ψ	PROPN
ejpam-4468	220	12	,	,	PUNCT
ejpam-4468	220	13	υuxx	υuxx	X
ejpam-4468	220	14	=	=	SYM
ejpam-4468	220	15	υ(φ′′⊗ψ	υ(φ′′⊗ψ	NUM
ejpam-4468	220	16	)	)	PUNCT
ejpam-4468	220	17	=	=	SYM
ejpam-4468	220	18	υ(0⊗ψ	υ(0⊗ψ	PROPN
ejpam-4468	220	19	)	)	PUNCT
ejpam-4468	221	1	=	=	VERB
ejpam-4468	221	2	υ0⊗ψ	υ0⊗ψ	NOUN
ejpam-4468	222	1	=	=	PUNCT
ejpam-4468	222	2	0⊗ψ	0⊗ψ	NUM
ejpam-4468	222	3	=	=	SYM
ejpam-4468	222	4	0	0	NUM
ejpam-4468	222	5	,	,	PUNCT
ejpam-4468	222	6	ut	ut	PROPN
ejpam-4468	222	7	=	=	SYM
ejpam-4468	222	8	φ⊗ψ′.	φ⊗ψ′.	NOUN
ejpam-4468	222	9	ut	ut	PROPN
ejpam-4468	223	1	+	+	CCONJ
ejpam-4468	223	2	αuux	αuux	NOUN
ejpam-4468	223	3	=	=	SYM
ejpam-4468	223	4	φ⊗ψ′	φ⊗ψ′	PROPN
ejpam-4468	223	5	+	+	NUM
ejpam-4468	223	6	α(φ⊗ψ)(φ′	α(φ⊗ψ)(φ′	NOUN
ejpam-4468	223	7	⊗ψ	⊗ψ	NOUN
ejpam-4468	223	8	)	)	PUNCT
ejpam-4468	224	1	=	=	PUNCT
ejpam-4468	224	2	φ⊗−ψ2	φ⊗−ψ2	VERB
ejpam-4468	224	3	+	+	CCONJ
ejpam-4468	224	4	α(φ⊗ψ)(φ′	α(φ⊗ψ)(φ′	NOUN
ejpam-4468	224	5	⊗ψ	⊗ψ	NOUN
ejpam-4468	224	6	)	)	PUNCT
ejpam-4468	225	1	=	=	VERB
ejpam-4468	225	2	φ⊗−ψ2	φ⊗−ψ2	VERB
ejpam-4468	225	3	+	+	CCONJ
ejpam-4468	225	4	α(φφ′	α(φφ′	PROPN
ejpam-4468	225	5	⊗ψ2	⊗ψ2	NOUN
ejpam-4468	225	6	)	)	PUNCT
ejpam-4468	226	1	=	=	SYM
ejpam-4468	226	2	−φ⊗ψ2	−φ⊗ψ2	NOUN
ejpam-4468	227	1	+	+	NUM
ejpam-4468	227	2	α(φφ′	α(φφ′	PROPN
ejpam-4468	227	3	⊗ψ2	⊗ψ2	NOUN
ejpam-4468	227	4	)	)	PUNCT
ejpam-4468	227	5	=	=	PUNCT
ejpam-4468	228	1	(	(	PUNCT
ejpam-4468	228	2	−φ+	−φ+	NOUN
ejpam-4468	228	3	αφφ′)⊗ψ2	αφφ′)⊗ψ2	NOUN
ejpam-4468	228	4	.	.	PUNCT
ejpam-4468	229	1	consequently	consequently	ADV
ejpam-4468	229	2	,	,	PUNCT
ejpam-4468	229	3	−φ+	−φ+	VERB
ejpam-4468	229	4	αφφ′	αφφ′	NOUN
ejpam-4468	229	5	=	=	PUNCT
ejpam-4468	230	1	−	−	PROPN
ejpam-4468	230	2	x	x	SYM
ejpam-4468	230	3	α	α	NOUN
ejpam-4468	230	4	+	+	X
ejpam-4468	231	1	α	α	NOUN
ejpam-4468	231	2	x	x	SYM
ejpam-4468	231	3	α	α	NOUN
ejpam-4468	231	4	1	1	NUM
ejpam-4468	231	5	α	α	NOUN
ejpam-4468	231	6	=	=	PUNCT
ejpam-4468	231	7	−	−	NOUN
ejpam-4468	232	1	x	x	SYM
ejpam-4468	233	1	α	α	NOUN
ejpam-4468	233	2	+	+	X
ejpam-4468	233	3	x	x	SYM
ejpam-4468	233	4	α	α	NOUN
ejpam-4468	233	5	=	=	NOUN
ejpam-4468	233	6	0	0	PROPN
ejpam-4468	233	7	.	.	PUNCT
ejpam-4468	234	1	so	so	ADV
ejpam-4468	234	2	ut	ut	PROPN
ejpam-4468	235	1	+	+	CCONJ
ejpam-4468	235	2	αuux	αuux	NOUN
ejpam-4468	235	3	=	=	PUNCT
ejpam-4468	235	4	0⊗ψ2	0⊗ψ2	NUM
ejpam-4468	236	1	=	=	SYM
ejpam-4468	236	2	0	0	X
ejpam-4468	236	3	=	=	SYM
ejpam-4468	236	4	υuxx	υuxx	NOUN
ejpam-4468	236	5	.	.	PUNCT
ejpam-4468	237	1	this	this	PRON
ejpam-4468	237	2	implies	imply	VERB
ejpam-4468	237	3	u	u	NOUN
ejpam-4468	237	4	=	=	PRON
ejpam-4468	237	5	φ⊗ψ	φ⊗ψ	PROPN
ejpam-4468	237	6	is	be	AUX
ejpam-4468	237	7	a	a	DET
ejpam-4468	237	8	solution	solution	NOUN
ejpam-4468	237	9	of	of	ADP
ejpam-4468	237	10	equation	equation	NOUN
ejpam-4468	237	11	(	(	PUNCT
ejpam-4468	237	12	6	6	NUM
ejpam-4468	237	13	)	)	PUNCT
ejpam-4468	237	14	,	,	PUNCT
ejpam-4468	237	15	where	where	SCONJ
ejpam-4468	237	16	φ	φ	PROPN
ejpam-4468	237	17	=	=	SYM
ejpam-4468	237	18	x	x	SYM
ejpam-4468	237	19	α	α	NOUN
ejpam-4468	237	20	and	and	CCONJ
ejpam-4468	237	21	ψ	ψ	X
ejpam-4468	237	22	=	=	SYM
ejpam-4468	237	23	1	1	NUM
ejpam-4468	237	24	t	t	NOUN
ejpam-4468	237	25	.	.	PUNCT
ejpam-4468	238	1	conclusion	conclusion	NOUN
ejpam-4468	238	2	in	in	ADP
ejpam-4468	238	3	this	this	DET
ejpam-4468	238	4	paper	paper	NOUN
ejpam-4468	238	5	we	we	PRON
ejpam-4468	238	6	find	find	VERB
ejpam-4468	238	7	an	an	DET
ejpam-4468	238	8	exact	exact	ADJ
ejpam-4468	238	9	solution	solution	NOUN
ejpam-4468	238	10	for	for	ADP
ejpam-4468	238	11	secand	secand	NOUN
ejpam-4468	238	12	order	order	NOUN
ejpam-4468	238	13	partial	partial	ADJ
ejpam-4468	238	14	diffrential	diffrential	ADJ
ejpam-4468	238	15	equation	equation	NOUN
ejpam-4468	238	16	of	of	ADP
ejpam-4468	238	17	linear	linear	PROPN
ejpam-4468	238	18	type	type	NOUN
ejpam-4468	238	19	.	.	PUNCT
ejpam-4468	239	1	further	far	ADV
ejpam-4468	239	2	,	,	PUNCT
ejpam-4468	239	3	exact	exact	ADJ
ejpam-4468	239	4	solution	solution	NOUN
ejpam-4468	239	5	using	use	VERB
ejpam-4468	239	6	tensor	tensor	NOUN
ejpam-4468	239	7	product	product	NOUN
ejpam-4468	239	8	technique	technique	NOUN
ejpam-4468	239	9	of	of	ADP
ejpam-4468	239	10	burger	burger	NOUN
ejpam-4468	239	11	equation	equation	NOUN
ejpam-4468	239	12	is	be	AUX
ejpam-4468	239	13	presented	present	VERB
ejpam-4468	239	14	.	.	PUNCT
ejpam-4468	240	1	references	reference	NOUN
ejpam-4468	240	2	[	[	X
ejpam-4468	240	3	1	1	NUM
ejpam-4468	240	4	]	]	PUNCT
ejpam-4468	240	5	h.	h.	PROPN
ejpam-4468	240	6	bateman	bateman	PROPN
ejpam-4468	240	7	.	.	PUNCT
ejpam-4468	241	1	some	some	DET
ejpam-4468	241	2	recent	recent	ADJ
ejpam-4468	241	3	researches	research	NOUN
ejpam-4468	241	4	on	on	ADP
ejpam-4468	241	5	the	the	DET
ejpam-4468	241	6	motion	motion	NOUN
ejpam-4468	241	7	of	of	ADP
ejpam-4468	241	8	fluids	fluid	NOUN
ejpam-4468	241	9	.	.	PUNCT
ejpam-4468	242	1	monthly	monthly	ADJ
ejpam-4468	242	2	weather	weather	NOUN
ejpam-4468	242	3	review	review	NOUN
ejpam-4468	242	4	,	,	PUNCT
ejpam-4468	242	5	43:163–170	43:163–170	PROPN
ejpam-4468	242	6	,	,	PUNCT
ejpam-4468	242	7	1915	1915	NUM
ejpam-4468	242	8	.	.	PUNCT
ejpam-4468	243	1	[	[	X
ejpam-4468	243	2	2	2	X
ejpam-4468	243	3	]	]	PUNCT
ejpam-4468	243	4	j.	j.	PROPN
ejpam-4468	243	5	biazar	biazar	PROPN
ejpam-4468	243	6	and	and	CCONJ
ejpam-4468	243	7	h.	h.	PROPN
ejpam-4468	243	8	ghazvini	ghazvini	PROPN
ejpam-4468	243	9	.	.	PUNCT
ejpam-4468	244	1	exact	exact	ADJ
ejpam-4468	244	2	solutions	solution	NOUN
ejpam-4468	244	3	for	for	ADP
ejpam-4468	244	4	nonlinear	nonlinear	ADJ
ejpam-4468	244	5	burger	burger	NOUN
ejpam-4468	244	6	’s	’s	PART
ejpam-4468	244	7	equation	equation	NOUN
ejpam-4468	244	8	by	by	ADP
ejpam-4468	244	9	homotopy	homotopy	NOUN
ejpam-4468	244	10	perturbation	perturbation	NOUN
ejpam-4468	244	11	method	method	NOUN
ejpam-4468	244	12	.	.	PUNCT
ejpam-4468	245	1	numerical	numerical	ADJ
ejpam-4468	245	2	methods	method	NOUN
ejpam-4468	245	3	for	for	ADP
ejpam-4468	245	4	partial	partial	ADJ
ejpam-4468	245	5	differential	differential	NOUN
ejpam-4468	245	6	equations	equation	NOUN
ejpam-4468	245	7	,	,	PUNCT
ejpam-4468	245	8	25:833	25:833	NUM
ejpam-4468	245	9	–	–	PUNCT
ejpam-4468	245	10	842	842	NUM
ejpam-4468	245	11	,	,	PUNCT
ejpam-4468	245	12	2009	2009	NUM
ejpam-4468	245	13	.	.	PUNCT
ejpam-4468	246	1	references	reference	NOUN
ejpam-4468	246	2	1454	1454	NUM
ejpam-4468	246	3	[	[	X
ejpam-4468	246	4	3	3	X
ejpam-4468	246	5	]	]	X
ejpam-4468	246	6	j.	j.	PROPN
ejpam-4468	246	7	biazar	biazar	PROPN
ejpam-4468	246	8	and	and	CCONJ
ejpam-4468	246	9	a.	a.	PROPN
ejpam-4468	246	10	hossein	hossein	PROPN
ejpam-4468	246	11	.	.	PUNCT
ejpam-4468	247	1	exact	exact	ADJ
ejpam-4468	247	2	and	and	CCONJ
ejpam-4468	247	3	numerical	numerical	ADJ
ejpam-4468	247	4	solutions	solution	NOUN
ejpam-4468	247	5	for	for	ADP
ejpam-4468	247	6	non	non	ADJ
ejpam-4468	247	7	-	-	ADJ
ejpam-4468	247	8	linear	linear	ADJ
ejpam-4468	247	9	burger	burger	NOUN
ejpam-4468	247	10	’s	’s	PART
ejpam-4468	247	11	equation	equation	NOUN
ejpam-4468	247	12	by	by	ADP
ejpam-4468	247	13	vim	vim	PROPN
ejpam-4468	247	14	.	.	PROPN
ejpam-4468	247	15	mathematical	mathematical	ADJ
ejpam-4468	247	16	and	and	CCONJ
ejpam-4468	247	17	computer	computer	NOUN
ejpam-4468	247	18	modelling	modelling	NOUN
ejpam-4468	247	19	,	,	PUNCT
ejpam-4468	247	20	49:1394–1400	49:1394–1400	NUM
ejpam-4468	247	21	,	,	PUNCT
ejpam-4468	247	22	2009	2009	NUM
ejpam-4468	247	23	.	.	PUNCT
ejpam-4468	248	1	[	[	X
ejpam-4468	248	2	4	4	X
ejpam-4468	248	3	]	]	PUNCT
ejpam-4468	248	4	j.	j.	PROPN
ejpam-4468	248	5	m.	m.	PROPN
ejpam-4468	248	6	burgers	burger	NOUN
ejpam-4468	248	7	.	.	PUNCT
ejpam-4468	249	1	a	a	DET
ejpam-4468	249	2	mathematical	mathematical	ADJ
ejpam-4468	249	3	model	model	NOUN
ejpam-4468	249	4	illustrating	illustrate	VERB
ejpam-4468	249	5	the	the	DET
ejpam-4468	249	6	theory	theory	NOUN
ejpam-4468	249	7	of	of	ADP
ejpam-4468	249	8	turbulence	turbulence	NOUN
ejpam-4468	249	9	.	.	PUNCT
ejpam-4468	250	1	in	in	ADP
ejpam-4468	250	2	advances	advance	NOUN
ejpam-4468	250	3	in	in	ADP
ejpam-4468	250	4	applied	apply	VERB
ejpam-4468	250	5	mechanics	mechanic	NOUN
ejpam-4468	250	6	,	,	PUNCT
ejpam-4468	250	7	1:171–199	1:171–199	NUM
ejpam-4468	250	8	,	,	PUNCT
ejpam-4468	250	9	1947	1947	NUM
ejpam-4468	250	10	.	.	PUNCT
ejpam-4468	251	1	[	[	X
ejpam-4468	251	2	5	5	NUM
ejpam-4468	251	3	]	]	PUNCT
ejpam-4468	251	4	m.	m.	NOUN
ejpam-4468	251	5	darvishi	darvishi	PROPN
ejpam-4468	251	6	and	and	CCONJ
ejpam-4468	251	7	m.	m.	NOUN
ejpam-4468	251	8	javidi	javidi	PROPN
ejpam-4468	251	9	.	.	PUNCT
ejpam-4468	252	1	a	a	DET
ejpam-4468	252	2	numerical	numerical	ADJ
ejpam-4468	252	3	solution	solution	NOUN
ejpam-4468	252	4	of	of	ADP
ejpam-4468	252	5	burger	burger	NOUN
ejpam-4468	252	6	’s	’s	PART
ejpam-4468	252	7	equation	equation	NOUN
ejpam-4468	252	8	by	by	ADP
ejpam-4468	252	9	pseudospectral	pseudospectral	ADJ
ejpam-4468	252	10	method	method	NOUN
ejpam-4468	252	11	and	and	CCONJ
ejpam-4468	252	12	darvishi	darvishi	NOUN
ejpam-4468	252	13	’s	’s	PART
ejpam-4468	252	14	preconditioning	precondition	VERB
ejpam-4468	252	15	.	.	PUNCT
ejpam-4468	253	1	applied	apply	VERB
ejpam-4468	253	2	mathematics	mathematic	NOUN
ejpam-4468	253	3	and	and	CCONJ
ejpam-4468	253	4	computation	computation	NOUN
ejpam-4468	253	5	,	,	PUNCT
ejpam-4468	253	6	pages	page	NOUN
ejpam-4468	253	7	421–429	421–429	NUM
ejpam-4468	253	8	,	,	PUNCT
ejpam-4468	253	9	2006	2006	NUM
ejpam-4468	253	10	.	.	PUNCT
ejpam-4468	254	1	[	[	X
ejpam-4468	254	2	6	6	NUM
ejpam-4468	254	3	]	]	PUNCT
ejpam-4468	254	4	m.	m.	NOUN
ejpam-4468	254	5	kapoor	kapoor	PROPN
ejpam-4468	254	6	and	and	CCONJ
ejpam-4468	254	7	v.	v.	PROPN
ejpam-4468	254	8	joshi	joshi	PROPN
ejpam-4468	254	9	.	.	PUNCT
ejpam-4468	255	1	numerical	numerical	PROPN
ejpam-4468	255	2	approximation	approximation	NOUN
ejpam-4468	255	3	of	of	ADP
ejpam-4468	255	4	coupled	couple	VERB
ejpam-4468	255	5	2d	2d	NUM
ejpam-4468	255	6	burgers	burger	NOUN
ejpam-4468	255	7	equation	equation	NOUN
ejpam-4468	255	8	by	by	ADP
ejpam-4468	255	9	employing	employ	VERB
ejpam-4468	255	10	non	non	ADJ
ejpam-4468	255	11	-	-	ADJ
ejpam-4468	255	12	uniform	uniform	ADJ
ejpam-4468	255	13	algebraic	algebraic	PROPN
ejpam-4468	255	14	hyperbolic	hyperbolic	ADJ
ejpam-4468	255	15	(	(	PUNCT
ejpam-4468	255	16	nuah	nuah	NOUN
ejpam-4468	255	17	)	)	PUNCT
ejpam-4468	255	18	b	b	NOUN
ejpam-4468	255	19	-	-	PUNCT
ejpam-4468	255	20	spline	spline	NOUN
ejpam-4468	255	21	based	base	VERB
ejpam-4468	255	22	differential	differential	ADJ
ejpam-4468	255	23	quadrature	quadrature	NOUN
ejpam-4468	255	24	method	method	NOUN
ejpam-4468	255	25	.	.	PUNCT
ejpam-4468	256	1	mathematics	mathematic	NOUN
ejpam-4468	256	2	in	in	ADP
ejpam-4468	256	3	engineering	engineering	NOUN
ejpam-4468	256	4	,	,	PUNCT
ejpam-4468	256	5	science	science	NOUN
ejpam-4468	256	6	and	and	CCONJ
ejpam-4468	256	7	aerospace	aerospace	NOUN
ejpam-4468	256	8	,	,	PUNCT
ejpam-4468	256	9	13(2):171	13(2):171	NUM
ejpam-4468	256	10	–	–	PUNCT
ejpam-4468	256	11	199	199	NUM
ejpam-4468	256	12	,	,	PUNCT
ejpam-4468	256	13	2022	2022	NUM
ejpam-4468	256	14	.	.	PUNCT
ejpam-4468	257	1	[	[	X
ejpam-4468	257	2	7	7	X
ejpam-4468	257	3	]	]	X
ejpam-4468	257	4	r.	r.	PROPN
ejpam-4468	257	5	khalil	khalil	PROPN
ejpam-4468	257	6	and	and	CCONJ
ejpam-4468	257	7	l.abdullah	l.abdullah	PROPN
ejpam-4468	257	8	.	.	PUNCT
ejpam-4468	257	9	atomic	atomic	ADJ
ejpam-4468	257	10	solution	solution	NOUN
ejpam-4468	257	11	of	of	ADP
ejpam-4468	257	12	certain	certain	ADJ
ejpam-4468	257	13	inverse	inverse	NOUN
ejpam-4468	257	14	problems	problem	NOUN
ejpam-4468	257	15	.	.	PUNCT
ejpam-4468	258	1	european	european	PROPN
ejpam-4468	258	2	journal	journal	PROPN
ejpam-4468	258	3	of	of	ADP
ejpam-4468	258	4	pure	pure	ADJ
ejpam-4468	258	5	and	and	CCONJ
ejpam-4468	258	6	applied	applied	ADJ
ejpam-4468	258	7	mathematics	mathematic	NOUN
ejpam-4468	258	8	,	,	PUNCT
ejpam-4468	258	9	3:725–729	3:725–729	NUM
ejpam-4468	258	10	,	,	PUNCT
ejpam-4468	258	11	2012	2012	NUM
ejpam-4468	258	12	.	.	PUNCT
ejpam-4468	259	1	[	[	X
ejpam-4468	259	2	8	8	NUM
ejpam-4468	259	3	]	]	X
ejpam-4468	259	4	ch	ch	NOUN
ejpam-4468	259	5	.	.	PUNCT
ejpam-4468	259	6	kuo	kuo	PROPN
ejpam-4468	259	7	and	and	CCONJ
ejpam-4468	259	8	s.	s.	PROPN
ejpam-4468	259	9	lee	lee	PROPN
ejpam-4468	259	10	.	.	PUNCT
ejpam-4468	260	1	a	a	DET
ejpam-4468	260	2	new	new	ADJ
ejpam-4468	260	3	exact	exact	ADJ
ejpam-4468	260	4	solution	solution	NOUN
ejpam-4468	260	5	of	of	ADP
ejpam-4468	260	6	burger	burger	NOUN
ejpam-4468	260	7	’s	’s	PART
ejpam-4468	260	8	equation	equation	NOUN
ejpam-4468	260	9	with	with	ADP
ejpam-4468	260	10	linearized	linearize	VERB
ejpam-4468	260	11	solution	solution	NOUN
ejpam-4468	260	12	.	.	PUNCT
ejpam-4468	261	1	mathematical	mathematical	ADJ
ejpam-4468	261	2	problems	problem	NOUN
ejpam-4468	261	3	in	in	ADP
ejpam-4468	261	4	engineering	engineering	NOUN
ejpam-4468	261	5	,	,	PUNCT
ejpam-4468	261	6	2015:1–7	2015:1–7	PROPN
ejpam-4468	261	7	,	,	PUNCT
ejpam-4468	261	8	2015	2015	NUM
ejpam-4468	261	9	.	.	PUNCT
ejpam-4468	262	1	[	[	X
ejpam-4468	262	2	9	9	NUM
ejpam-4468	262	3	]	]	PUNCT
ejpam-4468	262	4	w.	w.	NOUN
ejpam-4468	262	5	light	light	PROPN
ejpam-4468	262	6	and	and	CCONJ
ejpam-4468	262	7	e.	e.	PROPN
ejpam-4468	262	8	cheney	cheney	PROPN
ejpam-4468	262	9	.	.	PUNCT
ejpam-4468	263	1	approximation	approximation	NOUN
ejpam-4468	263	2	theory	theory	NOUN
ejpam-4468	263	3	in	in	ADP
ejpam-4468	263	4	tensor	tensor	NOUN
ejpam-4468	263	5	product	product	NOUN
ejpam-4468	263	6	spaces	space	NOUN
ejpam-4468	263	7	.	.	PUNCT
ejpam-4468	264	1	springer	springer	NOUN
ejpam-4468	264	2	verlag	verlag	PROPN
ejpam-4468	264	3	,	,	PUNCT
ejpam-4468	264	4	berlin	berlin	PROPN
ejpam-4468	264	5	,	,	PUNCT
ejpam-4468	264	6	new	new	PROPN
ejpam-4468	264	7	york	york	PROPN
ejpam-4468	264	8	,	,	PUNCT
ejpam-4468	264	9	1985	1985	NUM
ejpam-4468	264	10	.	.	PUNCT
ejpam-4468	265	1	[	[	X
ejpam-4468	265	2	10	10	NUM
ejpam-4468	265	3	]	]	X
ejpam-4468	265	4	r.	r.	PROPN
ejpam-4468	265	5	lynch	lynch	PROPN
ejpam-4468	265	6	,	,	PUNCT
ejpam-4468	265	7	j.	j.	PROPN
ejpam-4468	265	8	rice	rice	PROPN
ejpam-4468	265	9	,	,	PUNCT
ejpam-4468	265	10	and	and	CCONJ
ejpam-4468	265	11	d.	d.	PROPN
ejpam-4468	265	12	thomas	thomas	PROPN
ejpam-4468	265	13	.	.	PUNCT
ejpam-4468	266	1	tensor	tensor	NOUN
ejpam-4468	266	2	product	product	NOUN
ejpam-4468	266	3	analysis	analysis	NOUN
ejpam-4468	266	4	of	of	ADP
ejpam-4468	266	5	partial	partial	ADJ
ejpam-4468	266	6	difference	difference	NOUN
ejpam-4468	266	7	equations	equation	NOUN
ejpam-4468	266	8	.	.	PUNCT
ejpam-4468	267	1	bulletin	bulletin	NOUN
ejpam-4468	267	2	of	of	ADP
ejpam-4468	267	3	the	the	DET
ejpam-4468	267	4	american	american	PROPN
ejpam-4468	267	5	mathematical	mathematical	PROPN
ejpam-4468	267	6	society	society	NOUN
ejpam-4468	267	7	,	,	PUNCT
ejpam-4468	267	8	70:378–384	70:378–384	PROPN
ejpam-4468	267	9	,	,	PUNCT
ejpam-4468	267	10	1964	1964	NUM
ejpam-4468	267	11	.	.	PUNCT
ejpam-4468	268	1	[	[	X
ejpam-4468	268	2	11	11	NUM
ejpam-4468	268	3	]	]	X
ejpam-4468	268	4	r.	r.	PROPN
ejpam-4468	268	5	lynch	lynch	PROPN
ejpam-4468	268	6	,	,	PUNCT
ejpam-4468	268	7	j.	j.	PROPN
ejpam-4468	268	8	rice	rice	PROPN
ejpam-4468	268	9	,	,	PUNCT
ejpam-4468	268	10	and	and	CCONJ
ejpam-4468	268	11	d.	d.	PROPN
ejpam-4468	268	12	thomas	thomas	PROPN
ejpam-4468	268	13	.	.	PUNCT
ejpam-4468	269	1	direct	direct	ADJ
ejpam-4468	269	2	solution	solution	NOUN
ejpam-4468	269	3	of	of	ADP
ejpam-4468	269	4	partial	partial	ADJ
ejpam-4468	269	5	difference	difference	NOUN
ejpam-4468	269	6	equations	equation	NOUN
ejpam-4468	269	7	by	by	ADP
ejpam-4468	269	8	tensor	tensor	NOUN
ejpam-4468	269	9	product	product	NOUN
ejpam-4468	269	10	methods	method	NOUN
ejpam-4468	269	11	.	.	PUNCT
ejpam-4468	270	1	numerische	numerische	PROPN
ejpam-4468	270	2	mathematik	mathematik	PROPN
ejpam-4468	270	3	,	,	PUNCT
ejpam-4468	270	4	6:185–199	6:185–199	PROPN
ejpam-4468	270	5	,	,	PUNCT
ejpam-4468	270	6	1964	1964	NUM
ejpam-4468	270	7	.	.	PUNCT
ejpam-4468	271	1	[	[	X
ejpam-4468	271	2	12	12	NUM
ejpam-4468	271	3	]	]	PUNCT
ejpam-4468	271	4	k.	k.	PROPN
ejpam-4468	271	5	selçuk	selçuk	PROPN
ejpam-4468	271	6	,	,	PUNCT
ejpam-4468	271	7	e.	e.	PROPN
ejpam-4468	271	8	alaattin	alaattin	PROPN
ejpam-4468	271	9	,	,	PUNCT
ejpam-4468	271	10	and	and	CCONJ
ejpam-4468	271	11	d.	d.	PROPN
ejpam-4468	271	12	idris	idris	PROPN
ejpam-4468	271	13	.	.	PROPN
ejpam-4468	272	1	numerical	numerical	ADJ
ejpam-4468	272	2	solution	solution	NOUN
ejpam-4468	272	3	of	of	ADP
ejpam-4468	272	4	the	the	DET
ejpam-4468	272	5	burger	burger	NOUN
ejpam-4468	272	6	’s	’s	PART
ejpam-4468	272	7	equation	equation	NOUN
ejpam-4468	272	8	by	by	ADP
ejpam-4468	272	9	the	the	DET
ejpam-4468	272	10	least	least	ADJ
ejpam-4468	272	11	-	-	PUNCT
ejpam-4468	272	12	squares	square	NOUN
ejpam-4468	272	13	quadratic	quadratic	ADJ
ejpam-4468	272	14	b	b	NOUN
ejpam-4468	272	15	-	-	PUNCT
ejpam-4468	272	16	spline	spline	ADJ
ejpam-4468	272	17	finite	finite	PROPN
ejpam-4468	272	18	element	element	NOUN
ejpam-4468	272	19	method	method	NOUN
ejpam-4468	272	20	.	.	PUNCT
ejpam-4468	273	1	journal	journal	NOUN
ejpam-4468	273	2	of	of	ADP
ejpam-4468	273	3	computational	computational	ADJ
ejpam-4468	273	4	and	and	CCONJ
ejpam-4468	273	5	applied	applied	ADJ
ejpam-4468	273	6	mathematics	mathematic	NOUN
ejpam-4468	273	7	,	,	PUNCT
ejpam-4468	273	8	167:21–33	167:21–33	NUM
ejpam-4468	273	9	,	,	PUNCT
ejpam-4468	273	10	2004	2004	NUM
ejpam-4468	273	11	.	.	PUNCT
ejpam-4468	274	1	[	[	X
ejpam-4468	274	2	13	13	NUM
ejpam-4468	274	3	]	]	PUNCT
ejpam-4468	274	4	k.	k.	PROPN
ejpam-4468	274	5	selçuk	selçuk	PROPN
ejpam-4468	274	6	,	,	PUNCT
ejpam-4468	274	7	a.r	a.r	PROPN
ejpam-4468	274	8	.	.	PROPN
ejpam-4468	274	9	bahadir	bahadir	PROPN
ejpam-4468	274	10	,	,	PUNCT
ejpam-4468	274	11	and	and	CCONJ
ejpam-4468	274	12	a.	a.	PROPN
ejpam-4468	274	13	özdeş.	özdeş.	PROPN
ejpam-4468	274	14	numerical	numerical	ADJ
ejpam-4468	274	15	solution	solution	NOUN
ejpam-4468	274	16	of	of	ADP
ejpam-4468	274	17	one	one	NUM
ejpam-4468	274	18	-	-	PUNCT
ejpam-4468	274	19	dimensional	dimensional	ADJ
ejpam-4468	274	20	burger	burger	NOUN
ejpam-4468	274	21	’s	’s	PART
ejpam-4468	274	22	equation	equation	NOUN
ejpam-4468	274	23	:	:	PUNCT
ejpam-4468	274	24	explicit	explicit	ADJ
ejpam-4468	274	25	and	and	CCONJ
ejpam-4468	274	26	exact	exact	ADJ
ejpam-4468	274	27	-	-	PUNCT
ejpam-4468	274	28	explicit	explicit	ADJ
ejpam-4468	274	29	finite	finite	ADJ
ejpam-4468	274	30	difference	difference	NOUN
ejpam-4468	274	31	methods	method	NOUN
ejpam-4468	274	32	.	.	PUNCT
ejpam-4468	275	1	journal	journal	NOUN
ejpam-4468	275	2	of	of	ADP
ejpam-4468	275	3	computational	computational	ADJ
ejpam-4468	275	4	and	and	CCONJ
ejpam-4468	275	5	applied	applied	ADJ
ejpam-4468	275	6	mathematics	mathematic	NOUN
ejpam-4468	275	7	,	,	PUNCT
ejpam-4468	275	8	103:251–261	103:251–261	NUM
ejpam-4468	275	9	,	,	PUNCT
ejpam-4468	275	10	1999	1999	NUM
ejpam-4468	275	11	.	.	PUNCT
ejpam-4468	276	1	[	[	X
ejpam-4468	276	2	14	14	NUM
ejpam-4468	276	3	]	]	PUNCT
ejpam-4468	276	4	s.	s.	PROPN
ejpam-4468	276	5	xie	xie	PROPN
ejpam-4468	276	6	,	,	PUNCT
ejpam-4468	276	7	s.	s.	PROPN
ejpam-4468	276	8	heo	heo	PROPN
ejpam-4468	276	9	,	,	PUNCT
ejpam-4468	276	10	s.	s.	PROPN
ejpam-4468	276	11	kim	kim	PROPN
ejpam-4468	276	12	,	,	PUNCT
ejpam-4468	276	13	g.	g.	PROPN
ejpam-4468	276	14	woo	woo	PROPN
ejpam-4468	276	15	,	,	PUNCT
ejpam-4468	276	16	and	and	CCONJ
ejpam-4468	276	17	s.	s.	PROPN
ejpam-4468	276	18	yi	yi	PROPN
ejpam-4468	276	19	.	.	PUNCT
ejpam-4468	277	1	numerical	numerical	PROPN
ejpam-4468	277	2	solution	solution	NOUN
ejpam-4468	277	3	one	one	NUM
ejpam-4468	277	4	-	-	PUNCT
ejpam-4468	277	5	dimensional	dimensional	ADJ
ejpam-4468	277	6	burger	burger	NOUN
ejpam-4468	277	7	’s	’s	PART
ejpam-4468	277	8	equation	equation	NOUN
ejpam-4468	277	9	using	use	VERB
ejpam-4468	277	10	reproducing	reproduce	VERB
ejpam-4468	277	11	kernel	kernel	PROPN
ejpam-4468	277	12	function	function	NOUN
ejpam-4468	277	13	.	.	PUNCT
ejpam-4468	278	1	journal	journal	PROPN
ejpam-4468	278	2	of	of	ADP
ejpam-4468	278	3	computational	computational	ADJ
ejpam-4468	278	4	and	and	CCONJ
ejpam-4468	278	5	applied	applied	ADJ
ejpam-4468	278	6	mathematics	mathematic	NOUN
ejpam-4468	278	7	,	,	PUNCT
ejpam-4468	278	8	214:417–434	214:417–434	NUM
ejpam-4468	278	9	,	,	PUNCT
ejpam-4468	278	10	1999	1999	NUM
ejpam-4468	278	11	.	.	PUNCT
ejpam-4468	279	1	[	[	X
ejpam-4468	279	2	15	15	NUM
ejpam-4468	279	3	]	]	X
ejpam-4468	279	4	a.	a.	NOUN
ejpam-4468	279	5	ziqan	ziqan	PROPN
ejpam-4468	279	6	,	,	PUNCT
ejpam-4468	279	7	m.	m.	PROPN
ejpam-4468	279	8	al	al	PROPN
ejpam-4468	279	9	horani	horani	PROPN
ejpam-4468	279	10	,	,	PUNCT
ejpam-4468	279	11	and	and	CCONJ
ejpam-4468	279	12	r.	r.	PROPN
ejpam-4468	279	13	khalil	khalil	PROPN
ejpam-4468	279	14	.	.	PUNCT
ejpam-4468	280	1	tensor	tensor	NOUN
ejpam-4468	280	2	product	product	NOUN
ejpam-4468	280	3	technique	technique	NOUN
ejpam-4468	280	4	and	and	CCONJ
ejpam-4468	280	5	the	the	DET
ejpam-4468	280	6	degenerate	degenerate	ADJ
ejpam-4468	280	7	nonhomogeneous	nonhomogeneous	ADJ
ejpam-4468	280	8	abstract	abstract	ADJ
ejpam-4468	280	9	cauchy	cauchy	PROPN
ejpam-4468	280	10	problem	problem	NOUN
ejpam-4468	280	11	.	.	PUNCT
ejpam-4468	281	1	journal	journal	NOUN
ejpam-4468	281	2	of	of	ADP
ejpam-4468	281	3	applied	apply	VERB
ejpam-4468	281	4	functional	functional	ADJ
ejpam-4468	281	5	analysis	analysis	NOUN
ejpam-4468	281	6	,	,	PUNCT
ejpam-4468	281	7	5:121–138	5:121–138	NUM
ejpam-4468	281	8	,	,	PUNCT
ejpam-4468	281	9	2010	2010	NUM
ejpam-4468	281	10	.	.	PUNCT