id	sid	tid	token	lemma	pos
ejpam-6073	1	1	european	european	PROPN
ejpam-6073	1	2	journal	journal	PROPN
ejpam-6073	1	3	of	of	ADP
ejpam-6073	1	4	pure	pure	ADJ
ejpam-6073	1	5	and	and	CCONJ
ejpam-6073	1	6	applied	applied	ADJ
ejpam-6073	1	7	mathematics	mathematic	NOUN
ejpam-6073	1	8	2025	2025	NUM
ejpam-6073	1	9	,	,	PUNCT
ejpam-6073	1	10	vol	vol	NOUN
ejpam-6073	1	11	.	.	PROPN
ejpam-6073	1	12	18	18	NUM
ejpam-6073	1	13	,	,	PUNCT
ejpam-6073	1	14	issue	issue	NOUN
ejpam-6073	1	15	3	3	NUM
ejpam-6073	1	16	,	,	PUNCT
ejpam-6073	1	17	article	article	NOUN
ejpam-6073	1	18	number	number	NOUN
ejpam-6073	1	19	6073	6073	NUM
ejpam-6073	1	20	issn	issn	VERB
ejpam-6073	1	21	1307	1307	NUM
ejpam-6073	1	22	-	-	SYM
ejpam-6073	1	23	5543	5543	NUM
ejpam-6073	1	24	–	–	PUNCT
ejpam-6073	1	25	ejpam.com	ejpam.com	X
ejpam-6073	1	26	published	publish	VERB
ejpam-6073	1	27	by	by	ADP
ejpam-6073	1	28	new	new	PROPN
ejpam-6073	1	29	york	york	PROPN
ejpam-6073	1	30	business	business	PROPN
ejpam-6073	1	31	global	global	ADJ
ejpam-6073	1	32	controllability	controllability	NOUN
ejpam-6073	1	33	of	of	ADP
ejpam-6073	1	34	a	a	DET
ejpam-6073	1	35	system	system	NOUN
ejpam-6073	1	36	with	with	ADP
ejpam-6073	1	37	nonlinear	nonlinear	ADJ
ejpam-6073	1	38	damping	damp	VERB
ejpam-6073	1	39	devices	device	NOUN
ejpam-6073	1	40	and	and	CCONJ
ejpam-6073	1	41	nonlinear	nonlinear	ADJ
ejpam-6073	1	42	source	source	NOUN
ejpam-6073	1	43	terms	term	NOUN
ejpam-6073	1	44	in	in	ADP
ejpam-6073	1	45	elasticity	elasticity	NOUN
ejpam-6073	1	46	problems	problem	NOUN
ejpam-6073	1	47	:	:	PUNCT
ejpam-6073	1	48	existence	existence	NOUN
ejpam-6073	1	49	,	,	PUNCT
ejpam-6073	1	50	time	time	NOUN
ejpam-6073	1	51	blow	blow	NOUN
ejpam-6073	1	52	-	-	PUNCT
ejpam-6073	1	53	up	up	NOUN
ejpam-6073	1	54	,	,	PUNCT
ejpam-6073	1	55	and	and	CCONJ
ejpam-6073	1	56	numerical	numerical	PROPN
ejpam-6073	1	57	results	result	NOUN
ejpam-6073	1	58	adel	adel	PROPN
ejpam-6073	1	59	m.	m.	PROPN
ejpam-6073	1	60	al	al	PROPN
ejpam-6073	1	61	-	-	PUNCT
ejpam-6073	1	62	mahdi1,2,∗	mahdi1,2,∗	PROPN
ejpam-6073	1	63	,	,	PUNCT
ejpam-6073	1	64	mohammedm	mohammedm	NOUN
ejpam-6073	1	65	.	.	PUNCT
ejpam-6073	2	1	al	al	PROPN
ejpam-6073	2	2	-	-	PUNCT
ejpam-6073	2	3	gharabli1,2	gharabli1,2	PROPN
ejpam-6073	2	4	,	,	PUNCT
ejpam-6073	2	5	mohammed	mohammed	PROPN
ejpam-6073	2	6	d.	d.	PROPN
ejpam-6073	2	7	kassim3	kassim3	PROPN
ejpam-6073	2	8	,	,	PUNCT
ejpam-6073	2	9	abdelaziz	abdelaziz	PROPN
ejpam-6073	2	10	soufyane4	soufyane4	PROPN
ejpam-6073	2	11	,	,	PUNCT
ejpam-6073	2	12	mostafa	mostafa	PROPN
ejpam-6073	2	13	zahri4	zahri4	PROPN
ejpam-6073	2	14	,	,	PUNCT
ejpam-6073	2	15	soh	soh	PROPN
ejpam-6073	2	16	edwin	edwin	PROPN
ejpam-6073	2	17	mukiawa5	mukiawa5	PROPN
ejpam-6073	2	18	1	1	NUM
ejpam-6073	2	19	department	department	NOUN
ejpam-6073	2	20	of	of	ADP
ejpam-6073	2	21	mathematics	mathematic	NOUN
ejpam-6073	2	22	,	,	PUNCT
ejpam-6073	2	23	king	king	PROPN
ejpam-6073	2	24	fahd	fahd	PROPN
ejpam-6073	2	25	university	university	PROPN
ejpam-6073	2	26	of	of	ADP
ejpam-6073	2	27	petroleum	petroleum	NOUN
ejpam-6073	2	28	and	and	CCONJ
ejpam-6073	2	29	minerals	mineral	NOUN
ejpam-6073	2	30	,	,	PUNCT
ejpam-6073	2	31	dhahran	dhahran	ADJ
ejpam-6073	2	32	31261	31261	NUM
ejpam-6073	2	33	,	,	PUNCT
ejpam-6073	2	34	saudi	saudi	PROPN
ejpam-6073	2	35	arabia	arabia	PROPN
ejpam-6073	2	36	2	2	NUM
ejpam-6073	2	37	the	the	DET
ejpam-6073	2	38	interdisciplinary	interdisciplinary	ADJ
ejpam-6073	2	39	research	research	NOUN
ejpam-6073	2	40	center	center	NOUN
ejpam-6073	2	41	in	in	ADP
ejpam-6073	2	42	construction	construction	NOUN
ejpam-6073	2	43	and	and	CCONJ
ejpam-6073	2	44	building	building	NOUN
ejpam-6073	2	45	materials	material	NOUN
ejpam-6073	2	46	,	,	PUNCT
ejpam-6073	2	47	king	king	PROPN
ejpam-6073	2	48	fahd	fahd	PROPN
ejpam-6073	2	49	university	university	PROPN
ejpam-6073	2	50	of	of	ADP
ejpam-6073	2	51	petroleum	petroleum	NOUN
ejpam-6073	2	52	and	and	CCONJ
ejpam-6073	2	53	minerals	mineral	NOUN
ejpam-6073	2	54	,	,	PUNCT
ejpam-6073	2	55	dhahran	dhahran	ADJ
ejpam-6073	2	56	31261	31261	NUM
ejpam-6073	2	57	,	,	PUNCT
ejpam-6073	2	58	saudi	saudi	PROPN
ejpam-6073	2	59	arabia	arabia	PROPN
ejpam-6073	2	60	3	3	NUM
ejpam-6073	2	61	department	department	NOUN
ejpam-6073	2	62	of	of	ADP
ejpam-6073	2	63	basic	basic	ADJ
ejpam-6073	2	64	engineering	engineering	NOUN
ejpam-6073	2	65	sciences	science	NOUN
ejpam-6073	2	66	,	,	PUNCT
ejpam-6073	2	67	college	college	NOUN
ejpam-6073	2	68	of	of	ADP
ejpam-6073	2	69	engineering	engineering	PROPN
ejpam-6073	2	70	,	,	PUNCT
ejpam-6073	2	71	imam	imam	PROPN
ejpam-6073	2	72	abdulrahman	abdulrahman	PROPN
ejpam-6073	2	73	bin	bin	PROPN
ejpam-6073	2	74	faisal	faisal	PROPN
ejpam-6073	2	75	university	university	PROPN
ejpam-6073	2	76	,	,	PUNCT
ejpam-6073	2	77	p.o	p.o	PROPN
ejpam-6073	2	78	.	.	PROPN
ejpam-6073	2	79	box	box	PROPN
ejpam-6073	2	80	1982	1982	NUM
ejpam-6073	2	81	,	,	PUNCT
ejpam-6073	2	82	34151	34151	NUM
ejpam-6073	2	83	,	,	PUNCT
ejpam-6073	2	84	dammam	dammam	PROPN
ejpam-6073	2	85	,	,	PUNCT
ejpam-6073	2	86	saudi	saudi	PROPN
ejpam-6073	2	87	arabia	arabia	PROPN
ejpam-6073	2	88	4	4	NUM
ejpam-6073	2	89	department	department	NOUN
ejpam-6073	2	90	of	of	ADP
ejpam-6073	2	91	mathematics	mathematic	NOUN
ejpam-6073	2	92	and	and	CCONJ
ejpam-6073	2	93	statistics	statistic	NOUN
ejpam-6073	2	94	,	,	PUNCT
ejpam-6073	2	95	university	university	PROPN
ejpam-6073	2	96	of	of	ADP
ejpam-6073	2	97	sharjah	sharjah	PROPN
ejpam-6073	2	98	,	,	PUNCT
ejpam-6073	2	99	sharjah	sharjah	PROPN
ejpam-6073	2	100	,	,	PUNCT
ejpam-6073	2	101	united	united	PROPN
ejpam-6073	2	102	arab	arab	PROPN
ejpam-6073	2	103	emirates	emirates	PROPN
ejpam-6073	2	104	5	5	NUM
ejpam-6073	2	105	department	department	NOUN
ejpam-6073	2	106	of	of	ADP
ejpam-6073	2	107	mathematics	mathematic	NOUN
ejpam-6073	2	108	,	,	PUNCT
ejpam-6073	2	109	university	university	NOUN
ejpam-6073	2	110	of	of	ADP
ejpam-6073	2	111	hafr	hafr	PROPN
ejpam-6073	2	112	al	al	PROPN
ejpam-6073	2	113	batin	batin	PROPN
ejpam-6073	2	114	,	,	PUNCT
ejpam-6073	2	115	hafar	hafar	ADV
ejpam-6073	2	116	al	al	PROPN
ejpam-6073	2	117	batin	batin	PROPN
ejpam-6073	2	118	39524	39524	NUM
ejpam-6073	2	119	,	,	PUNCT
ejpam-6073	2	120	saudi	saudi	PROPN
ejpam-6073	2	121	arabia	arabia	PROPN
ejpam-6073	2	122	abstract	abstract	NOUN
ejpam-6073	2	123	.	.	PUNCT
ejpam-6073	3	1	swelling	swell	VERB
ejpam-6073	3	2	soil	soil	NOUN
ejpam-6073	3	3	problems	problem	NOUN
ejpam-6073	3	4	arise	arise	VERB
ejpam-6073	3	5	in	in	ADP
ejpam-6073	3	6	various	various	ADJ
ejpam-6073	3	7	real	real	ADJ
ejpam-6073	3	8	-	-	PUNCT
ejpam-6073	3	9	world	world	NOUN
ejpam-6073	3	10	applications	application	NOUN
ejpam-6073	3	11	,	,	PUNCT
ejpam-6073	3	12	such	such	ADJ
ejpam-6073	3	13	as	as	ADP
ejpam-6073	3	14	geomechanics	geomechanic	NOUN
ejpam-6073	3	15	,	,	PUNCT
ejpam-6073	3	16	biomedical	biomedical	ADJ
ejpam-6073	3	17	engineering	engineering	NOUN
ejpam-6073	3	18	,	,	PUNCT
ejpam-6073	3	19	and	and	CCONJ
ejpam-6073	3	20	hydrogel	hydrogel	NOUN
ejpam-6073	3	21	-	-	PUNCT
ejpam-6073	3	22	based	base	VERB
ejpam-6073	3	23	materials	material	NOUN
ejpam-6073	3	24	,	,	PUNCT
ejpam-6073	3	25	where	where	SCONJ
ejpam-6073	3	26	fluid	fluid	ADJ
ejpam-6073	3	27	interaction	interaction	NOUN
ejpam-6073	3	28	with	with	ADP
ejpam-6073	3	29	elastic	elastic	ADJ
ejpam-6073	3	30	structures	structure	NOUN
ejpam-6073	3	31	influences	influence	VERB
ejpam-6073	3	32	mechanical	mechanical	ADJ
ejpam-6073	3	33	stability	stability	NOUN
ejpam-6073	3	34	.	.	PUNCT
ejpam-6073	4	1	in	in	ADP
ejpam-6073	4	2	this	this	DET
ejpam-6073	4	3	study	study	NOUN
ejpam-6073	4	4	,	,	PUNCT
ejpam-6073	4	5	we	we	PRON
ejpam-6073	4	6	investigate	investigate	VERB
ejpam-6073	4	7	a	a	DET
ejpam-6073	4	8	swelling	swell	VERB
ejpam-6073	4	9	soil	soil	NOUN
ejpam-6073	4	10	system	system	NOUN
ejpam-6073	4	11	incorporating	incorporate	VERB
ejpam-6073	4	12	two	two	NUM
ejpam-6073	4	13	nonlinear	nonlinear	ADJ
ejpam-6073	4	14	variable	variable	ADJ
ejpam-6073	4	15	exponent	exponent	NOUN
ejpam-6073	4	16	damping	damp	VERB
ejpam-6073	4	17	and	and	CCONJ
ejpam-6073	4	18	source	source	NOUN
ejpam-6073	4	19	terms	term	NOUN
ejpam-6073	4	20	,	,	PUNCT
ejpam-6073	4	21	which	which	PRON
ejpam-6073	4	22	provide	provide	VERB
ejpam-6073	4	23	a	a	DET
ejpam-6073	4	24	more	more	ADV
ejpam-6073	4	25	adaptable	adaptable	ADJ
ejpam-6073	4	26	framework	framework	NOUN
ejpam-6073	4	27	for	for	ADP
ejpam-6073	4	28	capturing	capture	VERB
ejpam-6073	4	29	heterogeneous	heterogeneous	ADJ
ejpam-6073	4	30	material	material	NOUN
ejpam-6073	4	31	behaviors	behavior	NOUN
ejpam-6073	4	32	and	and	CCONJ
ejpam-6073	4	33	evolving	evolve	VERB
ejpam-6073	4	34	energy	energy	NOUN
ejpam-6073	4	35	dissipation	dissipation	NOUN
ejpam-6073	4	36	mechanisms	mechanism	NOUN
ejpam-6073	4	37	.	.	PUNCT
ejpam-6073	5	1	using	use	VERB
ejpam-6073	5	2	the	the	DET
ejpam-6073	5	3	faedo	faedo	ADJ
ejpam-6073	5	4	-	-	PUNCT
ejpam-6073	5	5	galerkin	galerkin	ADJ
ejpam-6073	5	6	method	method	NOUN
ejpam-6073	5	7	and	and	CCONJ
ejpam-6073	5	8	the	the	DET
ejpam-6073	5	9	banach	banach	NOUN
ejpam-6073	5	10	contraction	contraction	NOUN
ejpam-6073	5	11	theorem	theorem	VERB
ejpam-6073	5	12	,	,	PUNCT
ejpam-6073	5	13	we	we	PRON
ejpam-6073	5	14	establish	establish	VERB
ejpam-6073	5	15	the	the	DET
ejpam-6073	5	16	local	local	ADJ
ejpam-6073	5	17	existence	existence	NOUN
ejpam-6073	5	18	and	and	CCONJ
ejpam-6073	5	19	uniqueness	uniqueness	NOUN
ejpam-6073	5	20	of	of	ADP
ejpam-6073	5	21	weak	weak	ADJ
ejpam-6073	5	22	solutions	solution	NOUN
ejpam-6073	5	23	under	under	ADP
ejpam-6073	5	24	suitable	suitable	ADJ
ejpam-6073	5	25	conditions	condition	NOUN
ejpam-6073	5	26	on	on	ADP
ejpam-6073	5	27	the	the	DET
ejpam-6073	5	28	variable	variable	ADJ
ejpam-6073	5	29	exponent	exponent	NOUN
ejpam-6073	5	30	functions	function	NOUN
ejpam-6073	5	31	.	.	PUNCT
ejpam-6073	6	1	furthermore	furthermore	ADV
ejpam-6073	6	2	,	,	PUNCT
ejpam-6073	6	3	we	we	PRON
ejpam-6073	6	4	demonstrate	demonstrate	VERB
ejpam-6073	6	5	the	the	DET
ejpam-6073	6	6	global	global	ADJ
ejpam-6073	6	7	existence	existence	NOUN
ejpam-6073	6	8	of	of	ADP
ejpam-6073	6	9	solutions	solution	NOUN
ejpam-6073	6	10	and	and	CCONJ
ejpam-6073	6	11	identify	identify	VERB
ejpam-6073	6	12	conditions	condition	NOUN
ejpam-6073	6	13	leading	lead	VERB
ejpam-6073	6	14	to	to	ADP
ejpam-6073	6	15	finite	finite	ADJ
ejpam-6073	6	16	-	-	PUNCT
ejpam-6073	6	17	time	time	NOUN
ejpam-6073	6	18	blow	blow	NOUN
ejpam-6073	6	19	-	-	PUNCT
ejpam-6073	6	20	up	up	NOUN
ejpam-6073	6	21	,	,	PUNCT
ejpam-6073	6	22	offering	offer	VERB
ejpam-6073	6	23	insights	insight	NOUN
ejpam-6073	6	24	into	into	ADP
ejpam-6073	6	25	stability	stability	NOUN
ejpam-6073	6	26	and	and	CCONJ
ejpam-6073	6	27	failure	failure	NOUN
ejpam-6073	6	28	prediction	prediction	NOUN
ejpam-6073	6	29	in	in	ADP
ejpam-6073	6	30	porous	porous	ADJ
ejpam-6073	6	31	-	-	PUNCT
ejpam-6073	6	32	elastic	elastic	ADJ
ejpam-6073	6	33	media	medium	NOUN
ejpam-6073	6	34	.	.	PUNCT
ejpam-6073	7	1	to	to	PART
ejpam-6073	7	2	validate	validate	VERB
ejpam-6073	7	3	our	our	PRON
ejpam-6073	7	4	theoretical	theoretical	ADJ
ejpam-6073	7	5	findings	finding	NOUN
ejpam-6073	7	6	,	,	PUNCT
ejpam-6073	7	7	we	we	PRON
ejpam-6073	7	8	present	present	VERB
ejpam-6073	7	9	numerical	numerical	ADJ
ejpam-6073	7	10	simulations	simulation	NOUN
ejpam-6073	7	11	illustrating	illustrate	VERB
ejpam-6073	7	12	the	the	DET
ejpam-6073	7	13	blow	blow	NOUN
ejpam-6073	7	14	-	-	PUNCT
ejpam-6073	7	15	up	up	ADP
ejpam-6073	7	16	behavior	behavior	NOUN
ejpam-6073	7	17	,	,	PUNCT
ejpam-6073	7	18	emphasizing	emphasize	VERB
ejpam-6073	7	19	the	the	DET
ejpam-6073	7	20	role	role	NOUN
ejpam-6073	7	21	of	of	ADP
ejpam-6073	7	22	variable	variable	ADJ
ejpam-6073	7	23	exponent	exponent	NOUN
ejpam-6073	7	24	damping	damp	VERB
ejpam-6073	7	25	in	in	ADP
ejpam-6073	7	26	influencing	influence	VERB
ejpam-6073	7	27	system	system	NOUN
ejpam-6073	7	28	dynamics	dynamic	NOUN
ejpam-6073	7	29	.	.	PUNCT
ejpam-6073	8	1	2020	2020	NUM
ejpam-6073	8	2	mathematics	mathematic	NOUN
ejpam-6073	8	3	subject	subject	NOUN
ejpam-6073	8	4	classifications	classification	NOUN
ejpam-6073	8	5	:	:	PUNCT
ejpam-6073	8	6	93d20	93d20	NUM
ejpam-6073	8	7	,	,	PUNCT
ejpam-6073	8	8	35b40	35b40	NUM
ejpam-6073	8	9	key	key	ADJ
ejpam-6073	8	10	words	word	NOUN
ejpam-6073	8	11	and	and	CCONJ
ejpam-6073	8	12	phrases	phrase	NOUN
ejpam-6073	8	13	:	:	PUNCT
ejpam-6073	8	14	swelling	swell	VERB
ejpam-6073	8	15	soil	soil	NOUN
ejpam-6073	8	16	problems	problem	NOUN
ejpam-6073	8	17	,	,	PUNCT
ejpam-6073	8	18	faedo	faedo	NOUN
ejpam-6073	8	19	-	-	PUNCT
ejpam-6073	8	20	galerkin	galerkin	ADJ
ejpam-6073	8	21	method	method	NOUN
ejpam-6073	8	22	,	,	PUNCT
ejpam-6073	8	23	banach	banach	NOUN
ejpam-6073	8	24	contraction	contraction	NOUN
ejpam-6073	8	25	theorem	theorem	VERB
ejpam-6073	8	26	,	,	PUNCT
ejpam-6073	8	27	blow	blow	NOUN
ejpam-6073	8	28	-	-	PUNCT
ejpam-6073	8	29	up	up	NOUN
ejpam-6073	8	30	,	,	PUNCT
ejpam-6073	8	31	variable	variable	ADJ
ejpam-6073	8	32	exponents	exponent	NOUN
ejpam-6073	8	33	,	,	PUNCT
ejpam-6073	8	34	numerical	numerical	ADJ
ejpam-6073	8	35	methods	method	NOUN
ejpam-6073	8	36	∗corresponding	∗corresponde	VERB
ejpam-6073	8	37	author	author	NOUN
ejpam-6073	8	38	.	.	PUNCT
ejpam-6073	9	1	doi	doi	NOUN
ejpam-6073	9	2	:	:	PUNCT
ejpam-6073	9	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6073	https://doi.org/10.29020/nybg.ejpam.v18i3.6073	NOUN
ejpam-6073	9	4	email	email	NOUN
ejpam-6073	9	5	addresses	address	VERB
ejpam-6073	9	6	:	:	PUNCT
ejpam-6073	9	7	almahdi@kfupm.edu.sa	almahdi@kfupm.edu.sa	PROPN
ejpam-6073	9	8	(	(	PUNCT
ejpam-6073	9	9	a.	a.	NOUN
ejpam-6073	9	10	m.	m.	PROPN
ejpam-6073	9	11	al	al	PROPN
ejpam-6073	9	12	-	-	PUNCT
ejpam-6073	9	13	mahdi	mahdi	PROPN
ejpam-6073	9	14	)	)	PUNCT
ejpam-6073	9	15	,	,	PUNCT
ejpam-6073	9	16	mahfouz@kfupm.edu.sa	mahfouz@kfupm.edu.sa	PROPN
ejpam-6073	9	17	(	(	PUNCT
ejpam-6073	9	18	m.	m.	NOUN
ejpam-6073	9	19	m.	m.	PROPN
ejpam-6073	9	20	al	al	PROPN
ejpam-6073	9	21	-	-	PUNCT
ejpam-6073	9	22	gharabli	gharabli	PROPN
ejpam-6073	9	23	)	)	PUNCT
ejpam-6073	9	24	,	,	PUNCT
ejpam-6073	9	25	mdkassim@iau.edu.sa	mdkassim@iau.edu.sa	PROPN
ejpam-6073	9	26	(	(	PUNCT
ejpam-6073	9	27	m.	m.	PROPN
ejpam-6073	9	28	d.	d.	PROPN
ejpam-6073	9	29	kassim	kassim	PROPN
ejpam-6073	9	30	)	)	PUNCT
ejpam-6073	9	31	,	,	PUNCT
ejpam-6073	9	32	asoufyane@sharjah.ac.ae	asoufyane@sharjah.ac.ae	NOUN
ejpam-6073	9	33	(	(	PUNCT
ejpam-6073	9	34	a.	a.	NOUN
ejpam-6073	9	35	soufyane	soufyane	NOUN
ejpam-6073	9	36	)	)	PUNCT
ejpam-6073	9	37	,	,	PUNCT
ejpam-6073	9	38	mzahri@sharjah.ac.ae	mzahri@sharjah.ac.ae	PROPN
ejpam-6073	9	39	(	(	PUNCT
ejpam-6073	9	40	m.	m.	NOUN
ejpam-6073	9	41	zahri	zahri	PROPN
ejpam-6073	9	42	)	)	PUNCT
ejpam-6073	9	43	,	,	PUNCT
ejpam-6073	9	44	mukiawa@uhb.edu.sa	mukiawa@uhb.edu.sa	PROPN
ejpam-6073	9	45	(	(	PUNCT
ejpam-6073	9	46	s.	s.	PROPN
ejpam-6073	9	47	e.	e.	PROPN
ejpam-6073	9	48	mukiawa	mukiawa	PROPN
ejpam-6073	9	49	)	)	PUNCT
ejpam-6073	9	50	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6073	10	1	1	1	NUM
ejpam-6073	10	2	copyright	copyright	NOUN
ejpam-6073	10	3	:	:	PUNCT
ejpam-6073	10	4	©	©	PROPN
ejpam-6073	10	5	2025	2025	NUM
ejpam-6073	10	6	the	the	DET
ejpam-6073	10	7	author(s	author(s	NOUN
ejpam-6073	10	8	)	)	PUNCT
ejpam-6073	10	9	.	.	PUNCT
ejpam-6073	11	1	(	(	PUNCT
ejpam-6073	11	2	cc	cc	NOUN
ejpam-6073	11	3	by	by	ADP
ejpam-6073	11	4	-	-	PUNCT
ejpam-6073	11	5	nc	nc	PROPN
ejpam-6073	11	6	4.0	4.0	NUM
ejpam-6073	11	7	)	)	PUNCT
ejpam-6073	11	8	a.	a.	NOUN
ejpam-6073	11	9	m.	m.	PROPN
ejpam-6073	11	10	al	al	PROPN
ejpam-6073	11	11	-	-	PROPN
ejpam-6073	11	12	mahdi	mahdi	PROPN
ejpam-6073	11	13	et	et	PROPN
ejpam-6073	11	14	al	al	PROPN
ejpam-6073	11	15	.	.	PUNCT
ejpam-6073	11	16	/	/	SYM
ejpam-6073	11	17	eur	eur	PROPN
ejpam-6073	11	18	.	.	PUNCT
ejpam-6073	12	1	j.	j.	PROPN
ejpam-6073	12	2	pure	pure	PROPN
ejpam-6073	12	3	appl	appl	PROPN
ejpam-6073	12	4	.	.	PROPN
ejpam-6073	12	5	math	math	PROPN
ejpam-6073	12	6	,	,	PUNCT
ejpam-6073	12	7	18	18	NUM
ejpam-6073	12	8	(	(	PUNCT
ejpam-6073	12	9	3	3	NUM
ejpam-6073	12	10	)	)	PUNCT
ejpam-6073	12	11	(	(	PUNCT
ejpam-6073	12	12	2025	2025	NUM
ejpam-6073	12	13	)	)	PUNCT
ejpam-6073	12	14	,	,	PUNCT
ejpam-6073	12	15	6073	6073	NUM
ejpam-6073	12	16	2	2	NUM
ejpam-6073	12	17	of	of	ADP
ejpam-6073	12	18	29	29	NUM
ejpam-6073	12	19	1	1	NUM
ejpam-6073	12	20	.	.	PUNCT
ejpam-6073	13	1	introduction	introduction	NOUN
ejpam-6073	13	2	swelling	swell	VERB
ejpam-6073	13	3	soils	soil	NOUN
ejpam-6073	13	4	,	,	PUNCT
ejpam-6073	13	5	also	also	ADV
ejpam-6073	13	6	known	know	VERB
ejpam-6073	13	7	as	as	ADP
ejpam-6073	13	8	expansive	expansive	ADJ
ejpam-6073	13	9	soils	soil	NOUN
ejpam-6073	13	10	,	,	PUNCT
ejpam-6073	13	11	are	be	AUX
ejpam-6073	13	12	characterized	characterize	VERB
ejpam-6073	13	13	by	by	ADP
ejpam-6073	13	14	an	an	DET
ejpam-6073	13	15	increase	increase	NOUN
ejpam-6073	13	16	in	in	ADP
ejpam-6073	13	17	volume	volume	NOUN
ejpam-6073	13	18	when	when	SCONJ
ejpam-6073	13	19	exposed	expose	VERB
ejpam-6073	13	20	to	to	ADP
ejpam-6073	13	21	moisture	moisture	NOUN
ejpam-6073	13	22	.	.	PUNCT
ejpam-6073	14	1	the	the	DET
ejpam-6073	14	2	clay	clay	NOUN
ejpam-6073	14	3	minerals	mineral	NOUN
ejpam-6073	14	4	within	within	ADP
ejpam-6073	14	5	these	these	DET
ejpam-6073	14	6	soils	soil	NOUN
ejpam-6073	14	7	naturally	naturally	ADV
ejpam-6073	14	8	attract	attract	VERB
ejpam-6073	14	9	and	and	CCONJ
ejpam-6073	14	10	absorb	absorb	VERB
ejpam-6073	14	11	water	water	NOUN
ejpam-6073	14	12	.	.	PUNCT
ejpam-6073	15	1	as	as	SCONJ
ejpam-6073	15	2	described	describe	VERB
ejpam-6073	15	3	succinctly	succinctly	ADV
ejpam-6073	15	4	by	by	ADP
ejpam-6073	15	5	handy	handy	ADJ
ejpam-6073	15	6	[	[	X
ejpam-6073	15	7	1	1	NUM
ejpam-6073	15	8	]	]	PUNCT
ejpam-6073	15	9	,	,	PUNCT
ejpam-6073	15	10	”	"	PUNCT
ejpam-6073	15	11	when	when	SCONJ
ejpam-6073	15	12	water	water	NOUN
ejpam-6073	15	13	is	be	AUX
ejpam-6073	15	14	introduced	introduce	VERB
ejpam-6073	15	15	to	to	ADP
ejpam-6073	15	16	swelling	swell	VERB
ejpam-6073	15	17	soils	soil	NOUN
ejpam-6073	15	18	,	,	PUNCT
ejpam-6073	15	19	the	the	DET
ejpam-6073	15	20	water	water	NOUN
ejpam-6073	15	21	molecules	molecule	NOUN
ejpam-6073	15	22	are	be	AUX
ejpam-6073	15	23	pulled	pull	VERB
ejpam-6073	15	24	into	into	ADP
ejpam-6073	15	25	gaps	gap	NOUN
ejpam-6073	15	26	between	between	ADP
ejpam-6073	15	27	the	the	DET
ejpam-6073	15	28	soil	soil	NOUN
ejpam-6073	15	29	plates	plate	NOUN
ejpam-6073	15	30	.	.	PUNCT
ejpam-6073	16	1	as	as	SCONJ
ejpam-6073	16	2	more	more	ADJ
ejpam-6073	16	3	water	water	NOUN
ejpam-6073	16	4	is	be	AUX
ejpam-6073	16	5	absorbed	absorb	VERB
ejpam-6073	16	6	,	,	PUNCT
ejpam-6073	16	7	the	the	DET
ejpam-6073	16	8	plates	plate	NOUN
ejpam-6073	16	9	are	be	AUX
ejpam-6073	16	10	forced	force	VERB
ejpam-6073	16	11	further	far	ADV
ejpam-6073	16	12	apart	apart	ADV
ejpam-6073	16	13	,	,	PUNCT
ejpam-6073	16	14	leading	lead	VERB
ejpam-6073	16	15	to	to	ADP
ejpam-6073	16	16	an	an	DET
ejpam-6073	16	17	increase	increase	NOUN
ejpam-6073	16	18	in	in	ADP
ejpam-6073	16	19	soil	soil	NOUN
ejpam-6073	16	20	pore	pore	ADJ
ejpam-6073	16	21	pressure	pressure	NOUN
ejpam-6073	16	22	.	.	PUNCT
ejpam-6073	16	23	”	"	PUNCT
ejpam-6073	17	1	consequently	consequently	ADV
ejpam-6073	17	2	,	,	PUNCT
ejpam-6073	17	3	swelling	swell	VERB
ejpam-6073	17	4	soils	soil	NOUN
ejpam-6073	17	5	pose	pose	VERB
ejpam-6073	17	6	significant	significant	ADJ
ejpam-6073	17	7	geotechnical	geotechnical	ADJ
ejpam-6073	17	8	and	and	CCONJ
ejpam-6073	17	9	structural	structural	ADJ
ejpam-6073	17	10	challenges	challenge	NOUN
ejpam-6073	17	11	,	,	PUNCT
ejpam-6073	17	12	impacting	impact	VERB
ejpam-6073	17	13	both	both	CCONJ
ejpam-6073	17	14	the	the	DET
ejpam-6073	17	15	environment	environment	NOUN
ejpam-6073	17	16	and	and	CCONJ
ejpam-6073	17	17	society	society	NOUN
ejpam-6073	17	18	,	,	PUNCT
ejpam-6073	17	19	as	as	SCONJ
ejpam-6073	17	20	illustrated	illustrate	VERB
ejpam-6073	17	21	in	in	ADP
ejpam-6073	17	22	figures	figure	NOUN
ejpam-6073	17	23	(	(	PUNCT
ejpam-6073	17	24	1)-(2	1)-(2	NUM
ejpam-6073	17	25	)	)	PUNCT
ejpam-6073	17	26	.	.	PUNCT
ejpam-6073	18	1	figure	figure	VERB
ejpam-6073	18	2	1	1	NUM
ejpam-6073	18	3	:	:	PUNCT
ejpam-6073	18	4	cracking	crack	VERB
ejpam-6073	18	5	in	in	ADP
ejpam-6073	18	6	soil	soil	NOUN
ejpam-6073	18	7	figure	figure	NOUN
ejpam-6073	18	8	2	2	NUM
ejpam-6073	18	9	:	:	PUNCT
ejpam-6073	18	10	cracking	crack	VERB
ejpam-6073	18	11	in	in	ADP
ejpam-6073	18	12	a	a	DET
ejpam-6073	18	13	building	building	NOUN
ejpam-6073	18	14	structure	structure	NOUN
ejpam-6073	18	15	swelling	swell	VERB
ejpam-6073	18	16	soils	soil	NOUN
ejpam-6073	18	17	are	be	AUX
ejpam-6073	18	18	found	find	VERB
ejpam-6073	18	19	worldwide	worldwide	ADV
ejpam-6073	18	20	.	.	PUNCT
ejpam-6073	19	1	as	as	SCONJ
ejpam-6073	19	2	reported	report	VERB
ejpam-6073	19	3	by	by	ADP
ejpam-6073	19	4	nelson	nelson	PROPN
ejpam-6073	19	5	and	and	CCONJ
ejpam-6073	19	6	miller	miller	PROPN
ejpam-6073	20	1	[	[	X
ejpam-6073	20	2	2	2	NUM
ejpam-6073	20	3	]	]	PUNCT
ejpam-6073	20	4	,	,	PUNCT
ejpam-6073	20	5	the	the	DET
ejpam-6073	20	6	american	american	ADJ
ejpam-6073	20	7	society	society	NOUN
ejpam-6073	20	8	of	of	ADP
ejpam-6073	20	9	civil	civil	ADJ
ejpam-6073	20	10	engineers	engineer	NOUN
ejpam-6073	20	11	estimates	estimate	VERB
ejpam-6073	20	12	that	that	SCONJ
ejpam-6073	20	13	one	one	NUM
ejpam-6073	20	14	in	in	ADP
ejpam-6073	20	15	four	four	NUM
ejpam-6073	20	16	homes	home	NOUN
ejpam-6073	20	17	suffer	suffer	VERB
ejpam-6073	20	18	damage	damage	NOUN
ejpam-6073	20	19	caused	cause	VERB
ejpam-6073	20	20	by	by	ADP
ejpam-6073	20	21	expansive	expansive	ADJ
ejpam-6073	20	22	soils	soil	NOUN
ejpam-6073	20	23	.	.	PUNCT
ejpam-6073	21	1	typically	typically	ADV
ejpam-6073	21	2	,	,	PUNCT
ejpam-6073	21	3	such	such	ADJ
ejpam-6073	21	4	soils	soil	NOUN
ejpam-6073	21	5	result	result	VERB
ejpam-6073	21	6	in	in	ADP
ejpam-6073	21	7	greater	great	ADJ
ejpam-6073	21	8	financial	financial	ADJ
ejpam-6073	21	9	losses	loss	NOUN
ejpam-6073	21	10	for	for	ADP
ejpam-6073	21	11	property	property	NOUN
ejpam-6073	21	12	owners	owner	NOUN
ejpam-6073	21	13	than	than	ADP
ejpam-6073	21	14	earthquakes	earthquake	NOUN
ejpam-6073	21	15	,	,	PUNCT
ejpam-6073	21	16	floods	flood	NOUN
ejpam-6073	21	17	,	,	PUNCT
ejpam-6073	21	18	hurricanes	hurricane	NOUN
ejpam-6073	21	19	,	,	PUNCT
ejpam-6073	21	20	and	and	CCONJ
ejpam-6073	21	21	tornadoes	tornado	NOUN
ejpam-6073	21	22	combined	combine	VERB
ejpam-6073	21	23	.	.	PUNCT
ejpam-6073	22	1	therefore	therefore	ADV
ejpam-6073	22	2	,	,	PUNCT
ejpam-6073	22	3	it	it	PRON
ejpam-6073	22	4	is	be	AUX
ejpam-6073	22	5	crucial	crucial	ADJ
ejpam-6073	22	6	to	to	PART
ejpam-6073	22	7	explore	explore	VERB
ejpam-6073	22	8	effective	effective	ADJ
ejpam-6073	22	9	methods	method	NOUN
ejpam-6073	22	10	to	to	PART
ejpam-6073	22	11	mitigate	mitigate	VERB
ejpam-6073	22	12	or	or	CCONJ
ejpam-6073	22	13	eliminate	eliminate	VERB
ejpam-6073	22	14	the	the	DET
ejpam-6073	22	15	damage	damage	NOUN
ejpam-6073	22	16	caused	cause	VERB
ejpam-6073	22	17	by	by	ADP
ejpam-6073	22	18	swelling	swell	VERB
ejpam-6073	22	19	soils	soil	NOUN
ejpam-6073	22	20	.	.	PUNCT
ejpam-6073	23	1	further	further	ADJ
ejpam-6073	23	2	theoretical	theoretical	ADJ
ejpam-6073	23	3	background	background	NOUN
ejpam-6073	23	4	and	and	CCONJ
ejpam-6073	23	5	details	detail	NOUN
ejpam-6073	23	6	can	can	AUX
ejpam-6073	23	7	be	be	AUX
ejpam-6073	23	8	found	find	VERB
ejpam-6073	23	9	in	in	ADP
ejpam-6073	23	10	[	[	X
ejpam-6073	23	11	3–5	3–5	NOUN
ejpam-6073	23	12	]	]	PUNCT
ejpam-6073	23	13	.	.	PUNCT
ejpam-6073	24	1	although	although	SCONJ
ejpam-6073	24	2	various	various	ADJ
ejpam-6073	24	3	chemical	chemical	NOUN
ejpam-6073	24	4	admixtures	admixture	NOUN
ejpam-6073	24	5	and	and	CCONJ
ejpam-6073	24	6	other	other	ADJ
ejpam-6073	24	7	costly	costly	ADJ
ejpam-6073	24	8	methods	method	NOUN
ejpam-6073	24	9	have	have	AUX
ejpam-6073	24	10	been	be	AUX
ejpam-6073	24	11	employed	employ	VERB
ejpam-6073	24	12	to	to	PART
ejpam-6073	24	13	mitigate	mitigate	VERB
ejpam-6073	24	14	swelling	swell	VERB
ejpam-6073	24	15	soil	soil	NOUN
ejpam-6073	24	16	damage	damage	NOUN
ejpam-6073	24	17	,	,	PUNCT
ejpam-6073	24	18	these	these	DET
ejpam-6073	24	19	solutions	solution	NOUN
ejpam-6073	24	20	are	be	AUX
ejpam-6073	24	21	often	often	ADV
ejpam-6073	24	22	ineffective	ineffective	ADJ
ejpam-6073	24	23	in	in	ADP
ejpam-6073	24	24	the	the	DET
ejpam-6073	24	25	long	long	ADJ
ejpam-6073	24	26	term	term	NOUN
ejpam-6073	24	27	.	.	PUNCT
ejpam-6073	25	1	this	this	DET
ejpam-6073	25	2	research	research	NOUN
ejpam-6073	25	3	aims	aim	VERB
ejpam-6073	25	4	to	to	PART
ejpam-6073	25	5	stabilize	stabilize	VERB
ejpam-6073	25	6	swelling	swell	VERB
ejpam-6073	25	7	soils	soil	NOUN
ejpam-6073	25	8	by	by	ADP
ejpam-6073	25	9	utilizing	utilize	VERB
ejpam-6073	25	10	damping	damp	VERB
ejpam-6073	25	11	mechanisms	mechanism	NOUN
ejpam-6073	25	12	that	that	PRON
ejpam-6073	25	13	are	be	AUX
ejpam-6073	25	14	both	both	CCONJ
ejpam-6073	25	15	effective	effective	ADJ
ejpam-6073	25	16	and	and	CCONJ
ejpam-6073	25	17	environmentally	environmentally	ADV
ejpam-6073	25	18	sustainable	sustainable	ADJ
ejpam-6073	25	19	.	.	PUNCT
ejpam-6073	26	1	mathematically	mathematically	ADV
ejpam-6073	26	2	,	,	PUNCT
ejpam-6073	26	3	swelling	swell	VERB
ejpam-6073	26	4	soil	soil	NOUN
ejpam-6073	26	5	models	model	NOUN
ejpam-6073	26	6	consist	consist	VERB
ejpam-6073	26	7	of	of	ADP
ejpam-6073	26	8	two	two	NUM
ejpam-6073	26	9	coupled	couple	VERB
ejpam-6073	26	10	partial	partial	ADJ
ejpam-6073	26	11	differential	differential	NOUN
ejpam-6073	26	12	equations	equation	NOUN
ejpam-6073	26	13	that	that	PRON
ejpam-6073	26	14	describe	describe	VERB
ejpam-6073	26	15	the	the	DET
ejpam-6073	26	16	displacement	displacement	NOUN
ejpam-6073	26	17	of	of	ADP
ejpam-6073	26	18	both	both	CCONJ
ejpam-6073	26	19	the	the	DET
ejpam-6073	26	20	fluid	fluid	NOUN
ejpam-6073	26	21	and	and	CCONJ
ejpam-6073	26	22	the	the	DET
ejpam-6073	26	23	elastic	elastic	ADJ
ejpam-6073	26	24	solid	solid	ADJ
ejpam-6073	26	25	material	material	NOUN
ejpam-6073	26	26	.	.	PUNCT
ejpam-6073	27	1	to	to	ADP
ejpam-6073	27	2	the	the	DET
ejpam-6073	27	3	best	good	ADJ
ejpam-6073	27	4	of	of	ADP
ejpam-6073	27	5	our	our	PRON
ejpam-6073	27	6	knowledge	knowledge	NOUN
ejpam-6073	27	7	,	,	PUNCT
ejpam-6073	27	8	the	the	DET
ejpam-6073	27	9	swelling	swell	VERB
ejpam-6073	27	10	soil	soil	NOUN
ejpam-6073	27	11	system	system	NOUN
ejpam-6073	27	12	was	be	AUX
ejpam-6073	27	13	first	first	ADV
ejpam-6073	27	14	proposed	propose	VERB
ejpam-6073	27	15	by	by	ADP
ejpam-6073	27	16	ieş	ieş	NOUN
ejpam-6073	27	17	[	[	X
ejpam-6073	27	18	6	6	NUM
ejpam-6073	27	19	]	]	PUNCT
ejpam-6073	27	20	and	and	CCONJ
ejpam-6073	27	21	later	later	ADV
ejpam-6073	27	22	simplified	simplify	VERB
ejpam-6073	27	23	by	by	ADP
ejpam-6073	27	24	quintanilla	quintanilla	NOUN
ejpam-6073	28	1	[	[	X
ejpam-6073	28	2	7	7	NUM
ejpam-6073	28	3	]	]	PUNCT
ejpam-6073	28	4	.	.	PUNCT
ejpam-6073	29	1	the	the	DET
ejpam-6073	29	2	fundamental	fundamental	ADJ
ejpam-6073	29	3	field	field	NOUN
ejpam-6073	29	4	equations	equation	NOUN
ejpam-6073	29	5	for	for	ADP
ejpam-6073	29	6	the	the	DET
ejpam-6073	29	7	linear	linear	PROPN
ejpam-6073	29	8	theory	theory	NOUN
ejpam-6073	29	9	of	of	ADP
ejpam-6073	29	10	swelling	swell	VERB
ejpam-6073	29	11	soils	soil	NOUN
ejpam-6073	29	12	are	be	AUX
ejpam-6073	29	13	given	give	VERB
ejpam-6073	29	14	by	by	ADP
ejpam-6073	29	15	{	{	PUNCT
ejpam-6073	29	16	ρzztt	ρzztt	NOUN
ejpam-6073	29	17	=	=	NOUN
ejpam-6073	29	18	p1x	p1x	NOUN
ejpam-6073	29	19	−g1	−g1	VERB
ejpam-6073	29	20	+	+	SYM
ejpam-6073	29	21	f1	f1	ADJ
ejpam-6073	29	22	,	,	PUNCT
ejpam-6073	29	23	ρuutt	ρuutt	NOUN
ejpam-6073	29	24	=	=	PUNCT
ejpam-6073	29	25	p2x	p2x	NOUN
ejpam-6073	29	26	+	+	NUM
ejpam-6073	29	27	g2	g2	PROPN
ejpam-6073	29	28	+	+	CCONJ
ejpam-6073	29	29	f2	f2	PROPN
ejpam-6073	29	30	,	,	PUNCT
ejpam-6073	29	31	(	(	PUNCT
ejpam-6073	29	32	1	1	X
ejpam-6073	29	33	)	)	PUNCT
ejpam-6073	29	34	where	where	SCONJ
ejpam-6073	29	35	the	the	DET
ejpam-6073	29	36	variables	variable	NOUN
ejpam-6073	29	37	z	z	PROPN
ejpam-6073	29	38	and	and	CCONJ
ejpam-6073	29	39	u	u	PROPN
ejpam-6073	29	40	represent	represent	VERB
ejpam-6073	29	41	the	the	DET
ejpam-6073	29	42	displacement	displacement	NOUN
ejpam-6073	29	43	of	of	ADP
ejpam-6073	29	44	the	the	DET
ejpam-6073	29	45	fluid	fluid	NOUN
ejpam-6073	29	46	and	and	CCONJ
ejpam-6073	29	47	the	the	DET
ejpam-6073	29	48	elastic	elastic	ADJ
ejpam-6073	29	49	solid	solid	ADJ
ejpam-6073	29	50	material	material	NOUN
ejpam-6073	29	51	,	,	PUNCT
ejpam-6073	29	52	respectively	respectively	ADV
ejpam-6073	29	53	.	.	PUNCT
ejpam-6073	30	1	the	the	DET
ejpam-6073	30	2	positive	positive	ADJ
ejpam-6073	30	3	constants	constant	NOUN
ejpam-6073	30	4	ρz	ρz	VERB
ejpam-6073	30	5	and	and	CCONJ
ejpam-6073	30	6	ρu	ρu	PRON
ejpam-6073	30	7	denote	denote	VERB
ejpam-6073	30	8	the	the	DET
ejpam-6073	30	9	densities	density	NOUN
ejpam-6073	30	10	of	of	ADP
ejpam-6073	30	11	each	each	DET
ejpam-6073	30	12	constituent	constituent	NOUN
ejpam-6073	30	13	.	.	PUNCT
ejpam-6073	31	1	the	the	DET
ejpam-6073	31	2	terms	term	NOUN
ejpam-6073	31	3	(	(	PUNCT
ejpam-6073	31	4	p1	p1	NOUN
ejpam-6073	31	5	,	,	PUNCT
ejpam-6073	31	6	g1	g1	NOUN
ejpam-6073	31	7	,	,	PUNCT
ejpam-6073	31	8	f1	f1	NOUN
ejpam-6073	31	9	)	)	PUNCT
ejpam-6073	31	10	correspond	correspond	VERB
ejpam-6073	31	11	to	to	ADP
ejpam-6073	31	12	the	the	DET
ejpam-6073	31	13	partial	partial	ADJ
ejpam-6073	31	14	tension	tension	NOUN
ejpam-6073	31	15	,	,	PUNCT
ejpam-6073	31	16	internal	internal	ADJ
ejpam-6073	31	17	body	body	NOUN
ejpam-6073	31	18	forces	force	NOUN
ejpam-6073	31	19	,	,	PUNCT
ejpam-6073	31	20	a.	a.	NOUN
ejpam-6073	31	21	m.	m.	PROPN
ejpam-6073	31	22	al	al	PROPN
ejpam-6073	31	23	-	-	PROPN
ejpam-6073	31	24	mahdi	mahdi	PROPN
ejpam-6073	31	25	et	et	PROPN
ejpam-6073	31	26	al	al	PROPN
ejpam-6073	31	27	.	.	PUNCT
ejpam-6073	31	28	/	/	SYM
ejpam-6073	31	29	eur	eur	PROPN
ejpam-6073	31	30	.	.	PUNCT
ejpam-6073	32	1	j.	j.	PROPN
ejpam-6073	32	2	pure	pure	PROPN
ejpam-6073	32	3	appl	appl	PROPN
ejpam-6073	32	4	.	.	PROPN
ejpam-6073	32	5	math	math	PROPN
ejpam-6073	32	6	,	,	PUNCT
ejpam-6073	32	7	18	18	NUM
ejpam-6073	32	8	(	(	PUNCT
ejpam-6073	32	9	3	3	NUM
ejpam-6073	32	10	)	)	PUNCT
ejpam-6073	32	11	(	(	PUNCT
ejpam-6073	32	12	2025	2025	NUM
ejpam-6073	32	13	)	)	PUNCT
ejpam-6073	32	14	,	,	PUNCT
ejpam-6073	32	15	6073	6073	NUM
ejpam-6073	32	16	3	3	NUM
ejpam-6073	32	17	of	of	ADP
ejpam-6073	32	18	29	29	NUM
ejpam-6073	32	19	and	and	CCONJ
ejpam-6073	32	20	external	external	ADJ
ejpam-6073	32	21	forces	force	NOUN
ejpam-6073	32	22	acting	act	VERB
ejpam-6073	32	23	on	on	ADP
ejpam-6073	32	24	the	the	DET
ejpam-6073	32	25	displacement	displacement	NOUN
ejpam-6073	32	26	,	,	PUNCT
ejpam-6073	32	27	respectively	respectively	ADV
ejpam-6073	32	28	.	.	PUNCT
ejpam-6073	33	1	similarly	similarly	ADV
ejpam-6073	33	2	,	,	PUNCT
ejpam-6073	33	3	(	(	PUNCT
ejpam-6073	33	4	p2	p2	X
ejpam-6073	33	5	,	,	PUNCT
ejpam-6073	33	6	g2	g2	PROPN
ejpam-6073	33	7	,	,	PUNCT
ejpam-6073	33	8	f2	f2	PROPN
ejpam-6073	33	9	)	)	PUNCT
ejpam-6073	33	10	have	have	VERB
ejpam-6073	33	11	analogous	analogous	ADJ
ejpam-6073	33	12	definitions	definition	NOUN
ejpam-6073	33	13	for	for	ADP
ejpam-6073	33	14	the	the	DET
ejpam-6073	33	15	elastic	elastic	ADJ
ejpam-6073	33	16	solid	solid	NOUN
ejpam-6073	33	17	.	.	PUNCT
ejpam-6073	34	1	the	the	DET
ejpam-6073	34	2	constitutive	constitutive	ADJ
ejpam-6073	34	3	equations	equation	NOUN
ejpam-6073	34	4	of	of	ADP
ejpam-6073	34	5	partial	partial	ADJ
ejpam-6073	34	6	tensions	tension	NOUN
ejpam-6073	34	7	are	be	AUX
ejpam-6073	34	8	expressed	express	VERB
ejpam-6073	34	9	as	as	ADP
ejpam-6073	34	10	[	[	PUNCT
ejpam-6073	34	11	p1	p1	NOUN
ejpam-6073	34	12	p2	p2	X
ejpam-6073	34	13	]	]	PUNCT
ejpam-6073	35	1	=	=	PUNCT
ejpam-6073	35	2	[	[	PUNCT
ejpam-6073	35	3	a1	a1	NOUN
ejpam-6073	35	4	a2	a2	PROPN
ejpam-6073	35	5	a2	a2	PROPN
ejpam-6073	35	6	a3	a3	NOUN
ejpam-6073	35	7	]	]	PUNCT
ejpam-6073	36	1	︸	︸	X
ejpam-6073	36	2	︷︷	︷︷	NOUN
ejpam-6073	36	3	︸	︸	ADP
ejpam-6073	36	4	a	a	DET
ejpam-6073	36	5	[	[	PUNCT
ejpam-6073	36	6	zx	zx	NUM
ejpam-6073	36	7	ux	ux	NOUN
ejpam-6073	36	8	]	]	PUNCT
ejpam-6073	36	9	,	,	PUNCT
ejpam-6073	36	10	(	(	PUNCT
ejpam-6073	36	11	2	2	X
ejpam-6073	36	12	)	)	PUNCT
ejpam-6073	36	13	where	where	SCONJ
ejpam-6073	36	14	a1	a1	NOUN
ejpam-6073	36	15	,	,	PUNCT
ejpam-6073	36	16	a3	a3	NOUN
ejpam-6073	36	17	are	be	AUX
ejpam-6073	36	18	positive	positive	ADJ
ejpam-6073	36	19	constants	constant	NOUN
ejpam-6073	36	20	and	and	CCONJ
ejpam-6073	36	21	a2	a2	PROPN
ejpam-6073	36	22	̸=	̸=	PROPN
ejpam-6073	36	23	0	0	NUM
ejpam-6073	36	24	is	be	AUX
ejpam-6073	36	25	a	a	DET
ejpam-6073	36	26	real	real	ADJ
ejpam-6073	36	27	number	number	NOUN
ejpam-6073	36	28	.	.	PUNCT
ejpam-6073	37	1	the	the	DET
ejpam-6073	37	2	matrix	matrix	NOUN
ejpam-6073	37	3	a	a	PRON
ejpam-6073	37	4	is	be	AUX
ejpam-6073	37	5	positive	positive	ADJ
ejpam-6073	37	6	definite	definite	ADJ
ejpam-6073	37	7	in	in	ADP
ejpam-6073	37	8	the	the	DET
ejpam-6073	37	9	sense	sense	NOUN
ejpam-6073	37	10	that	that	SCONJ
ejpam-6073	37	11	a1a3	a1a3	X
ejpam-6073	37	12	>	>	X
ejpam-6073	37	13	a22	a22	PROPN
ejpam-6073	37	14	.	.	PUNCT
ejpam-6073	37	15	quintanilla	quintanilla	PROPN
ejpam-6073	38	1	[	[	X
ejpam-6073	38	2	7	7	NUM
ejpam-6073	38	3	]	]	PUNCT
ejpam-6073	38	4	investigated	investigate	VERB
ejpam-6073	38	5	the	the	DET
ejpam-6073	38	6	system	system	NOUN
ejpam-6073	38	7	:	:	PUNCT
ejpam-6073	38	8	{	{	PUNCT
ejpam-6073	38	9	ρzztt	ρzztt	NOUN
ejpam-6073	38	10	=	=	PUNCT
ejpam-6073	39	1	a1zxx	a1zxx	PROPN
ejpam-6073	39	2	+	+	PUNCT
ejpam-6073	39	3	a2uxx	a2uxx	NUM
ejpam-6073	39	4	−	−	ADP
ejpam-6073	40	1	ξ(zt	ξ(zt	NUM
ejpam-6073	40	2	−	−	PROPN
ejpam-6073	40	3	ut	ut	PROPN
ejpam-6073	40	4	)	)	PUNCT
ejpam-6073	41	1	+	+	CCONJ
ejpam-6073	41	2	a3zxxt	a3zxxt	NOUN
ejpam-6073	41	3	,	,	PUNCT
ejpam-6073	41	4	ρuutt	ρuutt	NOUN
ejpam-6073	41	5	=	=	PUNCT
ejpam-6073	42	1	a2zxx	a2zxx	PROPN
ejpam-6073	43	1	+	+	CCONJ
ejpam-6073	43	2	a3uxx	a3uxx	NUM
ejpam-6073	43	3	+	+	CCONJ
ejpam-6073	44	1	ξ(zt	ξ(zt	NUM
ejpam-6073	44	2	−	−	PROPN
ejpam-6073	44	3	ut	ut	PROPN
ejpam-6073	44	4	)	)	PUNCT
ejpam-6073	45	1	,	,	PUNCT
ejpam-6073	45	2	(	(	PUNCT
ejpam-6073	45	3	3	3	X
ejpam-6073	45	4	)	)	PUNCT
ejpam-6073	45	5	where	where	SCONJ
ejpam-6073	45	6	ξ	ξ	PROPN
ejpam-6073	45	7	is	be	AUX
ejpam-6073	45	8	a	a	DET
ejpam-6073	45	9	positive	positive	ADJ
ejpam-6073	45	10	coefficient	coefficient	NOUN
ejpam-6073	45	11	.	.	PUNCT
ejpam-6073	46	1	under	under	ADP
ejpam-6073	46	2	initial	initial	ADJ
ejpam-6073	46	3	and	and	CCONJ
ejpam-6073	46	4	homogeneous	homogeneous	ADJ
ejpam-6073	46	5	dirichlet	dirichlet	PROPN
ejpam-6073	46	6	boundary	boundary	PROPN
ejpam-6073	46	7	conditions	condition	NOUN
ejpam-6073	46	8	,	,	PUNCT
ejpam-6073	46	9	he	he	PRON
ejpam-6073	46	10	established	establish	VERB
ejpam-6073	46	11	an	an	DET
ejpam-6073	46	12	exponential	exponential	ADJ
ejpam-6073	46	13	stability	stability	NOUN
ejpam-6073	46	14	result	result	NOUN
ejpam-6073	46	15	.	.	PUNCT
ejpam-6073	47	1	similarly	similarly	ADV
ejpam-6073	47	2	,	,	PUNCT
ejpam-6073	47	3	wang	wang	PROPN
ejpam-6073	47	4	and	and	CCONJ
ejpam-6073	47	5	guo	guo	PROPN
ejpam-6073	48	1	[	[	X
ejpam-6073	48	2	8	8	NUM
ejpam-6073	48	3	]	]	PUNCT
ejpam-6073	48	4	considered	consider	VERB
ejpam-6073	48	5	:	:	PUNCT
ejpam-6073	48	6	{	{	PUNCT
ejpam-6073	48	7	ρzztt	ρzztt	NOUN
ejpam-6073	48	8	=	=	PUNCT
ejpam-6073	49	1	a1zxx	a1zxx	PROPN
ejpam-6073	49	2	+	+	NUM
ejpam-6073	49	3	a2uxx	a2uxx	NOUN
ejpam-6073	50	1	−	−	ADP
ejpam-6073	50	2	ρzγ(x)zt	ρzγ(x)zt	NOUN
ejpam-6073	50	3	,	,	PUNCT
ejpam-6073	50	4	ρuutt	ρuutt	NOUN
ejpam-6073	50	5	=	=	PUNCT
ejpam-6073	51	1	a2zxx	a2zxx	PROPN
ejpam-6073	52	1	+	+	CCONJ
ejpam-6073	52	2	a3uxx	a3uxx	ADJ
ejpam-6073	52	3	,	,	PUNCT
ejpam-6073	52	4	(	(	PUNCT
ejpam-6073	52	5	4	4	X
ejpam-6073	52	6	)	)	PUNCT
ejpam-6073	52	7	where	where	SCONJ
ejpam-6073	52	8	γ(x	γ(x	NOUN
ejpam-6073	52	9	)	)	PUNCT
ejpam-6073	52	10	represents	represent	VERB
ejpam-6073	52	11	an	an	DET
ejpam-6073	52	12	internal	internal	ADJ
ejpam-6073	52	13	viscous	viscous	ADJ
ejpam-6073	52	14	damping	damp	VERB
ejpam-6073	52	15	function	function	NOUN
ejpam-6073	52	16	with	with	ADP
ejpam-6073	52	17	a	a	DET
ejpam-6073	52	18	positive	positive	ADJ
ejpam-6073	52	19	mean	mean	NOUN
ejpam-6073	52	20	.	.	PUNCT
ejpam-6073	53	1	using	use	VERB
ejpam-6073	53	2	spectral	spectral	ADJ
ejpam-6073	53	3	analysis	analysis	NOUN
ejpam-6073	53	4	,	,	PUNCT
ejpam-6073	53	5	they	they	PRON
ejpam-6073	53	6	established	establish	VERB
ejpam-6073	53	7	an	an	DET
ejpam-6073	53	8	exponential	exponential	ADJ
ejpam-6073	53	9	stability	stability	NOUN
ejpam-6073	53	10	result	result	NOUN
ejpam-6073	53	11	.	.	PUNCT
ejpam-6073	54	1	several	several	ADJ
ejpam-6073	54	2	recent	recent	ADJ
ejpam-6073	54	3	studies	study	NOUN
ejpam-6073	54	4	have	have	AUX
ejpam-6073	54	5	introduced	introduce	VERB
ejpam-6073	54	6	new	new	ADJ
ejpam-6073	54	7	stabilization	stabilization	NOUN
ejpam-6073	54	8	mechanisms	mechanism	NOUN
ejpam-6073	54	9	for	for	ADP
ejpam-6073	54	10	swelling	swell	VERB
ejpam-6073	54	11	soil	soil	NOUN
ejpam-6073	54	12	models	model	NOUN
ejpam-6073	54	13	(	(	PUNCT
ejpam-6073	54	14	1	1	X
ejpam-6073	54	15	)	)	PUNCT
ejpam-6073	54	16	that	that	PRON
ejpam-6073	54	17	are	be	AUX
ejpam-6073	54	18	effective	effective	ADJ
ejpam-6073	54	19	,	,	PUNCT
ejpam-6073	54	20	economical	economical	ADJ
ejpam-6073	54	21	,	,	PUNCT
ejpam-6073	54	22	and	and	CCONJ
ejpam-6073	54	23	environmentally	environmentally	ADV
ejpam-6073	54	24	sustainable	sustainable	ADJ
ejpam-6073	54	25	[	[	PUNCT
ejpam-6073	54	26	9–12	9–12	NOUN
ejpam-6073	54	27	,	,	PUNCT
ejpam-6073	54	28	12	12	NUM
ejpam-6073	54	29	]	]	PUNCT
ejpam-6073	54	30	.	.	PUNCT
ejpam-6073	55	1	in	in	ADP
ejpam-6073	55	2	recent	recent	ADJ
ejpam-6073	55	3	years	year	NOUN
ejpam-6073	55	4	,	,	PUNCT
ejpam-6073	55	5	there	there	PRON
ejpam-6073	55	6	has	have	AUX
ejpam-6073	55	7	been	be	AUX
ejpam-6073	55	8	growing	grow	VERB
ejpam-6073	55	9	interest	interest	NOUN
ejpam-6073	55	10	in	in	ADP
ejpam-6073	55	11	treating	treat	VERB
ejpam-6073	55	12	equations	equation	NOUN
ejpam-6073	55	13	with	with	ADP
ejpam-6073	55	14	variable	variable	ADJ
ejpam-6073	55	15	exponent	exponent	NOUN
ejpam-6073	55	16	nonlinearities	nonlinearitie	NOUN
ejpam-6073	55	17	due	due	ADP
ejpam-6073	55	18	to	to	ADP
ejpam-6073	55	19	their	their	PRON
ejpam-6073	55	20	applications	application	NOUN
ejpam-6073	55	21	in	in	ADP
ejpam-6073	55	22	the	the	DET
ejpam-6073	55	23	mathematical	mathematical	ADJ
ejpam-6073	55	24	modeling	modeling	NOUN
ejpam-6073	55	25	of	of	ADP
ejpam-6073	55	26	non	non	ADJ
ejpam-6073	55	27	-	-	ADJ
ejpam-6073	55	28	newtonian	newtonian	ADJ
ejpam-6073	55	29	fluids	fluid	NOUN
ejpam-6073	55	30	.	.	PUNCT
ejpam-6073	56	1	one	one	NUM
ejpam-6073	56	2	prominent	prominent	ADJ
ejpam-6073	56	3	example	example	NOUN
ejpam-6073	56	4	is	be	AUX
ejpam-6073	56	5	electro	electro	ADJ
ejpam-6073	56	6	-	-	PUNCT
ejpam-6073	56	7	rheological	rheological	ADJ
ejpam-6073	56	8	fluids	fluid	NOUN
ejpam-6073	56	9	,	,	PUNCT
ejpam-6073	56	10	which	which	PRON
ejpam-6073	56	11	can	can	AUX
ejpam-6073	56	12	undergo	undergo	VERB
ejpam-6073	56	13	drastic	drastic	ADJ
ejpam-6073	56	14	changes	change	NOUN
ejpam-6073	56	15	under	under	ADP
ejpam-6073	56	16	the	the	DET
ejpam-6073	56	17	influence	influence	NOUN
ejpam-6073	56	18	of	of	ADP
ejpam-6073	56	19	external	external	ADJ
ejpam-6073	56	20	electromagnetic	electromagnetic	ADJ
ejpam-6073	56	21	fields	field	NOUN
ejpam-6073	56	22	.	.	PUNCT
ejpam-6073	57	1	in	in	ADP
ejpam-6073	57	2	these	these	DET
ejpam-6073	57	3	cases	case	NOUN
ejpam-6073	57	4	,	,	PUNCT
ejpam-6073	57	5	the	the	DET
ejpam-6073	57	6	variable	variable	ADJ
ejpam-6073	57	7	exponent	exponent	NOUN
ejpam-6073	57	8	nonlinearity	nonlinearity	NOUN
ejpam-6073	57	9	depends	depend	VERB
ejpam-6073	57	10	on	on	ADP
ejpam-6073	57	11	physical	physical	ADJ
ejpam-6073	57	12	parameters	parameter	NOUN
ejpam-6073	57	13	such	such	ADJ
ejpam-6073	57	14	as	as	ADP
ejpam-6073	57	15	density	density	NOUN
ejpam-6073	57	16	,	,	PUNCT
ejpam-6073	57	17	temperature	temperature	NOUN
ejpam-6073	57	18	,	,	PUNCT
ejpam-6073	57	19	saturation	saturation	NOUN
ejpam-6073	57	20	,	,	PUNCT
ejpam-6073	57	21	and	and	CCONJ
ejpam-6073	57	22	electric	electric	ADJ
ejpam-6073	57	23	field	field	NOUN
ejpam-6073	57	24	.	.	PUNCT
ejpam-6073	58	1	for	for	ADP
ejpam-6073	58	2	more	more	ADJ
ejpam-6073	58	3	results	result	NOUN
ejpam-6073	58	4	in	in	ADP
ejpam-6073	58	5	this	this	DET
ejpam-6073	58	6	direction	direction	NOUN
ejpam-6073	58	7	,	,	PUNCT
ejpam-6073	58	8	we	we	PRON
ejpam-6073	58	9	refer	refer	VERB
ejpam-6073	58	10	to	to	ADP
ejpam-6073	58	11	[	[	X
ejpam-6073	58	12	13–21	13–21	NUM
ejpam-6073	58	13	]	]	PUNCT
ejpam-6073	58	14	.	.	PUNCT
ejpam-6073	59	1	recently	recently	ADV
ejpam-6073	59	2	,	,	PUNCT
ejpam-6073	59	3	al	al	PROPN
ejpam-6073	59	4	-	-	PUNCT
ejpam-6073	59	5	mahdi	mahdi	PROPN
ejpam-6073	59	6	et	et	PROPN
ejpam-6073	59	7	al	al	PROPN
ejpam-6073	59	8	.	.	PUNCT
ejpam-6073	60	1	[	[	X
ejpam-6073	60	2	22	22	NUM
ejpam-6073	60	3	]	]	PUNCT
ejpam-6073	60	4	established	establish	VERB
ejpam-6073	60	5	exponential	exponential	ADJ
ejpam-6073	60	6	and	and	CCONJ
ejpam-6073	60	7	polynomial	polynomial	ADJ
ejpam-6073	60	8	decay	decay	NOUN
ejpam-6073	60	9	results	result	NOUN
ejpam-6073	60	10	for	for	ADP
ejpam-6073	60	11	swelling	swell	VERB
ejpam-6073	60	12	soils	soil	NOUN
ejpam-6073	60	13	governed	govern	VERB
ejpam-6073	60	14	by	by	ADP
ejpam-6073	60	15	the	the	DET
ejpam-6073	60	16	system	system	NOUN
ejpam-6073	60	17	:	:	PUNCT
ejpam-6073	60	18	{	{	PUNCT
ejpam-6073	60	19	ρzztt	ρzztt	NOUN
ejpam-6073	60	20	−	−	NOUN
ejpam-6073	60	21	a1zxx	a1zxx	NOUN
ejpam-6073	60	22	−	−	PROPN
ejpam-6073	60	23	a2uxx	a2uxx	PROPN
ejpam-6073	60	24	+	+	CCONJ
ejpam-6073	60	25	α|zt|m(·)−2zt	α|zt|m(·)−2zt	PROPN
ejpam-6073	60	26	=	=	SYM
ejpam-6073	60	27	β|z|m(·)−2z	β|z|m(·)−2z	PROPN
ejpam-6073	60	28	,	,	PUNCT
ejpam-6073	60	29	in	in	ADP
ejpam-6073	60	30	(	(	PUNCT
ejpam-6073	60	31	0	0	NUM
ejpam-6073	60	32	,	,	PUNCT
ejpam-6073	60	33	1)×	1)×	NUM
ejpam-6073	60	34	(	(	PUNCT
ejpam-6073	60	35	0,∞	0,∞	NUM
ejpam-6073	60	36	)	)	PUNCT
ejpam-6073	60	37	,	,	PUNCT
ejpam-6073	60	38	ρuutt	ρuutt	VERB
ejpam-6073	60	39	−	−	NOUN
ejpam-6073	60	40	a3uxx	a3uxx	NUM
ejpam-6073	60	41	−	−	PROPN
ejpam-6073	61	1	a2zxx	a2zxx	NOUN
ejpam-6073	61	2	=	=	SYM
ejpam-6073	61	3	0	0	NUM
ejpam-6073	61	4	,	,	PUNCT
ejpam-6073	61	5	in	in	ADP
ejpam-6073	61	6	(	(	PUNCT
ejpam-6073	61	7	0	0	NUM
ejpam-6073	61	8	,	,	PUNCT
ejpam-6073	61	9	1)×	1)×	NUM
ejpam-6073	61	10	(	(	PUNCT
ejpam-6073	61	11	0,∞	0,∞	NUM
ejpam-6073	61	12	)	)	PUNCT
ejpam-6073	61	13	,	,	PUNCT
ejpam-6073	61	14	(	(	PUNCT
ejpam-6073	61	15	5	5	X
ejpam-6073	61	16	)	)	PUNCT
ejpam-6073	61	17	under	under	ADP
ejpam-6073	61	18	suitable	suitable	ADJ
ejpam-6073	61	19	conditions	condition	NOUN
ejpam-6073	61	20	on	on	ADP
ejpam-6073	61	21	the	the	DET
ejpam-6073	61	22	variable	variable	ADJ
ejpam-6073	61	23	exponents	exponent	NOUN
ejpam-6073	61	24	.	.	PUNCT
ejpam-6073	62	1	however	however	ADV
ejpam-6073	62	2	,	,	PUNCT
ejpam-6073	62	3	an	an	DET
ejpam-6073	62	4	important	important	ADJ
ejpam-6073	62	5	question	question	NOUN
ejpam-6073	62	6	arises	arise	VERB
ejpam-6073	62	7	:	:	PUNCT
ejpam-6073	62	8	does	do	VERB
ejpam-6073	62	9	system	system	NOUN
ejpam-6073	62	10	(	(	PUNCT
ejpam-6073	62	11	5	5	NUM
ejpam-6073	62	12	)	)	PUNCT
ejpam-6073	62	13	with	with	ADP
ejpam-6073	62	14	γ	γ	PROPN
ejpam-6073	62	15	,	,	PUNCT
ejpam-6073	62	16	β	β	X
ejpam-6073	62	17	>	>	X
ejpam-6073	62	18	0	0	PUNCT
ejpam-6073	63	1	admit	admit	VERB
ejpam-6073	63	2	global	global	ADJ
ejpam-6073	63	3	existence	existence	NOUN
ejpam-6073	63	4	,	,	PUNCT
ejpam-6073	63	5	stability	stability	NOUN
ejpam-6073	63	6	,	,	PUNCT
ejpam-6073	63	7	or	or	CCONJ
ejpam-6073	63	8	blow	blow	NOUN
ejpam-6073	63	9	-	-	PUNCT
ejpam-6073	63	10	up	up	ADP
ejpam-6073	63	11	results	result	NOUN
ejpam-6073	63	12	under	under	ADP
ejpam-6073	63	13	certain	certain	ADJ
ejpam-6073	63	14	conditions	condition	NOUN
ejpam-6073	63	15	on	on	ADP
ejpam-6073	63	16	the	the	DET
ejpam-6073	63	17	variable	variable	ADJ
ejpam-6073	63	18	exponents	exponent	NOUN
ejpam-6073	63	19	?	?	PUNCT
ejpam-6073	64	1	in	in	ADP
ejpam-6073	64	2	this	this	DET
ejpam-6073	64	3	paper	paper	NOUN
ejpam-6073	64	4	,	,	PUNCT
ejpam-6073	64	5	we	we	PRON
ejpam-6073	64	6	address	address	VERB
ejpam-6073	64	7	this	this	DET
ejpam-6073	64	8	question	question	NOUN
ejpam-6073	64	9	by	by	ADP
ejpam-6073	64	10	considering	consider	VERB
ejpam-6073	64	11	the	the	DET
ejpam-6073	64	12	following	follow	VERB
ejpam-6073	64	13	swelling	swell	VERB
ejpam-6073	64	14	soil	soil	NOUN
ejpam-6073	64	15	system	system	NOUN
ejpam-6073	64	16	of	of	ADP
ejpam-6073	64	17	the	the	DET
ejpam-6073	64	18	form	form	NOUN
ejpam-6073	64	19	:	:	PUNCT
ejpam-6073	64	20	a.	a.	NOUN
ejpam-6073	64	21	m.	m.	PROPN
ejpam-6073	64	22	al	al	PROPN
ejpam-6073	64	23	-	-	PROPN
ejpam-6073	64	24	mahdi	mahdi	PROPN
ejpam-6073	64	25	et	et	PROPN
ejpam-6073	64	26	al	al	PROPN
ejpam-6073	64	27	.	.	PUNCT
ejpam-6073	64	28	/	/	SYM
ejpam-6073	64	29	eur	eur	PROPN
ejpam-6073	64	30	.	.	PUNCT
ejpam-6073	65	1	j.	j.	PROPN
ejpam-6073	65	2	pure	pure	PROPN
ejpam-6073	65	3	appl	appl	PROPN
ejpam-6073	65	4	.	.	PROPN
ejpam-6073	65	5	math	math	PROPN
ejpam-6073	65	6	,	,	PUNCT
ejpam-6073	65	7	18	18	NUM
ejpam-6073	65	8	(	(	PUNCT
ejpam-6073	65	9	3	3	NUM
ejpam-6073	65	10	)	)	PUNCT
ejpam-6073	65	11	(	(	PUNCT
ejpam-6073	65	12	2025	2025	NUM
ejpam-6073	65	13	)	)	PUNCT
ejpam-6073	65	14	,	,	PUNCT
ejpam-6073	65	15	6073	6073	NUM
ejpam-6073	65	16	4	4	NUM
ejpam-6073	65	17	of	of	ADP
ejpam-6073	65	18	29	29	NUM
ejpam-6073	65	19			NUM
ejpam-6073	65	20	ρzztt	ρzztt	NOUN
ejpam-6073	65	21	−	−	NOUN
ejpam-6073	65	22	a1zxx	a1zxx	NOUN
ejpam-6073	65	23	−	−	PROPN
ejpam-6073	65	24	a2uxx	a2uxx	PROPN
ejpam-6073	65	25	+	+	CCONJ
ejpam-6073	65	26	γ|zt|p(·)−2zt	γ|zt|p(·)−2zt	NOUN
ejpam-6073	65	27	=	=	SYM
ejpam-6073	65	28	c|z|m(·)−2z	c|z|m(·)−2z	NOUN
ejpam-6073	65	29	,	,	PUNCT
ejpam-6073	65	30	in	in	ADP
ejpam-6073	65	31	ω×	ω×	PROPN
ejpam-6073	65	32	(	(	PUNCT
ejpam-6073	65	33	0,∞	0,∞	NUM
ejpam-6073	65	34	)	)	PUNCT
ejpam-6073	65	35	,	,	PUNCT
ejpam-6073	65	36	ρuutt	ρuutt	VERB
ejpam-6073	65	37	−	−	NOUN
ejpam-6073	65	38	a3uxx	a3uxx	NUM
ejpam-6073	65	39	−	−	PROPN
ejpam-6073	66	1	a2zxx	a2zxx	NOUN
ejpam-6073	67	1	+	+	NUM
ejpam-6073	67	2	β|ut|q(·)−2ut	β|ut|q(·)−2ut	NOUN
ejpam-6073	67	3	=	=	SYM
ejpam-6073	67	4	d|u|ℓ(·)−2u	d|u|ℓ(·)−2u	PROPN
ejpam-6073	67	5	,	,	PUNCT
ejpam-6073	67	6	in	in	ADP
ejpam-6073	67	7	ω×	ω×	PROPN
ejpam-6073	67	8	(	(	PUNCT
ejpam-6073	67	9	0,∞	0,∞	NUM
ejpam-6073	67	10	)	)	PUNCT
ejpam-6073	67	11	,	,	PUNCT
ejpam-6073	67	12	u(x	u(x	NOUN
ejpam-6073	67	13	,	,	PUNCT
ejpam-6073	67	14	0	0	NUM
ejpam-6073	67	15	)	)	PUNCT
ejpam-6073	67	16	=	=	SYM
ejpam-6073	67	17	u0(x	u0(x	NOUN
ejpam-6073	67	18	)	)	PUNCT
ejpam-6073	67	19	,	,	PUNCT
ejpam-6073	67	20	ut(x	ut(x	NOUN
ejpam-6073	67	21	,	,	PUNCT
ejpam-6073	67	22	0	0	NUM
ejpam-6073	67	23	)	)	PUNCT
ejpam-6073	67	24	=	=	SYM
ejpam-6073	67	25	u1(x	u1(x	NOUN
ejpam-6073	67	26	)	)	PUNCT
ejpam-6073	67	27	,	,	PUNCT
ejpam-6073	67	28	z(x	z(x	NUM
ejpam-6073	67	29	,	,	PUNCT
ejpam-6073	67	30	0	0	NUM
ejpam-6073	67	31	)	)	PUNCT
ejpam-6073	67	32	=	=	SYM
ejpam-6073	67	33	z0(x	z0(x	NUM
ejpam-6073	67	34	)	)	PUNCT
ejpam-6073	67	35	,	,	PUNCT
ejpam-6073	67	36	zt(x	zt(x	NUM
ejpam-6073	67	37	,	,	PUNCT
ejpam-6073	67	38	0	0	NUM
ejpam-6073	67	39	)	)	PUNCT
ejpam-6073	67	40	=	=	SYM
ejpam-6073	67	41	z1(x	z1(x	NUM
ejpam-6073	67	42	)	)	PUNCT
ejpam-6073	67	43	x	x	SYM
ejpam-6073	67	44	∈	∈	PROPN
ejpam-6073	67	45	ω	ω	PROPN
ejpam-6073	67	46	,	,	PUNCT
ejpam-6073	67	47	z(0	z(0	PROPN
ejpam-6073	67	48	,	,	PUNCT
ejpam-6073	67	49	t	t	PROPN
ejpam-6073	67	50	)	)	PUNCT
ejpam-6073	67	51	=	=	SYM
ejpam-6073	68	1	z(1	z(1	PROPN
ejpam-6073	68	2	,	,	PUNCT
ejpam-6073	68	3	t	t	PROPN
ejpam-6073	68	4	)	)	PUNCT
ejpam-6073	68	5	=	=	SYM
ejpam-6073	69	1	u(0	u(0	PROPN
ejpam-6073	69	2	,	,	PUNCT
ejpam-6073	69	3	t	t	PROPN
ejpam-6073	69	4	)	)	PUNCT
ejpam-6073	69	5	=	=	SYM
ejpam-6073	70	1	u(1	u(1	PROPN
ejpam-6073	70	2	,	,	PUNCT
ejpam-6073	70	3	t	t	PROPN
ejpam-6073	70	4	)	)	PUNCT
ejpam-6073	70	5	=	=	SYM
ejpam-6073	70	6	0	0	NUM
ejpam-6073	70	7	t	t	PROPN
ejpam-6073	70	8	≥	≥	NOUN
ejpam-6073	70	9	0	0	NUM
ejpam-6073	70	10	,	,	PUNCT
ejpam-6073	70	11	(	(	PUNCT
ejpam-6073	70	12	6	6	NUM
ejpam-6073	70	13	)	)	PUNCT
ejpam-6073	70	14	where	where	SCONJ
ejpam-6073	70	15	ω	ω	PROPN
ejpam-6073	70	16	denotes	denote	VERB
ejpam-6073	70	17	the	the	DET
ejpam-6073	70	18	interval	interval	NOUN
ejpam-6073	70	19	(	(	PUNCT
ejpam-6073	70	20	0	0	NUM
ejpam-6073	70	21	,	,	PUNCT
ejpam-6073	70	22	1	1	NUM
ejpam-6073	70	23	)	)	PUNCT
ejpam-6073	70	24	.	.	PUNCT
ejpam-6073	71	1	the	the	DET
ejpam-6073	71	2	positive	positive	ADJ
ejpam-6073	71	3	constant	constant	ADJ
ejpam-6073	71	4	coefficients	coefficient	NOUN
ejpam-6073	71	5	ρu	ρu	PRON
ejpam-6073	71	6	and	and	CCONJ
ejpam-6073	71	7	ρz	ρz	NOUN
ejpam-6073	71	8	are	be	AUX
ejpam-6073	71	9	the	the	DET
ejpam-6073	71	10	densities	density	NOUN
ejpam-6073	71	11	of	of	ADP
ejpam-6073	71	12	each	each	DET
ejpam-6073	71	13	constituent	constituent	NOUN
ejpam-6073	71	14	.	.	PUNCT
ejpam-6073	72	1	the	the	DET
ejpam-6073	72	2	coefficients	coefficient	NOUN
ejpam-6073	72	3	a1	a1	PROPN
ejpam-6073	72	4	,	,	PUNCT
ejpam-6073	72	5	a2	a2	PROPN
ejpam-6073	72	6	and	and	CCONJ
ejpam-6073	72	7	a3	a3	NOUN
ejpam-6073	72	8	are	be	AUX
ejpam-6073	72	9	positive	positive	ADJ
ejpam-6073	72	10	constants	constant	NOUN
ejpam-6073	72	11	satisfying	satisfy	VERB
ejpam-6073	72	12	specific	specific	ADJ
ejpam-6073	72	13	conditions	condition	NOUN
ejpam-6073	72	14	.	.	PUNCT
ejpam-6073	73	1	the	the	DET
ejpam-6073	73	2	coefficients	coefficient	NOUN
ejpam-6073	73	3	γ	γ	PROPN
ejpam-6073	73	4	,	,	PUNCT
ejpam-6073	73	5	β	β	X
ejpam-6073	73	6	,	,	PUNCT
ejpam-6073	73	7	c	c	X
ejpam-6073	73	8	,	,	PUNCT
ejpam-6073	73	9	d	d	X
ejpam-6073	73	10	>	>	X
ejpam-6073	73	11	0	0	NUM
ejpam-6073	73	12	,	,	PUNCT
ejpam-6073	73	13	z0	z0	PROPN
ejpam-6073	73	14	,	,	PUNCT
ejpam-6073	73	15	z1	z1	PROPN
ejpam-6073	73	16	,	,	PUNCT
ejpam-6073	73	17	u0	u0	ADJ
ejpam-6073	73	18	,	,	PUNCT
ejpam-6073	73	19	u1	u1	NOUN
ejpam-6073	73	20	are	be	AUX
ejpam-6073	73	21	given	give	VERB
ejpam-6073	73	22	data	datum	NOUN
ejpam-6073	73	23	and	and	CCONJ
ejpam-6073	73	24	p	p	X
ejpam-6073	73	25	(	(	PUNCT
ejpam-6073	73	26	.	.	PUNCT
ejpam-6073	73	27	)	)	PUNCT
ejpam-6073	73	28	,	,	PUNCT
ejpam-6073	73	29	q(.),m	q(.),m	PROPN
ejpam-6073	73	30	(	(	PUNCT
ejpam-6073	73	31	.	.	PUNCT
ejpam-6073	73	32	)	)	PUNCT
ejpam-6073	73	33	,	,	PUNCT
ejpam-6073	73	34	ℓ	ℓ	X
ejpam-6073	73	35	(	(	PUNCT
ejpam-6073	73	36	.	.	PUNCT
ejpam-6073	73	37	)	)	PUNCT
ejpam-6073	74	1	are	be	AUX
ejpam-6073	74	2	function	function	NOUN
ejpam-6073	74	3	satisfying	satisfy	VERB
ejpam-6073	74	4	some	some	DET
ejpam-6073	74	5	conditions	condition	NOUN
ejpam-6073	74	6	to	to	PART
ejpam-6073	74	7	be	be	AUX
ejpam-6073	74	8	specified	specify	VERB
ejpam-6073	74	9	in	in	ADP
ejpam-6073	74	10	the	the	DET
ejpam-6073	74	11	next	next	ADJ
ejpam-6073	74	12	section	section	NOUN
ejpam-6073	74	13	.	.	PUNCT
ejpam-6073	75	1	system	system	NOUN
ejpam-6073	75	2	(	(	PUNCT
ejpam-6073	75	3	6	6	NUM
ejpam-6073	75	4	)	)	PUNCT
ejpam-6073	75	5	exhibits	exhibit	VERB
ejpam-6073	75	6	several	several	ADJ
ejpam-6073	75	7	key	key	ADJ
ejpam-6073	75	8	differences	difference	NOUN
ejpam-6073	75	9	from	from	ADP
ejpam-6073	75	10	previously	previously	ADV
ejpam-6073	75	11	studied	study	VERB
ejpam-6073	75	12	swelling	swell	VERB
ejpam-6073	75	13	porous	porous	ADJ
ejpam-6073	75	14	-	-	PUNCT
ejpam-6073	75	15	elastic	elastic	ADJ
ejpam-6073	75	16	models	model	NOUN
ejpam-6073	75	17	.	.	PUNCT
ejpam-6073	76	1	unlike	unlike	ADP
ejpam-6073	76	2	classical	classical	ADJ
ejpam-6073	76	3	models	model	NOUN
ejpam-6073	76	4	,	,	PUNCT
ejpam-6073	76	5	where	where	SCONJ
ejpam-6073	76	6	damping	damp	VERB
ejpam-6073	76	7	and	and	CCONJ
ejpam-6073	76	8	source	source	NOUN
ejpam-6073	76	9	terms	term	NOUN
ejpam-6073	76	10	are	be	AUX
ejpam-6073	76	11	typically	typically	ADV
ejpam-6073	76	12	governed	govern	VERB
ejpam-6073	76	13	by	by	ADP
ejpam-6073	76	14	constant	constant	ADJ
ejpam-6073	76	15	power	power	NOUN
ejpam-6073	76	16	-	-	PUNCT
ejpam-6073	76	17	law	law	NOUN
ejpam-6073	76	18	exponents	exponent	NOUN
ejpam-6073	76	19	,	,	PUNCT
ejpam-6073	76	20	our	our	PRON
ejpam-6073	76	21	system	system	NOUN
ejpam-6073	76	22	introduces	introduce	VERB
ejpam-6073	76	23	variable	variable	ADJ
ejpam-6073	76	24	exponent	exponent	NOUN
ejpam-6073	76	25	functions	function	NOUN
ejpam-6073	76	26	p(x	p(x	PROPN
ejpam-6073	76	27	)	)	PUNCT
ejpam-6073	76	28	,	,	PUNCT
ejpam-6073	76	29	q(x	q(x	PROPN
ejpam-6073	76	30	)	)	PUNCT
ejpam-6073	76	31	,	,	PUNCT
ejpam-6073	76	32	m(x	m(x	PROPN
ejpam-6073	76	33	)	)	PUNCT
ejpam-6073	76	34	,	,	PUNCT
ejpam-6073	76	35	and	and	CCONJ
ejpam-6073	76	36	ℓ(x	ℓ(x	PROPN
ejpam-6073	76	37	)	)	PUNCT
ejpam-6073	76	38	.	.	PUNCT
ejpam-6073	77	1	this	this	DET
ejpam-6073	77	2	formulation	formulation	NOUN
ejpam-6073	77	3	provides	provide	VERB
ejpam-6073	77	4	a	a	DET
ejpam-6073	77	5	more	more	ADV
ejpam-6073	77	6	flexible	flexible	ADJ
ejpam-6073	77	7	and	and	CCONJ
ejpam-6073	77	8	generalized	generalized	ADJ
ejpam-6073	77	9	framework	framework	NOUN
ejpam-6073	77	10	for	for	ADP
ejpam-6073	77	11	capturing	capture	VERB
ejpam-6073	77	12	energy	energy	NOUN
ejpam-6073	77	13	dissipation	dissipation	NOUN
ejpam-6073	77	14	and	and	CCONJ
ejpam-6073	77	15	nonlinear	nonlinear	ADJ
ejpam-6073	77	16	interactions	interaction	NOUN
ejpam-6073	77	17	,	,	PUNCT
ejpam-6073	77	18	accommodating	accommodate	VERB
ejpam-6073	77	19	spatial	spatial	ADJ
ejpam-6073	77	20	heterogeneity	heterogeneity	NOUN
ejpam-6073	77	21	in	in	ADP
ejpam-6073	77	22	material	material	NOUN
ejpam-6073	77	23	properties	property	NOUN
ejpam-6073	77	24	.	.	PUNCT
ejpam-6073	78	1	as	as	ADP
ejpam-6073	78	2	a	a	DET
ejpam-6073	78	3	result	result	NOUN
ejpam-6073	78	4	,	,	PUNCT
ejpam-6073	78	5	our	our	PRON
ejpam-6073	78	6	model	model	NOUN
ejpam-6073	78	7	is	be	AUX
ejpam-6073	78	8	more	more	ADV
ejpam-6073	78	9	adaptable	adaptable	ADJ
ejpam-6073	78	10	to	to	ADP
ejpam-6073	78	11	real	real	ADJ
ejpam-6073	78	12	-	-	PUNCT
ejpam-6073	78	13	world	world	NOUN
ejpam-6073	78	14	applications	application	NOUN
ejpam-6073	78	15	,	,	PUNCT
ejpam-6073	78	16	including	include	VERB
ejpam-6073	78	17	soil	soil	NOUN
ejpam-6073	78	18	swelling	swelling	NOUN
ejpam-6073	78	19	,	,	PUNCT
ejpam-6073	78	20	biomechanics	biomechanic	NOUN
ejpam-6073	78	21	,	,	PUNCT
ejpam-6073	78	22	and	and	CCONJ
ejpam-6073	78	23	geomechanics	geomechanic	NOUN
ejpam-6073	78	24	.	.	PUNCT
ejpam-6073	79	1	the	the	DET
ejpam-6073	79	2	presence	presence	NOUN
ejpam-6073	79	3	of	of	ADP
ejpam-6073	79	4	variable	variable	ADJ
ejpam-6073	79	5	exponent	exponent	NOUN
ejpam-6073	79	6	damping	damp	VERB
ejpam-6073	79	7	and	and	CCONJ
ejpam-6073	79	8	source	source	NOUN
ejpam-6073	79	9	terms	term	NOUN
ejpam-6073	79	10	introduces	introduce	VERB
ejpam-6073	79	11	new	new	ADJ
ejpam-6073	79	12	challenges	challenge	NOUN
ejpam-6073	79	13	in	in	ADP
ejpam-6073	79	14	the	the	DET
ejpam-6073	79	15	global	global	ADJ
ejpam-6073	79	16	existence	existence	NOUN
ejpam-6073	79	17	and	and	CCONJ
ejpam-6073	79	18	the	the	DET
ejpam-6073	79	19	blow	blow	NOUN
ejpam-6073	79	20	-	-	PUNCT
ejpam-6073	79	21	up	up	ADP
ejpam-6073	79	22	analysis	analysis	NOUN
ejpam-6073	79	23	.	.	PUNCT
ejpam-6073	80	1	we	we	PRON
ejpam-6073	80	2	establish	establish	VERB
ejpam-6073	80	3	conditions	condition	NOUN
ejpam-6073	80	4	under	under	ADP
ejpam-6073	80	5	which	which	PRON
ejpam-6073	80	6	solutions	solution	NOUN
ejpam-6073	80	7	exhibit	exhibit	VERB
ejpam-6073	80	8	finite	finite	ADJ
ejpam-6073	80	9	-	-	PUNCT
ejpam-6073	80	10	time	time	NOUN
ejpam-6073	80	11	blow	blow	NOUN
ejpam-6073	80	12	-	-	PUNCT
ejpam-6073	80	13	up	up	NOUN
ejpam-6073	80	14	,	,	PUNCT
ejpam-6073	80	15	extending	extend	VERB
ejpam-6073	80	16	classical	classical	ADJ
ejpam-6073	80	17	results	result	NOUN
ejpam-6073	80	18	from	from	ADP
ejpam-6073	80	19	constant	constant	ADJ
ejpam-6073	80	20	exponent	exponent	ADJ
ejpam-6073	80	21	cases	case	NOUN
ejpam-6073	80	22	to	to	ADP
ejpam-6073	80	23	more	more	ADJ
ejpam-6073	80	24	general	general	ADJ
ejpam-6073	80	25	variable	variable	ADJ
ejpam-6073	80	26	exponent	exponent	NOUN
ejpam-6073	80	27	settings	setting	NOUN
ejpam-6073	80	28	.	.	PUNCT
ejpam-6073	81	1	these	these	DET
ejpam-6073	81	2	advancements	advancement	NOUN
ejpam-6073	81	3	mark	mark	VERB
ejpam-6073	81	4	a	a	DET
ejpam-6073	81	5	significant	significant	ADJ
ejpam-6073	81	6	generalization	generalization	NOUN
ejpam-6073	81	7	of	of	ADP
ejpam-6073	81	8	existing	exist	VERB
ejpam-6073	81	9	studies	study	NOUN
ejpam-6073	81	10	on	on	ADP
ejpam-6073	81	11	swelling	swell	VERB
ejpam-6073	81	12	porous	porous	ADJ
ejpam-6073	81	13	-	-	PUNCT
ejpam-6073	81	14	elastic	elastic	ADJ
ejpam-6073	81	15	systems	system	NOUN
ejpam-6073	81	16	.	.	PUNCT
ejpam-6073	82	1	by	by	ADP
ejpam-6073	82	2	incorporating	incorporate	VERB
ejpam-6073	82	3	variable	variable	ADJ
ejpam-6073	82	4	exponent	exponent	NOUN
ejpam-6073	82	5	nonlinearities	nonlinearitie	NOUN
ejpam-6073	82	6	,	,	PUNCT
ejpam-6073	82	7	our	our	PRON
ejpam-6073	82	8	work	work	NOUN
ejpam-6073	82	9	provides	provide	VERB
ejpam-6073	82	10	novel	novel	ADJ
ejpam-6073	82	11	insights	insight	NOUN
ejpam-6073	82	12	into	into	ADP
ejpam-6073	82	13	the	the	DET
ejpam-6073	82	14	behavior	behavior	NOUN
ejpam-6073	82	15	of	of	ADP
ejpam-6073	82	16	complex	complex	ADJ
ejpam-6073	82	17	porous	porous	ADJ
ejpam-6073	82	18	-	-	PUNCT
ejpam-6073	82	19	elastic	elastic	ADJ
ejpam-6073	82	20	media	medium	NOUN
ejpam-6073	82	21	under	under	ADP
ejpam-6073	82	22	nonlinear	nonlinear	ADJ
ejpam-6073	82	23	stress	stress	NOUN
ejpam-6073	82	24	conditions	condition	NOUN
ejpam-6073	82	25	.	.	PUNCT
ejpam-6073	83	1	first	first	ADV
ejpam-6073	83	2	,	,	PUNCT
ejpam-6073	83	3	we	we	PRON
ejpam-6073	83	4	establish	establish	VERB
ejpam-6073	83	5	the	the	DET
ejpam-6073	83	6	existence	existence	NOUN
ejpam-6073	83	7	and	and	CCONJ
ejpam-6073	83	8	uniqueness	uniqueness	NOUN
ejpam-6073	83	9	results	result	NOUN
ejpam-6073	83	10	of	of	ADP
ejpam-6073	83	11	a	a	DET
ejpam-6073	83	12	weak	weak	ADJ
ejpam-6073	83	13	solution	solution	NOUN
ejpam-6073	83	14	and	and	CCONJ
ejpam-6073	83	15	then	then	ADV
ejpam-6073	83	16	we	we	PRON
ejpam-6073	83	17	prove	prove	VERB
ejpam-6073	83	18	the	the	DET
ejpam-6073	83	19	global	global	ADJ
ejpam-6073	83	20	existence	existence	NOUN
ejpam-6073	83	21	of	of	ADP
ejpam-6073	83	22	the	the	DET
ejpam-6073	83	23	solutions	solution	NOUN
ejpam-6073	83	24	under	under	ADP
ejpam-6073	83	25	suitable	suitable	ADJ
ejpam-6073	83	26	assumptions	assumption	NOUN
ejpam-6073	83	27	on	on	ADP
ejpam-6073	83	28	the	the	DET
ejpam-6073	83	29	variable	variable	ADJ
ejpam-6073	83	30	exponents	exponent	NOUN
ejpam-6073	83	31	.	.	PUNCT
ejpam-6073	84	1	second	second	ADV
ejpam-6073	84	2	,	,	PUNCT
ejpam-6073	84	3	we	we	PRON
ejpam-6073	84	4	show	show	VERB
ejpam-6073	84	5	that	that	SCONJ
ejpam-6073	84	6	the	the	DET
ejpam-6073	84	7	solutions	solution	NOUN
ejpam-6073	84	8	with	with	ADP
ejpam-6073	84	9	negative	negative	ADJ
ejpam-6073	84	10	-	-	PUNCT
ejpam-6073	84	11	initial	initial	ADJ
ejpam-6073	84	12	energy	energy	NOUN
ejpam-6073	84	13	blow	blow	NOUN
ejpam-6073	84	14	-	-	PUNCT
ejpam-6073	84	15	up	up	NOUN
ejpam-6073	84	16	in	in	ADP
ejpam-6073	84	17	a	a	DET
ejpam-6073	84	18	finite	finite	ADJ
ejpam-6073	84	19	time	time	NOUN
ejpam-6073	84	20	.	.	PUNCT
ejpam-6073	85	1	finally	finally	ADV
ejpam-6073	85	2	,	,	PUNCT
ejpam-6073	85	3	we	we	PRON
ejpam-6073	85	4	produce	produce	VERB
ejpam-6073	85	5	some	some	DET
ejpam-6073	85	6	numerical	numerical	ADJ
ejpam-6073	85	7	tests	test	NOUN
ejpam-6073	85	8	and	and	CCONJ
ejpam-6073	85	9	examples	example	NOUN
ejpam-6073	85	10	to	to	PART
ejpam-6073	85	11	illustrate	illustrate	VERB
ejpam-6073	85	12	our	our	PRON
ejpam-6073	85	13	blow	blow	VERB
ejpam-6073	85	14	-	-	PUNCT
ejpam-6073	85	15	up	up	ADP
ejpam-6073	85	16	results	result	NOUN
ejpam-6073	85	17	.	.	PUNCT
ejpam-6073	86	1	the	the	DET
ejpam-6073	86	2	interaction	interaction	NOUN
ejpam-6073	86	3	between	between	ADP
ejpam-6073	86	4	the	the	DET
ejpam-6073	86	5	damping	damping	NOUN
ejpam-6073	86	6	and	and	CCONJ
ejpam-6073	86	7	the	the	DET
ejpam-6073	86	8	source	source	NOUN
ejpam-6073	86	9	terms	term	NOUN
ejpam-6073	86	10	was	be	AUX
ejpam-6073	86	11	first	first	ADV
ejpam-6073	86	12	considered	consider	VERB
ejpam-6073	86	13	by	by	ADP
ejpam-6073	86	14	levine	levine	PROPN
ejpam-6073	86	15	[	[	X
ejpam-6073	86	16	23	23	NUM
ejpam-6073	86	17	,	,	PUNCT
ejpam-6073	86	18	24	24	NUM
ejpam-6073	86	19	]	]	PUNCT
ejpam-6073	86	20	in	in	ADP
ejpam-6073	86	21	the	the	DET
ejpam-6073	86	22	linear	linear	ADJ
ejpam-6073	86	23	damping	damp	VERB
ejpam-6073	86	24	case	case	NOUN
ejpam-6073	86	25	,	,	PUNCT
ejpam-6073	86	26	(	(	PUNCT
ejpam-6073	86	27	m	m	NOUN
ejpam-6073	86	28	=	=	NOUN
ejpam-6073	86	29	2	2	NUM
ejpam-6073	86	30	)	)	PUNCT
ejpam-6073	86	31	,	,	PUNCT
ejpam-6073	86	32	in	in	ADP
ejpam-6073	86	33	the	the	DET
ejpam-6073	86	34	following	follow	VERB
ejpam-6073	86	35	wave	wave	NOUN
ejpam-6073	86	36	equation	equation	NOUN
ejpam-6073	86	37	utt	utt	NOUN
ejpam-6073	86	38	−∆u+	−∆u+	NOUN
ejpam-6073	86	39	a|ut|m−2ut	a|ut|m−2ut	NOUN
ejpam-6073	86	40	=	=	SYM
ejpam-6073	86	41	b|u|p−2u	b|u|p−2u	PROPN
ejpam-6073	86	42	,	,	PUNCT
ejpam-6073	86	43	in	in	ADP
ejpam-6073	86	44	ω	ω	PROPN
ejpam-6073	86	45	,	,	PUNCT
ejpam-6073	86	46	t	t	X
ejpam-6073	86	47	>	>	X
ejpam-6073	86	48	0	0	NUM
ejpam-6073	86	49	,	,	PUNCT
ejpam-6073	86	50	(	(	PUNCT
ejpam-6073	86	51	7	7	X
ejpam-6073	86	52	)	)	PUNCT
ejpam-6073	86	53	where	where	SCONJ
ejpam-6073	86	54	a	a	DET
ejpam-6073	86	55	,	,	PUNCT
ejpam-6073	86	56	b	b	X
ejpam-6073	86	57	>	>	X
ejpam-6073	86	58	0	0	NUM
ejpam-6073	86	59	,	,	PUNCT
ejpam-6073	86	60	p	p	X
ejpam-6073	86	61	>	>	X
ejpam-6073	86	62	2	2	NUM
ejpam-6073	86	63	,	,	PUNCT
ejpam-6073	86	64	m	m	VERB
ejpam-6073	86	65	≥	≥	NOUN
ejpam-6073	86	66	1	1	NUM
ejpam-6073	86	67	,	,	PUNCT
ejpam-6073	86	68	ω	ω	PROPN
ejpam-6073	86	69	is	be	AUX
ejpam-6073	86	70	a	a	DET
ejpam-6073	86	71	bounded	bounded	ADJ
ejpam-6073	86	72	domain	domain	NOUN
ejpam-6073	86	73	in	in	ADP
ejpam-6073	86	74	rn	rn	PROPN
ejpam-6073	86	75	.	.	PUNCT
ejpam-6073	87	1	he	he	PRON
ejpam-6073	87	2	showed	show	VERB
ejpam-6073	87	3	that	that	SCONJ
ejpam-6073	87	4	solutions	solution	NOUN
ejpam-6073	87	5	with	with	ADP
ejpam-6073	87	6	negative	negative	ADJ
ejpam-6073	87	7	initial	initial	ADJ
ejpam-6073	87	8	energy	energy	NOUN
ejpam-6073	87	9	blow	blow	NOUN
ejpam-6073	87	10	up	up	ADP
ejpam-6073	87	11	in	in	ADP
ejpam-6073	87	12	finite	finite	ADJ
ejpam-6073	87	13	time	time	NOUN
ejpam-6073	87	14	.	.	PUNCT
ejpam-6073	88	1	then	then	ADV
ejpam-6073	88	2	,	,	PUNCT
ejpam-6073	88	3	georgiev	georgiev	NOUN
ejpam-6073	88	4	and	and	CCONJ
ejpam-6073	88	5	todorova	todorova	PRON
ejpam-6073	88	6	[	[	X
ejpam-6073	88	7	25	25	NUM
ejpam-6073	88	8	]	]	X
ejpam-6073	88	9	extended	extended	PROPN
ejpam-6073	88	10	levine	levine	PROPN
ejpam-6073	88	11	’s	’s	PART
ejpam-6073	88	12	result	result	NOUN
ejpam-6073	88	13	to	to	ADP
ejpam-6073	88	14	the	the	DET
ejpam-6073	88	15	nonlinear	nonlinear	ADJ
ejpam-6073	88	16	damping	damp	VERB
ejpam-6073	88	17	case	case	NOUN
ejpam-6073	88	18	(	(	PUNCT
ejpam-6073	88	19	m	m	VERB
ejpam-6073	88	20	>	>	X
ejpam-6073	88	21	2	2	NUM
ejpam-6073	88	22	)	)	PUNCT
ejpam-6073	88	23	.	.	PUNCT
ejpam-6073	89	1	in	in	ADP
ejpam-6073	89	2	their	their	PRON
ejpam-6073	89	3	work	work	NOUN
ejpam-6073	89	4	,	,	PUNCT
ejpam-6073	89	5	the	the	DET
ejpam-6073	89	6	a.	a.	NOUN
ejpam-6073	89	7	m.	m.	PROPN
ejpam-6073	89	8	al	al	PROPN
ejpam-6073	89	9	-	-	PROPN
ejpam-6073	89	10	mahdi	mahdi	PROPN
ejpam-6073	89	11	et	et	PROPN
ejpam-6073	89	12	al	al	PROPN
ejpam-6073	89	13	.	.	PUNCT
ejpam-6073	89	14	/	/	SYM
ejpam-6073	89	15	eur	eur	PROPN
ejpam-6073	89	16	.	.	PUNCT
ejpam-6073	90	1	j.	j.	PROPN
ejpam-6073	90	2	pure	pure	PROPN
ejpam-6073	90	3	appl	appl	PROPN
ejpam-6073	90	4	.	.	PROPN
ejpam-6073	90	5	math	math	PROPN
ejpam-6073	90	6	,	,	PUNCT
ejpam-6073	90	7	18	18	NUM
ejpam-6073	90	8	(	(	PUNCT
ejpam-6073	90	9	3	3	NUM
ejpam-6073	90	10	)	)	PUNCT
ejpam-6073	90	11	(	(	PUNCT
ejpam-6073	90	12	2025	2025	NUM
ejpam-6073	90	13	)	)	PUNCT
ejpam-6073	90	14	,	,	PUNCT
ejpam-6073	90	15	6073	6073	NUM
ejpam-6073	90	16	5	5	NUM
ejpam-6073	90	17	of	of	ADP
ejpam-6073	90	18	29	29	NUM
ejpam-6073	90	19	authors	author	NOUN
ejpam-6073	90	20	introduced	introduce	VERB
ejpam-6073	90	21	a	a	DET
ejpam-6073	90	22	different	different	ADJ
ejpam-6073	90	23	method	method	NOUN
ejpam-6073	90	24	and	and	CCONJ
ejpam-6073	90	25	determined	determine	VERB
ejpam-6073	90	26	suitable	suitable	ADJ
ejpam-6073	90	27	relations	relation	NOUN
ejpam-6073	90	28	between	between	ADP
ejpam-6073	90	29	m	m	PROPN
ejpam-6073	90	30	and	and	CCONJ
ejpam-6073	90	31	p	p	NOUN
ejpam-6073	90	32	for	for	ADP
ejpam-6073	90	33	which	which	PRON
ejpam-6073	90	34	there	there	PRON
ejpam-6073	90	35	is	be	VERB
ejpam-6073	90	36	global	global	ADJ
ejpam-6073	90	37	existence	existence	NOUN
ejpam-6073	90	38	or	or	CCONJ
ejpam-6073	90	39	alternatively	alternatively	ADV
ejpam-6073	90	40	finite	finite	VERB
ejpam-6073	90	41	time	time	NOUN
ejpam-6073	90	42	blow	blow	VERB
ejpam-6073	90	43	up	up	ADP
ejpam-6073	90	44	.	.	PUNCT
ejpam-6073	91	1	more	more	ADV
ejpam-6073	91	2	precisely	precisely	ADV
ejpam-6073	91	3	:	:	PUNCT
ejpam-6073	91	4	they	they	PRON
ejpam-6073	91	5	showed	show	VERB
ejpam-6073	91	6	that	that	SCONJ
ejpam-6073	91	7	solutions	solution	NOUN
ejpam-6073	91	8	with	with	ADP
ejpam-6073	91	9	any	any	DET
ejpam-6073	91	10	initial	initial	ADJ
ejpam-6073	91	11	data	datum	NOUN
ejpam-6073	91	12	continue	continue	VERB
ejpam-6073	91	13	to	to	PART
ejpam-6073	91	14	exist	exist	VERB
ejpam-6073	91	15	globally	globally	ADV
ejpam-6073	91	16	(	(	PUNCT
ejpam-6073	91	17	in	in	ADP
ejpam-6073	91	18	time	time	NOUN
ejpam-6073	91	19	)	)	PUNCT
ejpam-6073	91	20	if	if	SCONJ
ejpam-6073	91	21	m	m	PROPN
ejpam-6073	91	22	≥	≥	VERB
ejpam-6073	91	23	p	p	NOUN
ejpam-6073	91	24	and	and	CCONJ
ejpam-6073	91	25	blow	blow	VERB
ejpam-6073	91	26	up	up	ADP
ejpam-6073	91	27	in	in	ADP
ejpam-6073	91	28	finite	finite	ADJ
ejpam-6073	91	29	time	time	NOUN
ejpam-6073	91	30	if	if	SCONJ
ejpam-6073	91	31	m	m	VERB
ejpam-6073	91	32	<	<	X
ejpam-6073	91	33	p	p	NOUN
ejpam-6073	91	34	and	and	CCONJ
ejpam-6073	91	35	the	the	DET
ejpam-6073	91	36	initial	initial	ADJ
ejpam-6073	91	37	energy	energy	NOUN
ejpam-6073	91	38	is	be	AUX
ejpam-6073	91	39	sufficiently	sufficiently	ADV
ejpam-6073	91	40	negative	negative	ADJ
ejpam-6073	91	41	.	.	PUNCT
ejpam-6073	92	1	without	without	ADP
ejpam-6073	92	2	imposing	impose	VERB
ejpam-6073	92	3	the	the	DET
ejpam-6073	92	4	condition	condition	NOUN
ejpam-6073	92	5	that	that	SCONJ
ejpam-6073	92	6	the	the	DET
ejpam-6073	92	7	initial	initial	ADJ
ejpam-6073	92	8	energy	energy	NOUN
ejpam-6073	92	9	is	be	AUX
ejpam-6073	92	10	sufficiently	sufficiently	ADV
ejpam-6073	92	11	negative	negative	ADJ
ejpam-6073	92	12	,	,	PUNCT
ejpam-6073	92	13	messaoudi	messaoudi	ADJ
ejpam-6073	92	14	[	[	X
ejpam-6073	92	15	26	26	NUM
ejpam-6073	92	16	]	]	PUNCT
ejpam-6073	92	17	extended	extend	VERB
ejpam-6073	92	18	the	the	DET
ejpam-6073	92	19	blow	blow	NOUN
ejpam-6073	92	20	up	up	ADP
ejpam-6073	92	21	result	result	NOUN
ejpam-6073	92	22	of	of	ADP
ejpam-6073	92	23	[	[	X
ejpam-6073	92	24	25	25	NUM
ejpam-6073	92	25	]	]	PUNCT
ejpam-6073	92	26	to	to	ADP
ejpam-6073	92	27	solutions	solution	NOUN
ejpam-6073	92	28	with	with	ADP
ejpam-6073	92	29	negative	negative	ADJ
ejpam-6073	92	30	initial	initial	ADJ
ejpam-6073	92	31	energy	energy	NOUN
ejpam-6073	92	32	only	only	ADV
ejpam-6073	92	33	.	.	PUNCT
ejpam-6073	93	1	messaoudi	messaoudi	PROPN
ejpam-6073	94	1	[	[	X
ejpam-6073	94	2	27]considered	27]considered	NUM
ejpam-6073	94	3	the	the	DET
ejpam-6073	94	4	following	follow	VERB
ejpam-6073	94	5	nonlinear	nonlinear	ADJ
ejpam-6073	94	6	viscoelastic	viscoelastic	ADJ
ejpam-6073	94	7	wave	wave	NOUN
ejpam-6073	94	8	equation	equation	NOUN
ejpam-6073	94	9	utt	utt	PROPN
ejpam-6073	94	10	−∆u+	−∆u+	NOUN
ejpam-6073	94	11	∫	∫	PROPN
ejpam-6073	94	12	t	t	PROPN
ejpam-6073	94	13	0	0	NUM
ejpam-6073	94	14	g(t−	g(t−	PROPN
ejpam-6073	94	15	s)∆u(s)ds+	s)∆u(s)ds+	PUNCT
ejpam-6073	94	16	a|ut|m−2ut	a|ut|m−2ut	NOUN
ejpam-6073	94	17	=	=	SYM
ejpam-6073	94	18	b|u|p−2u	b|u|p−2u	PROPN
ejpam-6073	94	19	,	,	PUNCT
ejpam-6073	94	20	x	x	X
ejpam-6073	94	21	∈	∈	PROPN
ejpam-6073	94	22	ω	ω	PROPN
ejpam-6073	94	23	,	,	PUNCT
ejpam-6073	94	24	t	t	X
ejpam-6073	94	25	>	>	X
ejpam-6073	94	26	0	0	NUM
ejpam-6073	94	27	,	,	PUNCT
ejpam-6073	94	28	(	(	PUNCT
ejpam-6073	94	29	8)	8)	NUM
ejpam-6073	94	30	where	where	SCONJ
ejpam-6073	94	31	ω	ω	PROPN
ejpam-6073	94	32	is	be	AUX
ejpam-6073	94	33	a	a	DET
ejpam-6073	94	34	bounded	bounded	ADJ
ejpam-6073	94	35	domain	domain	NOUN
ejpam-6073	94	36	of	of	ADP
ejpam-6073	94	37	rn	rn	PROPN
ejpam-6073	94	38	.	.	PUNCT
ejpam-6073	95	1	he	he	PRON
ejpam-6073	95	2	proved	prove	VERB
ejpam-6073	95	3	that	that	SCONJ
ejpam-6073	95	4	any	any	DET
ejpam-6073	95	5	weak	weak	ADJ
ejpam-6073	95	6	solution	solution	NOUN
ejpam-6073	95	7	with	with	ADP
ejpam-6073	95	8	negative	negative	ADJ
ejpam-6073	95	9	initial	initial	ADJ
ejpam-6073	95	10	energy	energy	NOUN
ejpam-6073	95	11	blows	blow	NOUN
ejpam-6073	95	12	-	-	PUNCT
ejpam-6073	95	13	up	up	NOUN
ejpam-6073	95	14	in	in	ADP
ejpam-6073	95	15	finite	finite	ADJ
ejpam-6073	95	16	time	time	NOUN
ejpam-6073	95	17	if	if	SCONJ
ejpam-6073	95	18	p	p	PROPN
ejpam-6073	95	19	>	>	X
ejpam-6073	95	20	m.	m.	NOUN
ejpam-6073	95	21	also	also	ADV
ejpam-6073	95	22	the	the	DET
ejpam-6073	95	23	case	case	NOUN
ejpam-6073	95	24	of	of	ADP
ejpam-6073	95	25	a	a	DET
ejpam-6073	95	26	stronger	strong	ADJ
ejpam-6073	95	27	damping	damping	NOUN
ejpam-6073	95	28	is	be	AUX
ejpam-6073	95	29	considered	consider	VERB
ejpam-6073	95	30	and	and	CCONJ
ejpam-6073	95	31	it	it	PRON
ejpam-6073	95	32	is	be	AUX
ejpam-6073	95	33	showed	show	VERB
ejpam-6073	95	34	that	that	SCONJ
ejpam-6073	95	35	solutions	solution	NOUN
ejpam-6073	95	36	exist	exist	VERB
ejpam-6073	95	37	globally	globally	ADV
ejpam-6073	95	38	for	for	ADP
ejpam-6073	95	39	any	any	DET
ejpam-6073	95	40	initial	initial	ADJ
ejpam-6073	95	41	data	datum	NOUN
ejpam-6073	95	42	,	,	PUNCT
ejpam-6073	95	43	in	in	ADP
ejpam-6073	95	44	the	the	DET
ejpam-6073	95	45	appropriate	appropriate	ADJ
ejpam-6073	95	46	space	space	NOUN
ejpam-6073	95	47	,	,	PUNCT
ejpam-6073	95	48	provided	provide	VERB
ejpam-6073	95	49	that	that	SCONJ
ejpam-6073	95	50	m	m	VERB
ejpam-6073	95	51	≤	≤	ADJ
ejpam-6073	96	1	p.	p.	NOUN
ejpam-6073	96	2	for	for	ADP
ejpam-6073	96	3	more	more	ADJ
ejpam-6073	96	4	results	result	NOUN
ejpam-6073	96	5	in	in	ADP
ejpam-6073	96	6	blow	blow	NOUN
ejpam-6073	96	7	-	-	PUNCT
ejpam-6073	96	8	up	up	NOUN
ejpam-6073	96	9	,	,	PUNCT
ejpam-6073	96	10	we	we	PRON
ejpam-6073	96	11	refer	refer	VERB
ejpam-6073	96	12	the	the	DET
ejpam-6073	96	13	reader	reader	NOUN
ejpam-6073	96	14	to	to	PART
ejpam-6073	96	15	see	see	VERB
ejpam-6073	96	16	[	[	X
ejpam-6073	96	17	28–32	28–32	NUM
ejpam-6073	96	18	]	]	PUNCT
ejpam-6073	96	19	and	and	CCONJ
ejpam-6073	96	20	the	the	DET
ejpam-6073	96	21	references	reference	NOUN
ejpam-6073	96	22	therein	therein	ADV
ejpam-6073	96	23	.	.	PUNCT
ejpam-6073	97	1	2	2	X
ejpam-6073	97	2	.	.	X
ejpam-6073	97	3	preliminaries	preliminary	NOUN
ejpam-6073	97	4	in	in	ADP
ejpam-6073	97	5	this	this	DET
ejpam-6073	97	6	section	section	NOUN
ejpam-6073	97	7	,	,	PUNCT
ejpam-6073	97	8	we	we	PRON
ejpam-6073	97	9	present	present	VERB
ejpam-6073	97	10	some	some	DET
ejpam-6073	97	11	material	material	NOUN
ejpam-6073	97	12	needed	need	VERB
ejpam-6073	97	13	in	in	ADP
ejpam-6073	97	14	the	the	DET
ejpam-6073	97	15	proof	proof	NOUN
ejpam-6073	97	16	of	of	ADP
ejpam-6073	97	17	our	our	PRON
ejpam-6073	97	18	results	result	NOUN
ejpam-6073	97	19	.	.	PUNCT
ejpam-6073	98	1	throughout	throughout	ADP
ejpam-6073	98	2	this	this	DET
ejpam-6073	98	3	paper	paper	NOUN
ejpam-6073	98	4	ω	ω	NOUN
ejpam-6073	98	5	=	=	SYM
ejpam-6073	98	6	(	(	PUNCT
ejpam-6073	98	7	0	0	NUM
ejpam-6073	98	8	,	,	PUNCT
ejpam-6073	98	9	1	1	NUM
ejpam-6073	98	10	)	)	PUNCT
ejpam-6073	98	11	and	and	CCONJ
ejpam-6073	98	12	c	c	PROPN
ejpam-6073	98	13	is	be	AUX
ejpam-6073	98	14	used	use	VERB
ejpam-6073	98	15	to	to	PART
ejpam-6073	98	16	denote	denote	VERB
ejpam-6073	98	17	a	a	DET
ejpam-6073	98	18	generic	generic	ADJ
ejpam-6073	98	19	positive	positive	ADJ
ejpam-6073	98	20	constant	constant	NOUN
ejpam-6073	98	21	.	.	PUNCT
ejpam-6073	99	1	•	•	NUM
ejpam-6073	99	2	(	(	PUNCT
ejpam-6073	99	3	a1	a1	NOUN
ejpam-6073	99	4	):	):	PUNCT
ejpam-6073	99	5	p	p	X
ejpam-6073	99	6	,	,	PUNCT
ejpam-6073	99	7	q	q	ADJ
ejpam-6073	99	8	,	,	PUNCT
ejpam-6073	99	9	m	m	PROPN
ejpam-6073	99	10	,	,	PUNCT
ejpam-6073	99	11	ℓ	ℓ	INTJ
ejpam-6073	99	12	:	:	PUNCT
ejpam-6073	100	1	ω	ω	X
ejpam-6073	100	2	→	→	PUNCT
ejpam-6073	101	1	[	[	X
ejpam-6073	101	2	1,∞	1,∞	NUM
ejpam-6073	101	3	)	)	PUNCT
ejpam-6073	101	4	are	be	AUX
ejpam-6073	101	5	measurable	measurable	ADJ
ejpam-6073	101	6	functions	function	NOUN
ejpam-6073	101	7	on	on	ADP
ejpam-6073	101	8	ω	ω	NUM
ejpam-6073	101	9	satisfying	satisfy	VERB
ejpam-6073	101	10	all	all	DET
ejpam-6073	101	11	the	the	DET
ejpam-6073	101	12	following	follow	VERB
ejpam-6073	101	13	conditions	condition	NOUN
ejpam-6073	101	14	2	2	NUM
ejpam-6073	101	15	≤	≤	NOUN
ejpam-6073	101	16	p1	p1	NOUN
ejpam-6073	101	17	≤	≤	NOUN
ejpam-6073	101	18	p(x	p(x	PROPN
ejpam-6073	101	19	)	)	PUNCT
ejpam-6073	101	20	≤	≤	NUM
ejpam-6073	101	21	p2	p2	PROPN
ejpam-6073	101	22	<	<	X
ejpam-6073	101	23	m1	m1	PROPN
ejpam-6073	101	24	≤	≤	NOUN
ejpam-6073	101	25	m(x	m(x	PROPN
ejpam-6073	101	26	)	)	PUNCT
ejpam-6073	101	27	≤	≤	PUNCT
ejpam-6073	102	1	m2	m2	PROPN
ejpam-6073	102	2	<	<	X
ejpam-6073	102	3	∞	∞	PROPN
ejpam-6073	102	4	,	,	PUNCT
ejpam-6073	102	5	2	2	NUM
ejpam-6073	102	6	≤	≤	NUM
ejpam-6073	102	7	q1	q1	PROPN
ejpam-6073	102	8	≤	≤	NUM
ejpam-6073	102	9	q(x	q(x	PROPN
ejpam-6073	102	10	)	)	PUNCT
ejpam-6073	102	11	≤	≤	NUM
ejpam-6073	102	12	q2	q2	NOUN
ejpam-6073	102	13	<	<	X
ejpam-6073	102	14	ℓ1	ℓ1	NOUN
ejpam-6073	102	15	≤	≤	NOUN
ejpam-6073	102	16	ℓ(x	ℓ(x	NOUN
ejpam-6073	102	17	)	)	PUNCT
ejpam-6073	102	18	≤	≤	NOUN
ejpam-6073	102	19	ℓ2	ℓ2	NOUN
ejpam-6073	102	20	<	<	X
ejpam-6073	102	21	∞	∞	PROPN
ejpam-6073	102	22	,	,	PUNCT
ejpam-6073	102	23	where	where	SCONJ
ejpam-6073	102	24	p1	p1	NOUN
ejpam-6073	102	25	:	:	PUNCT
ejpam-6073	102	26	=	=	SYM
ejpam-6073	102	27	essinfx∈ωp(x	essinfx∈ωp(x	PROPN
ejpam-6073	102	28	)	)	PUNCT
ejpam-6073	102	29	,	,	PUNCT
ejpam-6073	102	30	p2	p2	PROPN
ejpam-6073	102	31	:	:	PUNCT
ejpam-6073	102	32	=	=	SYM
ejpam-6073	102	33	esssupx∈ωp(x	esssupx∈ωp(x	NOUN
ejpam-6073	102	34	)	)	PUNCT
ejpam-6073	102	35	,	,	PUNCT
ejpam-6073	102	36	m1	m1	PROPN
ejpam-6073	102	37	:	:	PUNCT
ejpam-6073	102	38	=	=	SYM
ejpam-6073	102	39	essinfx∈ωm(x	essinfx∈ωm(x	X
ejpam-6073	102	40	)	)	PUNCT
ejpam-6073	102	41	,	,	PUNCT
ejpam-6073	102	42	m2	m2	PROPN
ejpam-6073	102	43	:	:	PUNCT
ejpam-6073	102	44	=	=	SYM
ejpam-6073	102	45	esssupx∈ωm(x	esssupx∈ωm(x	NOUN
ejpam-6073	102	46	)	)	PUNCT
ejpam-6073	102	47	,	,	PUNCT
ejpam-6073	102	48	q1	q1	NOUN
ejpam-6073	102	49	:	:	PUNCT
ejpam-6073	102	50	=	=	SYM
ejpam-6073	102	51	essinfx∈ωq(x	essinfx∈ωq(x	ADJ
ejpam-6073	102	52	)	)	PUNCT
ejpam-6073	102	53	,	,	PUNCT
ejpam-6073	102	54	q2	q2	NOUN
ejpam-6073	102	55	:	:	PUNCT
ejpam-6073	102	56	=	=	SYM
ejpam-6073	102	57	esssupx∈ωq(x	esssupx∈ωq(x	NOUN
ejpam-6073	102	58	)	)	PUNCT
ejpam-6073	102	59	,	,	PUNCT
ejpam-6073	102	60	ℓ1	ℓ1	NOUN
ejpam-6073	102	61	:	:	PUNCT
ejpam-6073	102	62	=	=	SYM
ejpam-6073	102	63	essinfx∈ωℓ(x	essinfx∈ωℓ(x	NOUN
ejpam-6073	102	64	)	)	PUNCT
ejpam-6073	102	65	,	,	PUNCT
ejpam-6073	102	66	ℓ2	ℓ2	NOUN
ejpam-6073	102	67	:	:	PUNCT
ejpam-6073	102	68	=	=	SYM
ejpam-6073	102	69	esssupx∈ωℓ(x	esssupx∈ωℓ(x	ADP
ejpam-6073	102	70	)	)	PUNCT
ejpam-6073	102	71	.	.	PUNCT
ejpam-6073	103	1	and	and	CCONJ
ejpam-6073	103	2	satisfy	satisfy	VERB
ejpam-6073	103	3	the	the	DET
ejpam-6073	103	4	log	log	NOUN
ejpam-6073	103	5	-	-	PUNCT
ejpam-6073	103	6	hölder	hölder	NOUN
ejpam-6073	103	7	continuity	continuity	NOUN
ejpam-6073	103	8	condition	condition	NOUN
ejpam-6073	103	9	;	;	PUNCT
ejpam-6073	103	10	that	that	PRON
ejpam-6073	103	11	is	be	AUX
ejpam-6073	103	12	for	for	ADP
ejpam-6073	103	13	any	any	DET
ejpam-6073	103	14	δ	δ	NOUN
ejpam-6073	103	15	with	with	ADP
ejpam-6073	103	16	0	0	NUM
ejpam-6073	103	17	<	<	X
ejpam-6073	103	18	δ	δ	X
ejpam-6073	103	19	<	<	X
ejpam-6073	103	20	1	1	NUM
ejpam-6073	103	21	,	,	PUNCT
ejpam-6073	103	22	there	there	PRON
ejpam-6073	103	23	exists	exist	VERB
ejpam-6073	103	24	a	a	DET
ejpam-6073	103	25	constant	constant	ADJ
ejpam-6073	103	26	a	a	DET
ejpam-6073	103	27	>	>	X
ejpam-6073	103	28	0	0	NUM
ejpam-6073	103	29	such	such	ADJ
ejpam-6073	103	30	that	that	SCONJ
ejpam-6073	103	31	,	,	PUNCT
ejpam-6073	103	32	|f(x)−	|f(x)−	PROPN
ejpam-6073	103	33	f(y)|	f(y)|	PROPN
ejpam-6073	103	34	≤	≤	PROPN
ejpam-6073	104	1	−	−	PROPN
ejpam-6073	104	2	a	a	DET
ejpam-6073	104	3	log	log	NOUN
ejpam-6073	104	4	|x−	|x−	NOUN
ejpam-6073	104	5	y|	y|	NOUN
ejpam-6073	104	6	,	,	PUNCT
ejpam-6073	104	7	for	for	ADP
ejpam-6073	104	8	all	all	DET
ejpam-6073	104	9	x	x	NOUN
ejpam-6073	104	10	,	,	PUNCT
ejpam-6073	104	11	y	y	PROPN
ejpam-6073	104	12	∈	∈	PROPN
ejpam-6073	104	13	ω	ω	PROPN
ejpam-6073	104	14	,	,	PUNCT
ejpam-6073	104	15	with	with	ADP
ejpam-6073	104	16	|x−	|x−	PUNCT
ejpam-6073	104	17	y|	y|	VERB
ejpam-6073	104	18	<	<	X
ejpam-6073	104	19	δ	δ	PROPN
ejpam-6073	104	20	.	.	PUNCT
ejpam-6073	105	1	(	(	PUNCT
ejpam-6073	105	2	9	9	NUM
ejpam-6073	105	3	)	)	PUNCT
ejpam-6073	105	4	•	•	NOUN
ejpam-6073	105	5	(	(	PUNCT
ejpam-6073	105	6	a2	a2	PROPN
ejpam-6073	105	7	):	):	PUNCT
ejpam-6073	105	8	the	the	DET
ejpam-6073	105	9	coefficients	coefficient	NOUN
ejpam-6073	105	10	ai	ai	VERB
ejpam-6073	105	11	,	,	PUNCT
ejpam-6073	105	12	i	i	PRON
ejpam-6073	105	13	=	=	NOUN
ejpam-6073	105	14	1	1	NUM
ejpam-6073	105	15	,	,	PUNCT
ejpam-6073	105	16	...	...	PUNCT
ejpam-6073	105	17	,	,	PUNCT
ejpam-6073	105	18	3	3	NUM
ejpam-6073	105	19	satisfy	satisfy	NOUN
ejpam-6073	105	20	a1a3	a1a3	X
ejpam-6073	105	21	−	−	PROPN
ejpam-6073	105	22	a22	a22	PROPN
ejpam-6073	105	23	>	>	X
ejpam-6073	105	24	0	0	NUM
ejpam-6073	105	25	.	.	PROPN
ejpam-6073	105	26	3	3	X
ejpam-6073	105	27	.	.	X
ejpam-6073	105	28	technical	technical	ADJ
ejpam-6073	105	29	lemmas	lemma	NOUN
ejpam-6073	105	30	in	in	ADP
ejpam-6073	105	31	this	this	DET
ejpam-6073	105	32	section	section	NOUN
ejpam-6073	105	33	,	,	PUNCT
ejpam-6073	105	34	we	we	PRON
ejpam-6073	105	35	present	present	VERB
ejpam-6073	105	36	and	and	CCONJ
ejpam-6073	105	37	establish	establish	VERB
ejpam-6073	105	38	some	some	DET
ejpam-6073	105	39	lemmas	lemma	NOUN
ejpam-6073	105	40	needed	need	VERB
ejpam-6073	105	41	for	for	ADP
ejpam-6073	105	42	the	the	DET
ejpam-6073	105	43	proof	proof	NOUN
ejpam-6073	105	44	of	of	ADP
ejpam-6073	105	45	our	our	PRON
ejpam-6073	105	46	main	main	ADJ
ejpam-6073	105	47	results	result	NOUN
ejpam-6073	105	48	.	.	PUNCT
ejpam-6073	106	1	a.	a.	PROPN
ejpam-6073	106	2	m.	m.	PROPN
ejpam-6073	106	3	al	al	PROPN
ejpam-6073	106	4	-	-	PROPN
ejpam-6073	106	5	mahdi	mahdi	PROPN
ejpam-6073	106	6	et	et	PROPN
ejpam-6073	106	7	al	al	PROPN
ejpam-6073	106	8	.	.	PUNCT
ejpam-6073	106	9	/	/	SYM
ejpam-6073	106	10	eur	eur	PROPN
ejpam-6073	106	11	.	.	PUNCT
ejpam-6073	107	1	j.	j.	PROPN
ejpam-6073	107	2	pure	pure	PROPN
ejpam-6073	107	3	appl	appl	PROPN
ejpam-6073	107	4	.	.	PROPN
ejpam-6073	107	5	math	math	PROPN
ejpam-6073	107	6	,	,	PUNCT
ejpam-6073	107	7	18	18	NUM
ejpam-6073	107	8	(	(	PUNCT
ejpam-6073	107	9	3	3	NUM
ejpam-6073	107	10	)	)	PUNCT
ejpam-6073	107	11	(	(	PUNCT
ejpam-6073	107	12	2025	2025	NUM
ejpam-6073	107	13	)	)	PUNCT
ejpam-6073	107	14	,	,	PUNCT
ejpam-6073	107	15	6073	6073	NUM
ejpam-6073	107	16	6	6	NUM
ejpam-6073	107	17	of	of	ADP
ejpam-6073	107	18	29	29	NUM
ejpam-6073	107	19	lemma	lemma	PROPN
ejpam-6073	107	20	1	1	NUM
ejpam-6073	107	21	.	.	PUNCT
ejpam-6073	108	1	the	the	DET
ejpam-6073	108	2	energy	energy	NOUN
ejpam-6073	108	3	of	of	ADP
ejpam-6073	108	4	the	the	DET
ejpam-6073	108	5	problem	problem	NOUN
ejpam-6073	108	6	(	(	PUNCT
ejpam-6073	108	7	6	6	NUM
ejpam-6073	108	8	)	)	PUNCT
ejpam-6073	108	9	is	be	AUX
ejpam-6073	108	10	defined	define	VERB
ejpam-6073	108	11	by	by	ADP
ejpam-6073	108	12	e(t	e(t	NOUN
ejpam-6073	108	13	)	)	PUNCT
ejpam-6073	108	14	=	=	SYM
ejpam-6073	108	15	1	1	NUM
ejpam-6073	108	16	2	2	NUM
ejpam-6073	108	17	∫	∫	NOUN
ejpam-6073	108	18	ω	ω	NOUN
ejpam-6073	108	19	[	[	PUNCT
ejpam-6073	108	20	ρzz	ρzz	NOUN
ejpam-6073	108	21	2	2	NUM
ejpam-6073	108	22	t	t	NOUN
ejpam-6073	108	23	+	+	CCONJ
ejpam-6073	108	24	ρuu	ρuu	PROPN
ejpam-6073	108	25	2	2	NUM
ejpam-6073	108	26	t	t	NOUN
ejpam-6073	108	27	+	+	CCONJ
ejpam-6073	108	28	a3u	a3u	ADP
ejpam-6073	108	29	2	2	NUM
ejpam-6073	108	30	x	x	SYM
ejpam-6073	108	31	+	+	CCONJ
ejpam-6073	108	32	a1z	a1z	PROPN
ejpam-6073	108	33	2	2	NUM
ejpam-6073	108	34	x	x	SYM
ejpam-6073	108	35	+	+	X
ejpam-6073	108	36	2a2zxux	2a2zxux	NUM
ejpam-6073	108	37	]	]	PUNCT
ejpam-6073	108	38	dx	dx	PROPN
ejpam-6073	108	39	−c	−c	PROPN
ejpam-6073	108	40	∫	∫	PROPN
ejpam-6073	108	41	ω	ω	PROPN
ejpam-6073	108	42	|z|m(x	|z|m(x	PROPN
ejpam-6073	108	43	)	)	PUNCT
ejpam-6073	108	44	m(x	m(x	PROPN
ejpam-6073	108	45	)	)	PUNCT
ejpam-6073	108	46	dx−	dx−	X
ejpam-6073	109	1	d	d	X
ejpam-6073	109	2	∫	∫	PROPN
ejpam-6073	109	3	ω	ω	NUM
ejpam-6073	109	4	|u|ℓ(x	|u|ℓ(x	NUM
ejpam-6073	109	5	)	)	PUNCT
ejpam-6073	109	6	ℓ(x	ℓ(x	PROPN
ejpam-6073	109	7	)	)	PUNCT
ejpam-6073	109	8	dx	dx	PROPN
ejpam-6073	109	9	,	,	PUNCT
ejpam-6073	109	10	(	(	PUNCT
ejpam-6073	109	11	10	10	NUM
ejpam-6073	109	12	)	)	PUNCT
ejpam-6073	109	13	and	and	CCONJ
ejpam-6073	109	14	satisfies	satisfy	VERB
ejpam-6073	109	15	the	the	DET
ejpam-6073	109	16	following	follow	VERB
ejpam-6073	109	17	e′(t	e′(t	PROPN
ejpam-6073	109	18	)	)	PUNCT
ejpam-6073	109	19	=	=	PUNCT
ejpam-6073	110	1	−γ	−γ	ADJ
ejpam-6073	110	2	∫	∫	PROPN
ejpam-6073	110	3	ω	ω	NUM
ejpam-6073	110	4	|zt|p(·)dx−	|zt|p(·)dx−	PROPN
ejpam-6073	110	5	β	β	PROPN
ejpam-6073	110	6	∫	∫	PROPN
ejpam-6073	110	7	ω	ω	NUM
ejpam-6073	110	8	|ut|q(·)dx	|ut|q(·)dx	ADJ
ejpam-6073	110	9	≤	≤	NOUN
ejpam-6073	110	10	0	0	NUM
ejpam-6073	110	11	.	.	PUNCT
ejpam-6073	111	1	(	(	PUNCT
ejpam-6073	111	2	11	11	NUM
ejpam-6073	111	3	)	)	PUNCT
ejpam-6073	111	4	proof	proof	NOUN
ejpam-6073	111	5	.	.	PUNCT
ejpam-6073	112	1	multiplying	multiply	VERB
ejpam-6073	112	2	the	the	DET
ejpam-6073	112	3	equations	equation	NOUN
ejpam-6073	112	4	in	in	ADP
ejpam-6073	112	5	(	(	PUNCT
ejpam-6073	112	6	6	6	NUM
ejpam-6073	112	7	)	)	PUNCT
ejpam-6073	112	8	by	by	ADP
ejpam-6073	112	9	zt	zt	PROPN
ejpam-6073	112	10	and	and	CCONJ
ejpam-6073	112	11	ut	ut	PROPN
ejpam-6073	112	12	respectively	respectively	ADV
ejpam-6073	112	13	and	and	CCONJ
ejpam-6073	112	14	then	then	ADV
ejpam-6073	112	15	integrating	integrate	VERB
ejpam-6073	112	16	over	over	ADP
ejpam-6073	112	17	the	the	DET
ejpam-6073	112	18	interval	interval	NOUN
ejpam-6073	112	19	ω	ω	NOUN
ejpam-6073	112	20	=	=	SYM
ejpam-6073	112	21	(	(	PUNCT
ejpam-6073	112	22	0	0	NUM
ejpam-6073	112	23	,	,	PUNCT
ejpam-6073	112	24	1	1	NUM
ejpam-6073	112	25	)	)	PUNCT
ejpam-6073	112	26	to	to	PART
ejpam-6073	112	27	get	get	VERB
ejpam-6073	112	28	ρz	ρz	NOUN
ejpam-6073	112	29	∫	∫	PROPN
ejpam-6073	112	30	ω	ω	NOUN
ejpam-6073	112	31	ztzttdx−	ztzttdx−	PROPN
ejpam-6073	112	32	a1	a1	PROPN
ejpam-6073	112	33	∫	∫	PROPN
ejpam-6073	112	34	ω	ω	PROPN
ejpam-6073	112	35	ztzxxdx−	ztzxxdx−	PROPN
ejpam-6073	112	36	a2	a2	PROPN
ejpam-6073	112	37	∫	∫	PROPN
ejpam-6073	113	1	ω	ω	PROPN
ejpam-6073	113	2	ztuxxdx+	ztuxxdx+	X
ejpam-6073	113	3	γ	γ	PROPN
ejpam-6073	113	4	∫	∫	PROPN
ejpam-6073	113	5	ω	ω	PROPN
ejpam-6073	113	6	zt|zt|p(·)−2ztdx	zt|zt|p(·)−2ztdx	PROPN
ejpam-6073	114	1	+	+	CCONJ
ejpam-6073	114	2	ρu	ρu	PROPN
ejpam-6073	114	3	∫	∫	PROPN
ejpam-6073	114	4	ω	ω	PROPN
ejpam-6073	114	5	ututtdx−	ututtdx−	PROPN
ejpam-6073	114	6	a3	a3	PROPN
ejpam-6073	114	7	∫	∫	PROPN
ejpam-6073	114	8	ω	ω	PROPN
ejpam-6073	114	9	utuxxdx−	utuxxdx−	PROPN
ejpam-6073	114	10	a2	a2	PROPN
ejpam-6073	114	11	∫	∫	PROPN
ejpam-6073	114	12	ω	ω	PROPN
ejpam-6073	115	1	utzxxdx+	utzxxdx+	NOUN
ejpam-6073	115	2	β	β	X
ejpam-6073	115	3	∫	∫	PROPN
ejpam-6073	115	4	ω	ω	NUM
ejpam-6073	115	5	ut|ut|q(·)−2utdx	ut|ut|q(·)−2utdx	PROPN
ejpam-6073	116	1	=	=	X
ejpam-6073	116	2	c	c	PROPN
ejpam-6073	116	3	∫	∫	PROPN
ejpam-6073	116	4	ω	ω	PROPN
ejpam-6073	116	5	zt|z|m(·)−2zdx+	zt|z|m(·)−2zdx+	PROPN
ejpam-6073	116	6	d	d	PROPN
ejpam-6073	116	7	∫	∫	PROPN
ejpam-6073	116	8	ω	ω	X
ejpam-6073	116	9	ut|u|ℓ(·)−2udx	ut|u|ℓ(·)−2udx	PROPN
ejpam-6073	116	10	.	.	PUNCT
ejpam-6073	117	1	(	(	PUNCT
ejpam-6073	117	2	12	12	NUM
ejpam-6073	117	3	)	)	PUNCT
ejpam-6073	117	4	using	use	VERB
ejpam-6073	117	5	the	the	DET
ejpam-6073	117	6	integration	integration	NOUN
ejpam-6073	117	7	by	by	ADP
ejpam-6073	117	8	parts	part	NOUN
ejpam-6073	117	9	and	and	CCONJ
ejpam-6073	117	10	the	the	DET
ejpam-6073	117	11	boundary	boundary	ADJ
ejpam-6073	117	12	conditions	condition	NOUN
ejpam-6073	117	13	and	and	CCONJ
ejpam-6073	117	14	summing	sum	VERB
ejpam-6073	117	15	up	up	ADP
ejpam-6073	117	16	all	all	DET
ejpam-6073	117	17	the	the	DET
ejpam-6073	117	18	results	result	NOUN
ejpam-6073	117	19	,	,	PUNCT
ejpam-6073	117	20	eq	eq	NOUN
ejpam-6073	117	21	.	.	PUNCT
ejpam-6073	118	1	(	(	PUNCT
ejpam-6073	118	2	12	12	NUM
ejpam-6073	118	3	)	)	PUNCT
ejpam-6073	118	4	becomes	become	VERB
ejpam-6073	118	5	ρz	ρz	NOUN
ejpam-6073	118	6	∫	∫	PROPN
ejpam-6073	118	7	ω	ω	PROPN
ejpam-6073	118	8	ztzttdx+	ztzttdx+	NUM
ejpam-6073	119	1	a1	a1	PROPN
ejpam-6073	119	2	∫	∫	PROPN
ejpam-6073	119	3	ω	ω	PROPN
ejpam-6073	119	4	zxzxtdx+	zxzxtdx+	PROPN
ejpam-6073	119	5	a2	a2	PROPN
ejpam-6073	119	6	∫	∫	PROPN
ejpam-6073	119	7	ω	ω	PROPN
ejpam-6073	119	8	zxtuxdx+	zxtuxdx+	X
ejpam-6073	119	9	γ	γ	PROPN
ejpam-6073	119	10	∫	∫	PROPN
ejpam-6073	119	11	ω	ω	PROPN
ejpam-6073	119	12	zt|zt|p(·)−2ztdx	zt|zt|p(·)−2ztdx	PROPN
ejpam-6073	119	13	ρu	ρu	INTJ
ejpam-6073	119	14	∫	∫	PROPN
ejpam-6073	119	15	ω	ω	PROPN
ejpam-6073	119	16	ututtdx+	ututtdx+	NOUN
ejpam-6073	119	17	a3	a3	NOUN
ejpam-6073	119	18	∫	∫	PROPN
ejpam-6073	119	19	ω	ω	PROPN
ejpam-6073	119	20	uxtuxdx+	uxtuxdx+	X
ejpam-6073	119	21	a2	a2	PROPN
ejpam-6073	119	22	∫	∫	PROPN
ejpam-6073	119	23	ω	ω	PROPN
ejpam-6073	120	1	uxtzxdx+	uxtzxdx+	X
ejpam-6073	120	2	β	β	X
ejpam-6073	120	3	∫	∫	PROPN
ejpam-6073	120	4	ω	ω	NUM
ejpam-6073	120	5	ut|ut|q(·)−2utdx	ut|ut|q(·)−2utdx	PROPN
ejpam-6073	121	1	=	=	X
ejpam-6073	121	2	c	c	PROPN
ejpam-6073	121	3	∫	∫	PROPN
ejpam-6073	121	4	ω	ω	PROPN
ejpam-6073	121	5	zt|z|m(·)−2zdx+	zt|z|m(·)−2zdx+	PROPN
ejpam-6073	121	6	d	d	PROPN
ejpam-6073	121	7	∫	∫	PROPN
ejpam-6073	121	8	ω	ω	X
ejpam-6073	121	9	ut|u|ℓ(·)−2udx	ut|u|ℓ(·)−2udx	PROPN
ejpam-6073	121	10	.	.	PUNCT
ejpam-6073	122	1	(	(	PUNCT
ejpam-6073	122	2	13	13	NUM
ejpam-6073	122	3	)	)	PUNCT
ejpam-6073	122	4	using	use	VERB
ejpam-6073	122	5	the	the	DET
ejpam-6073	122	6	following	follow	VERB
ejpam-6073	122	7	differential	differential	ADJ
ejpam-6073	122	8	equations	equation	NOUN
ejpam-6073	122	9	:	:	PUNCT
ejpam-6073	122	10	ρz	ρz	NOUN
ejpam-6073	122	11	∫	∫	PROPN
ejpam-6073	122	12	ω	ω	NUM
ejpam-6073	122	13	ztzttdx	ztzttdx	NOUN
ejpam-6073	122	14	=	=	SYM
ejpam-6073	123	1	ρz	ρz	NOUN
ejpam-6073	123	2	2	2	NUM
ejpam-6073	123	3	d	d	NOUN
ejpam-6073	123	4	dt	dt	X
ejpam-6073	123	5	∫	∫	PROPN
ejpam-6073	123	6	ω	ω	PROPN
ejpam-6073	123	7	z2	z2	PROPN
ejpam-6073	123	8	t	t	PROPN
ejpam-6073	123	9	dx	dx	PROPN
ejpam-6073	123	10	,	,	PUNCT
ejpam-6073	124	1	ρu	ρu	PROPN
ejpam-6073	124	2	∫	∫	PROPN
ejpam-6073	124	3	ω	ω	PROPN
ejpam-6073	124	4	ututtdx	ututtdx	PROPN
ejpam-6073	125	1	=	=	NOUN
ejpam-6073	125	2	ρu	ρu	ADP
ejpam-6073	125	3	2	2	NUM
ejpam-6073	125	4	d	d	NOUN
ejpam-6073	125	5	dt	dt	X
ejpam-6073	125	6	∫	∫	PROPN
ejpam-6073	125	7	ω	ω	PROPN
ejpam-6073	125	8	u2tdx	u2tdx	PROPN
ejpam-6073	125	9	,	,	PUNCT
ejpam-6073	125	10	a1	a1	PROPN
ejpam-6073	125	11	∫	∫	PROPN
ejpam-6073	125	12	ω	ω	PROPN
ejpam-6073	125	13	zxzxtdx	zxzxtdx	NOUN
ejpam-6073	125	14	=	=	SYM
ejpam-6073	125	15	a1	a1	NOUN
ejpam-6073	125	16	2	2	NUM
ejpam-6073	125	17	d	d	NOUN
ejpam-6073	125	18	dt	dt	X
ejpam-6073	125	19	∫	∫	PROPN
ejpam-6073	125	20	ω	ω	PROPN
ejpam-6073	125	21	z2xdx	z2xdx	PROPN
ejpam-6073	125	22	,	,	PUNCT
ejpam-6073	125	23	a3	a3	PROPN
ejpam-6073	125	24	∫	∫	PROPN
ejpam-6073	125	25	ω	ω	PROPN
ejpam-6073	125	26	uxuxtdx	uxuxtdx	PROPN
ejpam-6073	125	27	=	=	NOUN
ejpam-6073	125	28	a3	a3	NOUN
ejpam-6073	125	29	2	2	NUM
ejpam-6073	125	30	d	d	NOUN
ejpam-6073	125	31	dt	dt	X
ejpam-6073	125	32	∫	∫	PROPN
ejpam-6073	125	33	ω	ω	PROPN
ejpam-6073	125	34	u2xdx	u2xdx	PROPN
ejpam-6073	125	35	,	,	PUNCT
ejpam-6073	125	36	a2	a2	PROPN
ejpam-6073	125	37	∫	∫	PROPN
ejpam-6073	125	38	ω	ω	PROPN
ejpam-6073	125	39	(	(	PUNCT
ejpam-6073	125	40	zxtux	zxtux	PROPN
ejpam-6073	125	41	+	+	CCONJ
ejpam-6073	125	42	uxtzx	uxtzx	ADJ
ejpam-6073	125	43	)	)	PUNCT
ejpam-6073	125	44	dx	dx	PROPN
ejpam-6073	125	45	=	=	PROPN
ejpam-6073	125	46	a2	a2	PROPN
ejpam-6073	126	1	d	d	X
ejpam-6073	126	2	dt	dt	X
ejpam-6073	126	3	∫	∫	PROPN
ejpam-6073	126	4	ω	ω	PROPN
ejpam-6073	126	5	uxzxdx	uxzxdx	PROPN
ejpam-6073	126	6	,	,	PUNCT
ejpam-6073	126	7	c	c	PROPN
ejpam-6073	126	8	∫	∫	PROPN
ejpam-6073	126	9	ω	ω	X
ejpam-6073	126	10	zt|z|m(·)−2zdx	zt|z|m(·)−2zdx	PROPN
ejpam-6073	126	11	=	=	PUNCT
ejpam-6073	127	1	c	c	X
ejpam-6073	128	1	d	d	X
ejpam-6073	128	2	dt	dt	X
ejpam-6073	128	3	∫	∫	PROPN
ejpam-6073	128	4	ω	ω	PROPN
ejpam-6073	128	5	|z|m(x	|z|m(x	PROPN
ejpam-6073	128	6	)	)	PUNCT
ejpam-6073	128	7	m(x	m(x	PROPN
ejpam-6073	128	8	)	)	PUNCT
ejpam-6073	128	9	dx	dx	PROPN
ejpam-6073	128	10	,	,	PUNCT
ejpam-6073	128	11	and	and	CCONJ
ejpam-6073	128	12	d	d	ADP
ejpam-6073	128	13	∫	∫	PROPN
ejpam-6073	128	14	ω	ω	X
ejpam-6073	128	15	ut|u|ℓ(·)−2udx	ut|u|ℓ(·)−2udx	PROPN
ejpam-6073	128	16	=	=	PUNCT
ejpam-6073	128	17	d	d	SYM
ejpam-6073	128	18	d	d	X
ejpam-6073	128	19	dt	dt	X
ejpam-6073	128	20	∫	∫	PROPN
ejpam-6073	128	21	ω	ω	NUM
ejpam-6073	128	22	|u|ℓ(x	|u|ℓ(x	NUM
ejpam-6073	128	23	)	)	PUNCT
ejpam-6073	128	24	ℓ(x	ℓ(x	PROPN
ejpam-6073	128	25	)	)	PUNCT
ejpam-6073	128	26	dx	dx	PROPN
ejpam-6073	128	27	.	.	PUNCT
ejpam-6073	129	1	(	(	PUNCT
ejpam-6073	129	2	14	14	NUM
ejpam-6073	129	3	)	)	PUNCT
ejpam-6073	129	4	combing	combing	NOUN
ejpam-6073	129	5	(	(	PUNCT
ejpam-6073	129	6	14	14	NUM
ejpam-6073	129	7	)	)	PUNCT
ejpam-6073	129	8	and	and	CCONJ
ejpam-6073	129	9	(	(	PUNCT
ejpam-6073	129	10	13	13	NUM
ejpam-6073	129	11	)	)	PUNCT
ejpam-6073	129	12	,	,	PUNCT
ejpam-6073	129	13	we	we	PRON
ejpam-6073	129	14	obtain	obtain	VERB
ejpam-6073	129	15	a.	a.	NOUN
ejpam-6073	129	16	m.	m.	PROPN
ejpam-6073	129	17	al	al	PROPN
ejpam-6073	129	18	-	-	PROPN
ejpam-6073	129	19	mahdi	mahdi	PROPN
ejpam-6073	129	20	et	et	PROPN
ejpam-6073	129	21	al	al	PROPN
ejpam-6073	129	22	.	.	PUNCT
ejpam-6073	129	23	/	/	SYM
ejpam-6073	129	24	eur	eur	PROPN
ejpam-6073	129	25	.	.	PUNCT
ejpam-6073	130	1	j.	j.	PROPN
ejpam-6073	130	2	pure	pure	PROPN
ejpam-6073	130	3	appl	appl	PROPN
ejpam-6073	130	4	.	.	PROPN
ejpam-6073	130	5	math	math	PROPN
ejpam-6073	130	6	,	,	PUNCT
ejpam-6073	130	7	18	18	NUM
ejpam-6073	130	8	(	(	PUNCT
ejpam-6073	130	9	3	3	NUM
ejpam-6073	130	10	)	)	PUNCT
ejpam-6073	130	11	(	(	PUNCT
ejpam-6073	130	12	2025	2025	NUM
ejpam-6073	130	13	)	)	PUNCT
ejpam-6073	130	14	,	,	PUNCT
ejpam-6073	130	15	6073	6073	NUM
ejpam-6073	130	16	7	7	NUM
ejpam-6073	130	17	of	of	ADP
ejpam-6073	130	18	29	29	NUM
ejpam-6073	130	19	1	1	NUM
ejpam-6073	130	20	2	2	NUM
ejpam-6073	130	21	d	d	NOUN
ejpam-6073	130	22	dt	dt	X
ejpam-6073	130	23	∫	∫	PROPN
ejpam-6073	130	24	ω	ω	PROPN
ejpam-6073	130	25	[	[	PUNCT
ejpam-6073	130	26	ρzz	ρzz	NOUN
ejpam-6073	130	27	2	2	NUM
ejpam-6073	130	28	t	t	NOUN
ejpam-6073	130	29	+	+	CCONJ
ejpam-6073	130	30	ρuu	ρuu	PROPN
ejpam-6073	130	31	2	2	NUM
ejpam-6073	130	32	t	t	NOUN
ejpam-6073	130	33	+	+	CCONJ
ejpam-6073	130	34	a3u	a3u	ADP
ejpam-6073	130	35	2	2	NUM
ejpam-6073	130	36	x	x	SYM
ejpam-6073	130	37	+	+	CCONJ
ejpam-6073	130	38	a1z	a1z	PROPN
ejpam-6073	130	39	2	2	NUM
ejpam-6073	130	40	x	x	SYM
ejpam-6073	130	41	+	+	X
ejpam-6073	130	42	2a2zxux	2a2zxux	NUM
ejpam-6073	130	43	]	]	PUNCT
ejpam-6073	131	1	dx−	dx−	PUNCT
ejpam-6073	131	2	d	d	X
ejpam-6073	131	3	dt	dt	X
ejpam-6073	131	4	[	[	PUNCT
ejpam-6073	131	5	c	c	NOUN
ejpam-6073	131	6	∫	∫	PROPN
ejpam-6073	131	7	ω	ω	PROPN
ejpam-6073	131	8	|z|m(x	|z|m(x	PROPN
ejpam-6073	131	9	)	)	PUNCT
ejpam-6073	131	10	m(x	m(x	PROPN
ejpam-6073	131	11	)	)	PUNCT
ejpam-6073	131	12	dx−	dx−	X
ejpam-6073	132	1	d	d	X
ejpam-6073	132	2	∫	∫	PROPN
ejpam-6073	132	3	ω	ω	NUM
ejpam-6073	132	4	|u|ℓ(x	|u|ℓ(x	NUM
ejpam-6073	132	5	)	)	PUNCT
ejpam-6073	133	1	ℓ(x	ℓ(x	VERB
ejpam-6073	133	2	)	)	PUNCT
ejpam-6073	134	1	dx	dx	PROPN
ejpam-6073	134	2	]	]	PUNCT
ejpam-6073	135	1	=	=	PUNCT
ejpam-6073	135	2	−γ	−γ	ADJ
ejpam-6073	135	3	∫	∫	PROPN
ejpam-6073	135	4	ω	ω	NUM
ejpam-6073	135	5	|zt|p(·)dx−	|zt|p(·)dx−	PROPN
ejpam-6073	135	6	β	β	PROPN
ejpam-6073	135	7	∫	∫	PROPN
ejpam-6073	135	8	ω	ω	INTJ
ejpam-6073	136	1	|ut|q(·)dx	|ut|q(·)dx	PROPN
ejpam-6073	136	2	.	.	PUNCT
ejpam-6073	137	1	this	this	PRON
ejpam-6073	137	2	gives	give	VERB
ejpam-6073	137	3	d	d	PROPN
ejpam-6073	137	4	dt	dt	NOUN
ejpam-6073	137	5	e(t	e(t	PROPN
ejpam-6073	137	6	)	)	PUNCT
ejpam-6073	137	7	=	=	SYM
ejpam-6073	138	1	e′(t	e′(t	PROPN
ejpam-6073	138	2	)	)	PUNCT
ejpam-6073	138	3	=	=	PUNCT
ejpam-6073	139	1	−γ	−γ	ADJ
ejpam-6073	139	2	∫	∫	PROPN
ejpam-6073	139	3	ω	ω	NUM
ejpam-6073	139	4	|zt|p(·)dx−	|zt|p(·)dx−	PROPN
ejpam-6073	139	5	β	β	PROPN
ejpam-6073	139	6	∫	∫	PROPN
ejpam-6073	139	7	ω	ω	NUM
ejpam-6073	139	8	|ut|q(·)dx	|ut|q(·)dx	ADJ
ejpam-6073	139	9	≤	≤	NUM
ejpam-6073	139	10	0	0	NUM
ejpam-6073	139	11	,	,	PUNCT
ejpam-6073	139	12	where	where	SCONJ
ejpam-6073	139	13	e(t	e(t	NOUN
ejpam-6073	139	14	)	)	PUNCT
ejpam-6073	139	15	is	be	AUX
ejpam-6073	139	16	defined	define	VERB
ejpam-6073	139	17	in	in	ADP
ejpam-6073	139	18	(	(	PUNCT
ejpam-6073	139	19	10	10	NUM
ejpam-6073	139	20	)	)	PUNCT
ejpam-6073	139	21	and	and	CCONJ
ejpam-6073	139	22	this	this	PRON
ejpam-6073	139	23	completes	complete	VERB
ejpam-6073	139	24	the	the	DET
ejpam-6073	139	25	proof	proof	NOUN
ejpam-6073	139	26	of	of	ADP
ejpam-6073	139	27	(	(	PUNCT
ejpam-6073	139	28	11	11	NUM
ejpam-6073	139	29	)	)	PUNCT
ejpam-6073	139	30	.	.	PUNCT
ejpam-6073	140	1	lemma	lemma	PROPN
ejpam-6073	140	2	2	2	NUM
ejpam-6073	140	3	.	.	X
ejpam-6073	141	1	for	for	ADP
ejpam-6073	141	2	any	any	DET
ejpam-6073	141	3	z	z	NOUN
ejpam-6073	141	4	,	,	PUNCT
ejpam-6073	141	5	u	u	PROPN
ejpam-6073	141	6	∈	∈	PROPN
ejpam-6073	141	7	h1	h1	NOUN
ejpam-6073	141	8	0	0	NUM
ejpam-6073	141	9	(	(	PUNCT
ejpam-6073	141	10	ω	ω	NOUN
ejpam-6073	141	11	)	)	PUNCT
ejpam-6073	141	12	and	and	CCONJ
ejpam-6073	141	13	p	p	X
ejpam-6073	141	14	(	(	PUNCT
ejpam-6073	141	15	·	·	PUNCT
ejpam-6073	141	16	)	)	PUNCT
ejpam-6073	141	17	,	,	PUNCT
ejpam-6073	141	18	q	q	X
ejpam-6073	141	19	(	(	PUNCT
ejpam-6073	141	20	·	·	PUNCT
ejpam-6073	141	21	)	)	PUNCT
ejpam-6073	141	22	satisfying	satisfying	NOUN
ejpam-6073	141	23	(	(	PUNCT
ejpam-6073	141	24	a1	a1	NOUN
ejpam-6073	141	25	)	)	PUNCT
ejpam-6073	141	26	,	,	PUNCT
ejpam-6073	141	27	we	we	PRON
ejpam-6073	141	28	have∫	have∫	VERB
ejpam-6073	141	29	ω	ω	NUM
ejpam-6073	141	30	|z|p(x)dx	|z|p(x)dx	NOUN
ejpam-6073	141	31	≤	≤	NUM
ejpam-6073	141	32	cp1	cp1	NOUN
ejpam-6073	141	33	e	e	NOUN
ejpam-6073	141	34	||zx||p12	||zx||p12	NOUN
ejpam-6073	141	35	+	+	PROPN
ejpam-6073	141	36	cp2	cp2	PROPN
ejpam-6073	141	37	e	e	PROPN
ejpam-6073	141	38	||zx||p22∫	||zx||p22∫	PROPN
ejpam-6073	141	39	ω	ω	NUM
ejpam-6073	141	40	|u|q(x)dx	|u|q(x)dx	NOUN
ejpam-6073	141	41	≤	≤	ADJ
ejpam-6073	141	42	cq1	cq1	ADJ
ejpam-6073	141	43	e	e	NOUN
ejpam-6073	141	44	||ux||q12	||ux||q12	NOUN
ejpam-6073	141	45	+	+	CCONJ
ejpam-6073	141	46	cq2	cq2	NOUN
ejpam-6073	141	47	e	e	X
ejpam-6073	141	48	||ux||q22	||ux||q22	NOUN
ejpam-6073	141	49	,	,	PUNCT
ejpam-6073	141	50	(	(	PUNCT
ejpam-6073	141	51	15	15	NUM
ejpam-6073	141	52	)	)	PUNCT
ejpam-6073	141	53	where	where	SCONJ
ejpam-6073	141	54	ce	ce	PROPN
ejpam-6073	141	55	is	be	AUX
ejpam-6073	141	56	the	the	DET
ejpam-6073	141	57	embedding	embed	VERB
ejpam-6073	141	58	constant	constant	ADJ
ejpam-6073	141	59	.	.	PUNCT
ejpam-6073	142	1	proof	proof	NOUN
ejpam-6073	142	2	.	.	PUNCT
ejpam-6073	143	1	the	the	DET
ejpam-6073	143	2	proof	proof	NOUN
ejpam-6073	143	3	of	of	ADP
ejpam-6073	143	4	this	this	DET
ejpam-6073	143	5	lemma	lemma	PROPN
ejpam-6073	143	6	can	can	AUX
ejpam-6073	143	7	be	be	AUX
ejpam-6073	143	8	found	find	VERB
ejpam-6073	143	9	in	in	ADP
ejpam-6073	143	10	[	[	X
ejpam-6073	143	11	33	33	NUM
ejpam-6073	143	12	]	]	PUNCT
ejpam-6073	143	13	.	.	PUNCT
ejpam-6073	144	1	as	as	ADP
ejpam-6073	144	2	in	in	ADP
ejpam-6073	144	3	[	[	X
ejpam-6073	144	4	33	33	NUM
ejpam-6073	144	5	]	]	PUNCT
ejpam-6073	144	6	,	,	PUNCT
ejpam-6073	144	7	we	we	PRON
ejpam-6073	144	8	have	have	VERB
ejpam-6073	144	9	the	the	DET
ejpam-6073	144	10	following	follow	VERB
ejpam-6073	144	11	:	:	PUNCT
ejpam-6073	144	12	ϱ(z	ϱ(z	X
ejpam-6073	144	13	)	)	PUNCT
ejpam-6073	144	14	:	:	PUNCT
ejpam-6073	145	1	=	=	SYM
ejpam-6073	145	2	∫	∫	PROPN
ejpam-6073	145	3	ω	ω	PROPN
ejpam-6073	145	4	|z|m(x)dx	|z|m(x)dx	PROPN
ejpam-6073	145	5	≥	≥	NOUN
ejpam-6073	145	6	c||z||m1	c||z||m1	NOUN
ejpam-6073	145	7	m1	m1	PROPN
ejpam-6073	145	8	,	,	PUNCT
ejpam-6073	145	9	(	(	PUNCT
ejpam-6073	145	10	16	16	NUM
ejpam-6073	145	11	)	)	PUNCT
ejpam-6073	145	12	and	and	CCONJ
ejpam-6073	145	13	ϱ(u	ϱ(u	ADP
ejpam-6073	145	14	)	)	PUNCT
ejpam-6073	145	15	:	:	PUNCT
ejpam-6073	145	16	=	=	SYM
ejpam-6073	145	17	∫	∫	PROPN
ejpam-6073	145	18	ω	ω	PROPN
ejpam-6073	145	19	|u|ℓ(x)dx	|u|ℓ(x)dx	PROPN
ejpam-6073	145	20	≥	≥	NOUN
ejpam-6073	145	21	c||u||p1p1	c||u||p1p1	NOUN
ejpam-6073	145	22	.	.	PUNCT
ejpam-6073	146	1	(	(	PUNCT
ejpam-6073	146	2	17	17	NUM
ejpam-6073	146	3	)	)	PUNCT
ejpam-6073	146	4	lemma	lemma	PROPN
ejpam-6073	146	5	3	3	X
ejpam-6073	146	6	.	.	PUNCT
ejpam-6073	146	7	assume	assume	VERB
ejpam-6073	146	8	that	that	SCONJ
ejpam-6073	146	9	(	(	PUNCT
ejpam-6073	146	10	a1	a1	NOUN
ejpam-6073	146	11	)	)	PUNCT
ejpam-6073	146	12	holds	hold	NOUN
ejpam-6073	146	13	.	.	PUNCT
ejpam-6073	147	1	then	then	ADV
ejpam-6073	147	2	,	,	PUNCT
ejpam-6073	147	3	we	we	PRON
ejpam-6073	147	4	have∫	have∫	VERB
ejpam-6073	147	5	ω	ω	NUM
ejpam-6073	147	6	|z|p(x)dx	|z|p(x)dx	NOUN
ejpam-6073	147	7	≤	≤	NUM
ejpam-6073	147	8	c	c	NOUN
ejpam-6073	147	9	(	(	PUNCT
ejpam-6073	147	10	ϱ(z	ϱ(z	NOUN
ejpam-6073	147	11	)	)	PUNCT
ejpam-6073	147	12	p1	p1	NOUN
ejpam-6073	147	13	m1	m1	PROPN
ejpam-6073	147	14	+	+	CCONJ
ejpam-6073	147	15	ϱ(z	ϱ(z	PROPN
ejpam-6073	147	16	)	)	PUNCT
ejpam-6073	147	17	p2	p2	PROPN
ejpam-6073	147	18	m1	m1	PROPN
ejpam-6073	147	19	)	)	PUNCT
ejpam-6073	147	20	,	,	PUNCT
ejpam-6073	147	21	∫	∫	PROPN
ejpam-6073	147	22	ω	ω	NUM
ejpam-6073	147	23	|u|q(x)dx	|u|q(x)dx	PROPN
ejpam-6073	147	24	≤	≤	NOUN
ejpam-6073	147	25	c	c	NOUN
ejpam-6073	147	26	(	(	PUNCT
ejpam-6073	147	27	ϱ(u	ϱ(u	ADP
ejpam-6073	147	28	)	)	PUNCT
ejpam-6073	147	29	q1	q1	NOUN
ejpam-6073	147	30	ℓ1	ℓ1	NOUN
ejpam-6073	147	31	+	+	CCONJ
ejpam-6073	147	32	ϱ(u	ϱ(u	ADP
ejpam-6073	147	33	)	)	PUNCT
ejpam-6073	147	34	q2	q2	NOUN
ejpam-6073	147	35	ℓ1	ℓ1	NOUN
ejpam-6073	147	36	)	)	PUNCT
ejpam-6073	147	37	.	.	PUNCT
ejpam-6073	148	1	(	(	PUNCT
ejpam-6073	148	2	18	18	NUM
ejpam-6073	148	3	)	)	PUNCT
ejpam-6073	148	4	proof	proof	NOUN
ejpam-6073	148	5	.	.	PUNCT
ejpam-6073	149	1	the	the	DET
ejpam-6073	149	2	proof	proof	NOUN
ejpam-6073	149	3	of	of	ADP
ejpam-6073	149	4	this	this	DET
ejpam-6073	149	5	lemma	lemma	PROPN
ejpam-6073	149	6	can	can	AUX
ejpam-6073	149	7	be	be	AUX
ejpam-6073	149	8	found	find	VERB
ejpam-6073	149	9	in	in	ADP
ejpam-6073	149	10	[	[	X
ejpam-6073	149	11	33	33	NUM
ejpam-6073	149	12	]	]	PUNCT
ejpam-6073	149	13	.	.	PUNCT
ejpam-6073	150	1	a.	a.	PROPN
ejpam-6073	150	2	m.	m.	PROPN
ejpam-6073	150	3	al	al	PROPN
ejpam-6073	150	4	-	-	PROPN
ejpam-6073	150	5	mahdi	mahdi	PROPN
ejpam-6073	150	6	et	et	PROPN
ejpam-6073	150	7	al	al	PROPN
ejpam-6073	150	8	.	.	PUNCT
ejpam-6073	150	9	/	/	SYM
ejpam-6073	150	10	eur	eur	PROPN
ejpam-6073	150	11	.	.	PUNCT
ejpam-6073	151	1	j.	j.	PROPN
ejpam-6073	151	2	pure	pure	PROPN
ejpam-6073	151	3	appl	appl	PROPN
ejpam-6073	151	4	.	.	PROPN
ejpam-6073	151	5	math	math	PROPN
ejpam-6073	151	6	,	,	PUNCT
ejpam-6073	151	7	18	18	NUM
ejpam-6073	151	8	(	(	PUNCT
ejpam-6073	151	9	3	3	NUM
ejpam-6073	151	10	)	)	PUNCT
ejpam-6073	151	11	(	(	PUNCT
ejpam-6073	151	12	2025	2025	NUM
ejpam-6073	151	13	)	)	PUNCT
ejpam-6073	151	14	,	,	PUNCT
ejpam-6073	151	15	6073	6073	NUM
ejpam-6073	151	16	8	8	NUM
ejpam-6073	151	17	of	of	ADP
ejpam-6073	151	18	29	29	NUM
ejpam-6073	151	19	4	4	NUM
ejpam-6073	151	20	.	.	PUNCT
ejpam-6073	151	21	local	local	ADJ
ejpam-6073	151	22	existence	existence	NOUN
ejpam-6073	151	23	in	in	ADP
ejpam-6073	151	24	this	this	DET
ejpam-6073	151	25	section	section	NOUN
ejpam-6073	151	26	,	,	PUNCT
ejpam-6073	151	27	we	we	PRON
ejpam-6073	151	28	give	give	VERB
ejpam-6073	151	29	a	a	DET
ejpam-6073	151	30	detailed	detailed	ADJ
ejpam-6073	151	31	proof	proof	NOUN
ejpam-6073	151	32	of	of	ADP
ejpam-6073	151	33	the	the	DET
ejpam-6073	151	34	local	local	ADJ
ejpam-6073	151	35	existence	existence	NOUN
ejpam-6073	151	36	theorem	theorem	VERB
ejpam-6073	151	37	by	by	ADP
ejpam-6073	151	38	using	use	VERB
ejpam-6073	151	39	the	the	DET
ejpam-6073	151	40	faedogalerkin	faedogalerkin	NOUN
ejpam-6073	151	41	approximations	approximation	NOUN
ejpam-6073	151	42	and	and	CCONJ
ejpam-6073	151	43	the	the	DET
ejpam-6073	151	44	banach	banach	ADV
ejpam-6073	151	45	-	-	PUNCT
ejpam-6073	151	46	fixed	fix	VERB
ejpam-6073	151	47	-	-	PUNCT
ejpam-6073	151	48	point	point	NOUN
ejpam-6073	151	49	theorem	theorem	NOUN
ejpam-6073	151	50	.	.	PUNCT
ejpam-6073	152	1	we	we	PRON
ejpam-6073	152	2	multiply	multiply	VERB
ejpam-6073	152	3	the	the	DET
ejpam-6073	152	4	first	first	ADJ
ejpam-6073	152	5	equation	equation	NOUN
ejpam-6073	152	6	in	in	ADP
ejpam-6073	152	7	(	(	PUNCT
ejpam-6073	152	8	6	6	NUM
ejpam-6073	152	9	)	)	PUNCT
ejpam-6073	152	10	by	by	ADP
ejpam-6073	152	11	ϕ	ϕ	PROPN
ejpam-6073	152	12	∈	∈	PROPN
ejpam-6073	152	13	c∞	c∞	PROPN
ejpam-6073	152	14	0	0	NUM
ejpam-6073	152	15	(	(	PUNCT
ejpam-6073	152	16	ω	ω	NOUN
ejpam-6073	152	17	)	)	PUNCT
ejpam-6073	152	18	and	and	CCONJ
ejpam-6073	152	19	the	the	DET
ejpam-6073	152	20	second	second	ADJ
ejpam-6073	152	21	equation	equation	NOUN
ejpam-6073	152	22	by	by	ADP
ejpam-6073	152	23	ψ	ψ	X
ejpam-6073	152	24	∈	∈	PROPN
ejpam-6073	152	25	c∞	c∞	PROPN
ejpam-6073	152	26	0	0	NUM
ejpam-6073	152	27	(	(	PUNCT
ejpam-6073	152	28	ω	ω	NOUN
ejpam-6073	152	29	)	)	PUNCT
ejpam-6073	152	30	,	,	PUNCT
ejpam-6073	152	31	integrate	integrate	VERB
ejpam-6073	152	32	each	each	DET
ejpam-6073	152	33	result	result	NOUN
ejpam-6073	152	34	over	over	ADP
ejpam-6073	152	35	ω	ω	PROPN
ejpam-6073	152	36	,	,	PUNCT
ejpam-6073	152	37	use	use	VERB
ejpam-6073	152	38	green	green	PROPN
ejpam-6073	152	39	’s	’s	PART
ejpam-6073	152	40	formula	formula	NOUN
ejpam-6073	152	41	and	and	CCONJ
ejpam-6073	152	42	the	the	DET
ejpam-6073	152	43	boundary	boundary	ADJ
ejpam-6073	152	44	conditions	condition	NOUN
ejpam-6073	152	45	to	to	PART
ejpam-6073	152	46	obtain	obtain	VERB
ejpam-6073	152	47	the	the	DET
ejpam-6073	152	48	following	follow	VERB
ejpam-6073	152	49	definition	definition	NOUN
ejpam-6073	152	50	:	:	PUNCT
ejpam-6073	152	51	definition	definition	NOUN
ejpam-6073	152	52	1	1	NUM
ejpam-6073	152	53	.	.	PUNCT
ejpam-6073	153	1	let	let	VERB
ejpam-6073	153	2	t	t	PROPN
ejpam-6073	153	3	>	>	X
ejpam-6073	153	4	0	0	X
ejpam-6073	153	5	.	.	PUNCT
ejpam-6073	154	1	any	any	DET
ejpam-6073	154	2	pair	pair	NOUN
ejpam-6073	154	3	of	of	ADP
ejpam-6073	154	4	functions	function	NOUN
ejpam-6073	154	5	z	z	PROPN
ejpam-6073	154	6	,	,	PUNCT
ejpam-6073	154	7	u	u	PROPN
ejpam-6073	154	8	∈	∈	PROPN
ejpam-6073	154	9	l∞([0	l∞([0	PROPN
ejpam-6073	154	10	,	,	PUNCT
ejpam-6073	154	11	t	t	PROPN
ejpam-6073	154	12	)	)	PUNCT
ejpam-6073	154	13	,	,	PUNCT
ejpam-6073	154	14	h1	h1	PROPN
ejpam-6073	154	15	0	0	NUM
ejpam-6073	154	16	(	(	PUNCT
ejpam-6073	154	17	ω	ω	NOUN
ejpam-6073	154	18	)	)	PUNCT
ejpam-6073	154	19	)	)	PUNCT
ejpam-6073	154	20	,	,	PUNCT
ejpam-6073	154	21	zt	zt	PROPN
ejpam-6073	154	22	∈	∈	PROPN
ejpam-6073	154	23	l∞([0	l∞([0	PROPN
ejpam-6073	154	24	,	,	PUNCT
ejpam-6073	154	25	t	t	PROPN
ejpam-6073	154	26	)	)	PUNCT
ejpam-6073	154	27	,	,	PUNCT
ejpam-6073	154	28	l2(ω	l2(ω	NOUN
ejpam-6073	154	29	)	)	PUNCT
ejpam-6073	154	30	)	)	PUNCT
ejpam-6073	155	1	∩	∩	NOUN
ejpam-6073	155	2	lp(ω×	lp(ω×	PROPN
ejpam-6073	155	3	(	(	PUNCT
ejpam-6073	155	4	0	0	NUM
ejpam-6073	155	5	,	,	PUNCT
ejpam-6073	155	6	t	t	NOUN
ejpam-6073	155	7	)	)	PUNCT
ejpam-6073	155	8	)	)	PUNCT
ejpam-6073	155	9	and	and	CCONJ
ejpam-6073	155	10	ut	ut	PROPN
ejpam-6073	155	11	∈	∈	PROPN
ejpam-6073	155	12	l∞([0	l∞([0	PROPN
ejpam-6073	155	13	,	,	PUNCT
ejpam-6073	155	14	t	t	PROPN
ejpam-6073	155	15	)	)	PUNCT
ejpam-6073	155	16	,	,	PUNCT
ejpam-6073	155	17	l2(ω	l2(ω	NOUN
ejpam-6073	155	18	)	)	PUNCT
ejpam-6073	155	19	)	)	PUNCT
ejpam-6073	155	20	∩	∩	ADJ
ejpam-6073	155	21	lq(ω×	lq(ω×	NOUN
ejpam-6073	155	22	(	(	PUNCT
ejpam-6073	155	23	0	0	NUM
ejpam-6073	155	24	,	,	PUNCT
ejpam-6073	155	25	t	t	NOUN
ejpam-6073	155	26	)	)	PUNCT
ejpam-6073	155	27	)	)	PUNCT
ejpam-6073	155	28	is	be	AUX
ejpam-6073	155	29	called	call	VERB
ejpam-6073	155	30	a	a	DET
ejpam-6073	155	31	weak	weak	ADJ
ejpam-6073	155	32	solution	solution	NOUN
ejpam-6073	155	33	of	of	ADP
ejpam-6073	155	34	system	system	NOUN
ejpam-6073	155	35	(	(	PUNCT
ejpam-6073	155	36	6	6	NUM
ejpam-6073	155	37	)	)	PUNCT
ejpam-6073	155	38	,	,	PUNCT
ejpam-6073	155	39	if	if	PROPN
ejpam-6073	156	1	d	d	NOUN
ejpam-6073	156	2	dt	dt	X
ejpam-6073	156	3	∫	∫	PROPN
ejpam-6073	156	4	ω	ω	PROPN
ejpam-6073	156	5	ρzztϕ(x)dx+	ρzztϕ(x)dx+	NUM
ejpam-6073	156	6	a1	a1	NOUN
ejpam-6073	156	7	∫	∫	PROPN
ejpam-6073	156	8	ω	ω	PROPN
ejpam-6073	156	9	zxϕx(x)dx+	zxϕx(x)dx+	PROPN
ejpam-6073	156	10	a2	a2	PROPN
ejpam-6073	156	11	∫	∫	PROPN
ejpam-6073	156	12	ω	ω	PROPN
ejpam-6073	156	13	uxϕx(x)dx	uxϕx(x)dx	PROPN
ejpam-6073	156	14	+	+	PROPN
ejpam-6073	156	15	γ	γ	PROPN
ejpam-6073	156	16	∫	∫	PROPN
ejpam-6073	156	17	ω	ω	PROPN
ejpam-6073	156	18	|zt|p(.)−2ztϕ(x)dx	|zt|p(.)−2ztϕ(x)dx	VERB
ejpam-6073	156	19	=	=	PUNCT
ejpam-6073	156	20	c	c	PROPN
ejpam-6073	156	21	∫	∫	PROPN
ejpam-6073	156	22	ω	ω	PROPN
ejpam-6073	156	23	|z|m(.)−2zϕ(x)dx	|z|m(.)−2zϕ(x)dx	PROPN
ejpam-6073	156	24	d	d	X
ejpam-6073	156	25	dt	dt	X
ejpam-6073	156	26	∫	∫	PROPN
ejpam-6073	156	27	ω	ω	PROPN
ejpam-6073	156	28	ρuutψ(x)dx+	ρuutψ(x)dx+	PROPN
ejpam-6073	156	29	a3	a3	PROPN
ejpam-6073	156	30	∫	∫	PROPN
ejpam-6073	156	31	ω	ω	PROPN
ejpam-6073	157	1	uxψx(x)dx+	uxψx(x)dx+	PROPN
ejpam-6073	157	2	a2	a2	PROPN
ejpam-6073	157	3	∫	∫	PROPN
ejpam-6073	157	4	ω	ω	PROPN
ejpam-6073	157	5	zxψx(x)dx	zxψx(x)dx	NUM
ejpam-6073	157	6	+	+	NOUN
ejpam-6073	157	7	β	β	PROPN
ejpam-6073	157	8	∫	∫	PROPN
ejpam-6073	157	9	ω	ω	NUM
ejpam-6073	157	10	|ut|q(.)−2utψ(x)dx	|ut|q(.)−2utψ(x)dx	NOUN
ejpam-6073	157	11	=	=	PUNCT
ejpam-6073	158	1	d	d	X
ejpam-6073	158	2	∫	∫	PROPN
ejpam-6073	158	3	ω	ω	PROPN
ejpam-6073	158	4	|u|ℓ(.)−2uψ(x)dx	|u|ℓ(.)−2uψ(x)dx	X
ejpam-6073	158	5	z(0	z(0	NOUN
ejpam-6073	158	6	)	)	PUNCT
ejpam-6073	158	7	=	=	SYM
ejpam-6073	158	8	z0	z0	PROPN
ejpam-6073	158	9	,	,	PUNCT
ejpam-6073	158	10	zt(0	zt(0	PROPN
ejpam-6073	158	11	)	)	PUNCT
ejpam-6073	158	12	=	=	SYM
ejpam-6073	158	13	z1	z1	PROPN
ejpam-6073	158	14	,	,	PUNCT
ejpam-6073	158	15	u(0	u(0	NOUN
ejpam-6073	158	16	)	)	PUNCT
ejpam-6073	158	17	=	=	PUNCT
ejpam-6073	159	1	u0	u0	PROPN
ejpam-6073	159	2	,	,	PUNCT
ejpam-6073	159	3	ut(0	ut(0	PROPN
ejpam-6073	159	4	)	)	PUNCT
ejpam-6073	159	5	=	=	SYM
ejpam-6073	159	6	u1	u1	NOUN
ejpam-6073	159	7	,	,	PUNCT
ejpam-6073	159	8	(	(	PUNCT
ejpam-6073	159	9	19	19	NUM
ejpam-6073	159	10	)	)	PUNCT
ejpam-6073	159	11	for	for	ADP
ejpam-6073	159	12	a.e	a.e	PROPN
ejpam-6073	159	13	.	.	PROPN
ejpam-6073	159	14	t	t	PROPN
ejpam-6073	159	15	∈	∈	PROPN
ejpam-6073	160	1	[	[	X
ejpam-6073	160	2	0	0	NUM
ejpam-6073	160	3	,	,	PUNCT
ejpam-6073	160	4	t	t	NOUN
ejpam-6073	160	5	]	]	PUNCT
ejpam-6073	160	6	and	and	CCONJ
ejpam-6073	160	7	all	all	DET
ejpam-6073	160	8	test	test	NOUN
ejpam-6073	160	9	functions	function	NOUN
ejpam-6073	160	10	ϕ	ϕ	PROPN
ejpam-6073	160	11	,	,	PUNCT
ejpam-6073	160	12	ψ	ψ	X
ejpam-6073	160	13	∈	∈	PROPN
ejpam-6073	160	14	h1	h1	NOUN
ejpam-6073	160	15	0	0	NUM
ejpam-6073	160	16	(	(	PUNCT
ejpam-6073	160	17	ω	ω	NOUN
ejpam-6073	160	18	)	)	PUNCT
ejpam-6073	160	19	.	.	PUNCT
ejpam-6073	161	1	note	note	VERB
ejpam-6073	161	2	that	that	SCONJ
ejpam-6073	161	3	c∞	c∞	PROPN
ejpam-6073	161	4	0	0	NUM
ejpam-6073	161	5	(	(	PUNCT
ejpam-6073	161	6	ω	ω	NOUN
ejpam-6073	161	7	)	)	PUNCT
ejpam-6073	161	8	is	be	AUX
ejpam-6073	161	9	dense	dense	ADJ
ejpam-6073	161	10	in	in	ADP
ejpam-6073	161	11	h1	h1	PROPN
ejpam-6073	161	12	0	0	NUM
ejpam-6073	161	13	(	(	PUNCT
ejpam-6073	161	14	ω	ω	NOUN
ejpam-6073	161	15	)	)	PUNCT
ejpam-6073	161	16	.	.	PUNCT
ejpam-6073	162	1	in	in	ADP
ejpam-6073	162	2	addition	addition	NOUN
ejpam-6073	162	3	,	,	PUNCT
ejpam-6073	162	4	the	the	DET
ejpam-6073	162	5	spaces	space	NOUN
ejpam-6073	162	6	h1	h1	VERB
ejpam-6073	162	7	0	0	PROPN
ejpam-6073	162	8	(	(	PUNCT
ejpam-6073	162	9	ω	ω	NOUN
ejpam-6073	162	10	)	)	PUNCT
ejpam-6073	162	11	⊂	⊂	PROPN
ejpam-6073	162	12	lp(.)(ω	lp(.)(ω	PROPN
ejpam-6073	162	13	)	)	PUNCT
ejpam-6073	162	14	∩	∩	PROPN
ejpam-6073	162	15	lq(.)(ω	lq(.)(ω	PROPN
ejpam-6073	162	16	)	)	PUNCT
ejpam-6073	162	17	,	,	PUNCT
ejpam-6073	162	18	under	under	ADP
ejpam-6073	162	19	the	the	DET
ejpam-6073	162	20	conditions	condition	NOUN
ejpam-6073	162	21	(	(	PUNCT
ejpam-6073	162	22	a1	a1	NOUN
ejpam-6073	162	23	)	)	PUNCT
ejpam-6073	162	24	and	and	CCONJ
ejpam-6073	162	25	(	(	PUNCT
ejpam-6073	162	26	a2	a2	PROPN
ejpam-6073	162	27	)	)	PUNCT
ejpam-6073	162	28	.	.	PUNCT
ejpam-6073	163	1	before	before	ADP
ejpam-6073	163	2	establishing	establish	VERB
ejpam-6073	163	3	the	the	DET
ejpam-6073	163	4	existence	existence	NOUN
ejpam-6073	163	5	theorem	theorem	NOUN
ejpam-6073	163	6	of	of	ADP
ejpam-6073	163	7	a	a	DET
ejpam-6073	163	8	local	local	ADJ
ejpam-6073	163	9	weak	weak	ADJ
ejpam-6073	163	10	solution	solution	NOUN
ejpam-6073	163	11	of	of	ADP
ejpam-6073	163	12	problem	problem	NOUN
ejpam-6073	163	13	(	(	PUNCT
ejpam-6073	163	14	6	6	NUM
ejpam-6073	163	15	)	)	PUNCT
ejpam-6073	163	16	,	,	PUNCT
ejpam-6073	163	17	we	we	PRON
ejpam-6073	163	18	first	first	ADV
ejpam-6073	163	19	consider	consider	VERB
ejpam-6073	163	20	,	,	PUNCT
ejpam-6073	163	21	the	the	DET
ejpam-6073	163	22	following	follow	VERB
ejpam-6073	163	23	initial	initial	ADJ
ejpam-6073	163	24	-	-	PUNCT
ejpam-6073	163	25	boundary	boundary	ADJ
ejpam-6073	163	26	-	-	PUNCT
ejpam-6073	163	27	value	value	NOUN
ejpam-6073	163	28	problem:	problem:	NOUN
ejpam-6073	163	29	ρzztt	ρzztt	NOUN
ejpam-6073	163	30	−	−	PROPN
ejpam-6073	164	1	a1zxx	a1zxx	PROPN
ejpam-6073	164	2	−	−	PROPN
ejpam-6073	164	3	a2uxx	a2uxx	PROPN
ejpam-6073	164	4	+	+	CCONJ
ejpam-6073	164	5	γ|zt|p(·)−2zt	γ|zt|p(·)−2zt	PROPN
ejpam-6073	164	6	=	=	SYM
ejpam-6073	164	7	f(x	f(x	PROPN
ejpam-6073	164	8	,	,	PUNCT
ejpam-6073	164	9	t	t	PROPN
ejpam-6073	164	10	)	)	PUNCT
ejpam-6073	164	11	,	,	PUNCT
ejpam-6073	164	12	in	in	ADP
ejpam-6073	164	13	ω×	ω×	PROPN
ejpam-6073	164	14	(	(	PUNCT
ejpam-6073	164	15	0,∞	0,∞	NUM
ejpam-6073	164	16	)	)	PUNCT
ejpam-6073	164	17	,	,	PUNCT
ejpam-6073	164	18	ρuutt	ρuutt	VERB
ejpam-6073	164	19	−	−	NOUN
ejpam-6073	164	20	a3uxx	a3uxx	NUM
ejpam-6073	164	21	−	−	PROPN
ejpam-6073	165	1	a2zxx	a2zxx	NOUN
ejpam-6073	166	1	+	+	NUM
ejpam-6073	166	2	β|ut|q(·)−2ut	β|ut|q(·)−2ut	NOUN
ejpam-6073	166	3	=	=	SYM
ejpam-6073	166	4	g(x	g(x	PROPN
ejpam-6073	166	5	,	,	PUNCT
ejpam-6073	166	6	t	t	PROPN
ejpam-6073	166	7	)	)	PUNCT
ejpam-6073	166	8	,	,	PUNCT
ejpam-6073	166	9	in	in	ADP
ejpam-6073	166	10	ω×	ω×	PROPN
ejpam-6073	166	11	(	(	PUNCT
ejpam-6073	166	12	0,∞	0,∞	NUM
ejpam-6073	166	13	)	)	PUNCT
ejpam-6073	166	14	,	,	PUNCT
ejpam-6073	166	15	z(0	z(0	PROPN
ejpam-6073	166	16	,	,	PUNCT
ejpam-6073	166	17	t	t	PROPN
ejpam-6073	166	18	)	)	PUNCT
ejpam-6073	166	19	=	=	SYM
ejpam-6073	167	1	z(1	z(1	PROPN
ejpam-6073	167	2	,	,	PUNCT
ejpam-6073	167	3	t	t	PROPN
ejpam-6073	167	4	)	)	PUNCT
ejpam-6073	167	5	=	=	SYM
ejpam-6073	168	1	u(0	u(0	PROPN
ejpam-6073	168	2	,	,	PUNCT
ejpam-6073	168	3	t	t	PROPN
ejpam-6073	168	4	)	)	PUNCT
ejpam-6073	168	5	=	=	SYM
ejpam-6073	169	1	u(1	u(1	PROPN
ejpam-6073	169	2	,	,	PUNCT
ejpam-6073	169	3	t	t	PROPN
ejpam-6073	169	4	)	)	PUNCT
ejpam-6073	169	5	=	=	SYM
ejpam-6073	169	6	0	0	NUM
ejpam-6073	169	7	t	t	PROPN
ejpam-6073	169	8	≥	≥	NOUN
ejpam-6073	169	9	0	0	NUM
ejpam-6073	169	10	,	,	PUNCT
ejpam-6073	169	11	(	(	PUNCT
ejpam-6073	169	12	z(0	z(0	CCONJ
ejpam-6073	169	13	)	)	PUNCT
ejpam-6073	169	14	,	,	PUNCT
ejpam-6073	169	15	u(0	u(0	NOUN
ejpam-6073	169	16	)	)	PUNCT
ejpam-6073	169	17	)	)	PUNCT
ejpam-6073	170	1	=	=	PRON
ejpam-6073	170	2	(	(	PUNCT
ejpam-6073	170	3	z0	z0	PROPN
ejpam-6073	170	4	,	,	PUNCT
ejpam-6073	170	5	u0	u0	ADJ
ejpam-6073	170	6	)	)	PUNCT
ejpam-6073	170	7	,	,	PUNCT
ejpam-6073	170	8	(	(	PUNCT
ejpam-6073	170	9	zt(0	zt(0	NOUN
ejpam-6073	170	10	)	)	PUNCT
ejpam-6073	170	11	,	,	PUNCT
ejpam-6073	170	12	ut(0	ut(0	PROPN
ejpam-6073	170	13	)	)	PUNCT
ejpam-6073	170	14	)	)	PUNCT
ejpam-6073	170	15	=	=	SYM
ejpam-6073	170	16	(	(	PUNCT
ejpam-6073	170	17	z1	z1	NOUN
ejpam-6073	170	18	,	,	PUNCT
ejpam-6073	170	19	u1	u1	NOUN
ejpam-6073	170	20	)	)	PUNCT
ejpam-6073	170	21	,	,	PUNCT
ejpam-6073	170	22	in	in	ADP
ejpam-6073	170	23	ω	ω	NUM
ejpam-6073	170	24	,	,	PUNCT
ejpam-6073	170	25	(	(	PUNCT
ejpam-6073	170	26	q	q	X
ejpam-6073	170	27	)	)	PUNCT
ejpam-6073	170	28	where	where	SCONJ
ejpam-6073	170	29	f	f	X
ejpam-6073	170	30	,	,	PUNCT
ejpam-6073	170	31	g	g	PROPN
ejpam-6073	170	32	∈	∈	PROPN
ejpam-6073	170	33	l2	l2	NOUN
ejpam-6073	170	34	(	(	PUNCT
ejpam-6073	170	35	ω×	ω×	X
ejpam-6073	170	36	(	(	PUNCT
ejpam-6073	170	37	0	0	NUM
ejpam-6073	170	38	,	,	PUNCT
ejpam-6073	170	39	t	t	NOUN
ejpam-6073	170	40	)	)	PUNCT
ejpam-6073	170	41	)	)	PUNCT
ejpam-6073	170	42	and	and	CCONJ
ejpam-6073	170	43	(	(	PUNCT
ejpam-6073	170	44	u0	u0	ADJ
ejpam-6073	170	45	,	,	PUNCT
ejpam-6073	170	46	u1	u1	NOUN
ejpam-6073	170	47	)	)	PUNCT
ejpam-6073	170	48	,	,	PUNCT
ejpam-6073	170	49	(	(	PUNCT
ejpam-6073	170	50	v0	v0	NOUN
ejpam-6073	170	51	,	,	PUNCT
ejpam-6073	170	52	v1	v1	NOUN
ejpam-6073	170	53	)	)	PUNCT
ejpam-6073	170	54	∈	∈	PROPN
ejpam-6073	170	55	h1	h1	NOUN
ejpam-6073	170	56	0	0	NUM
ejpam-6073	170	57	(	(	PUNCT
ejpam-6073	170	58	ω)×	ω)×	PROPN
ejpam-6073	170	59	l2(ω	l2(ω	NUM
ejpam-6073	170	60	)	)	PUNCT
ejpam-6073	170	61	.	.	PUNCT
ejpam-6073	171	1	theorem	theorem	NOUN
ejpam-6073	171	2	1	1	NUM
ejpam-6073	171	3	.	.	PUNCT
ejpam-6073	171	4	assume	assume	VERB
ejpam-6073	171	5	that	that	SCONJ
ejpam-6073	171	6	(	(	PUNCT
ejpam-6073	171	7	a1	a1	NOUN
ejpam-6073	171	8	)	)	PUNCT
ejpam-6073	171	9	and	and	CCONJ
ejpam-6073	171	10	(	(	PUNCT
ejpam-6073	171	11	a2	a2	NOUN
ejpam-6073	171	12	)	)	PUNCT
ejpam-6073	171	13	hold	hold	VERB
ejpam-6073	171	14	and	and	CCONJ
ejpam-6073	171	15	let	let	VERB
ejpam-6073	171	16	(	(	PUNCT
ejpam-6073	171	17	u0	u0	ADJ
ejpam-6073	171	18	,	,	PUNCT
ejpam-6073	171	19	u1	u1	NOUN
ejpam-6073	171	20	)	)	PUNCT
ejpam-6073	171	21	,	,	PUNCT
ejpam-6073	171	22	(	(	PUNCT
ejpam-6073	171	23	v0	v0	NOUN
ejpam-6073	171	24	,	,	PUNCT
ejpam-6073	171	25	v1	v1	NOUN
ejpam-6073	171	26	)	)	PUNCT
ejpam-6073	171	27	∈	∈	PROPN
ejpam-6073	171	28	h1	h1	NOUN
ejpam-6073	171	29	0	0	NUM
ejpam-6073	171	30	(	(	PUNCT
ejpam-6073	171	31	ω)×l2(ω	ω)×l2(ω	NUM
ejpam-6073	171	32	)	)	PUNCT
ejpam-6073	171	33	,	,	PUNCT
ejpam-6073	171	34	then	then	ADV
ejpam-6073	171	35	problem	problem	NOUN
ejpam-6073	171	36	(	(	PUNCT
ejpam-6073	171	37	q	q	X
ejpam-6073	171	38	)	)	PUNCT
ejpam-6073	171	39	has	have	VERB
ejpam-6073	171	40	a	a	DET
ejpam-6073	171	41	unique	unique	ADJ
ejpam-6073	171	42	local	local	ADJ
ejpam-6073	171	43	weak	weak	ADJ
ejpam-6073	171	44	solution	solution	NOUN
ejpam-6073	171	45	(	(	PUNCT
ejpam-6073	171	46	u	u	NOUN
ejpam-6073	171	47	,	,	PUNCT
ejpam-6073	171	48	v	v	NOUN
ejpam-6073	171	49	)	)	PUNCT
ejpam-6073	171	50	on	on	ADP
ejpam-6073	171	51	[	[	X
ejpam-6073	171	52	0	0	NUM
ejpam-6073	171	53	,	,	PUNCT
ejpam-6073	171	54	t	t	NOUN
ejpam-6073	171	55	)	)	PUNCT
ejpam-6073	171	56	.	.	PUNCT
ejpam-6073	172	1	proof	proof	NOUN
ejpam-6073	172	2	.	.	PUNCT
ejpam-6073	173	1	uniqueness	uniqueness	NOUN
ejpam-6073	173	2	:	:	PUNCT
ejpam-6073	173	3	suppose	suppose	VERB
ejpam-6073	173	4	that	that	SCONJ
ejpam-6073	173	5	(	(	PUNCT
ejpam-6073	173	6	q	q	X
ejpam-6073	173	7	)	)	PUNCT
ejpam-6073	173	8	has	have	VERB
ejpam-6073	173	9	two	two	NUM
ejpam-6073	173	10	solutions	solution	NOUN
ejpam-6073	173	11	(	(	PUNCT
ejpam-6073	173	12	z1	z1	NOUN
ejpam-6073	173	13	,	,	PUNCT
ejpam-6073	173	14	u1	u1	NOUN
ejpam-6073	173	15	)	)	PUNCT
ejpam-6073	173	16	and	and	CCONJ
ejpam-6073	173	17	(	(	PUNCT
ejpam-6073	173	18	z2	z2	PROPN
ejpam-6073	173	19	,	,	PUNCT
ejpam-6073	173	20	u2	u2	PROPN
ejpam-6073	173	21	)	)	PUNCT
ejpam-6073	173	22	.	.	PUNCT
ejpam-6073	174	1	then	then	ADV
ejpam-6073	174	2	,	,	PUNCT
ejpam-6073	174	3	(	(	PUNCT
ejpam-6073	174	4	z	z	X
ejpam-6073	174	5	,	,	PUNCT
ejpam-6073	174	6	u	u	NOUN
ejpam-6073	174	7	)	)	PUNCT
ejpam-6073	174	8	=	=	SYM
ejpam-6073	174	9	(	(	PUNCT
ejpam-6073	174	10	z1−z2	z1−z2	NOUN
ejpam-6073	174	11	,	,	PUNCT
ejpam-6073	174	12	u1−u2	u1−u2	ADJ
ejpam-6073	174	13	)	)	PUNCT
ejpam-6073	174	14	satisfies	satisfie	NOUN
ejpam-6073	174	15	,	,	PUNCT
ejpam-6073	174	16	in	in	ADP
ejpam-6073	174	17	the	the	DET
ejpam-6073	174	18	sense	sense	NOUN
ejpam-6073	174	19	of	of	ADP
ejpam-6073	174	20	distribution	distribution	NOUN
ejpam-6073	174	21	,	,	PUNCT
ejpam-6073	174	22	the	the	DET
ejpam-6073	174	23	following	follow	VERB
ejpam-6073	174	24	problem:	problem:	PROPN
ejpam-6073	174	25	ρzztt	ρzztt	NOUN
ejpam-6073	174	26	−	−	PROPN
ejpam-6073	174	27	a1zxx	a1zxx	NOUN
ejpam-6073	174	28	−	−	PROPN
ejpam-6073	174	29	a2uxx	a2uxx	NOUN
ejpam-6073	174	30	+	+	CCONJ
ejpam-6073	174	31	γ	γ	PROPN
ejpam-6073	174	32	|z1t|p(x)−2	|z1t|p(x)−2	PROPN
ejpam-6073	174	33	z1	z1	PROPN
ejpam-6073	174	34	t	t	PROPN
ejpam-6073	174	35	−	−	NOUN
ejpam-6073	174	36	γ	γ	X
ejpam-6073	174	37	|z2t|p(x)−2	|z2t|p(x)−2	VERB
ejpam-6073	174	38	z2	z2	PROPN
ejpam-6073	174	39	t	t	NOUN
ejpam-6073	174	40	=	=	SYM
ejpam-6073	174	41	0	0	NUM
ejpam-6073	174	42	,	,	PUNCT
ejpam-6073	174	43	in	in	ADP
ejpam-6073	174	44	ω×	ω×	PROPN
ejpam-6073	174	45	(	(	PUNCT
ejpam-6073	174	46	0,∞	0,∞	NUM
ejpam-6073	174	47	)	)	PUNCT
ejpam-6073	174	48	,	,	PUNCT
ejpam-6073	174	49	ρuutt	ρuutt	VERB
ejpam-6073	174	50	−	−	NOUN
ejpam-6073	174	51	a3uxx	a3uxx	NUM
ejpam-6073	174	52	−	−	PROPN
ejpam-6073	175	1	a2zxx	a2zxx	NOUN
ejpam-6073	176	1	+	+	CCONJ
ejpam-6073	176	2	β	β	X
ejpam-6073	176	3	|u1t|q(x)−2	|u1t|q(x)−2	NOUN
ejpam-6073	176	4	u1	u1	NOUN
ejpam-6073	176	5	t	t	NOUN
ejpam-6073	176	6	−	−	NOUN
ejpam-6073	176	7	β	β	X
ejpam-6073	176	8	|u2t|q(x)−2	|u2t|q(x)−2	PROPN
ejpam-6073	176	9	u2	u2	PROPN
ejpam-6073	176	10	t	t	PROPN
ejpam-6073	176	11	=	=	SYM
ejpam-6073	176	12	0	0	NUM
ejpam-6073	176	13	,	,	PUNCT
ejpam-6073	176	14	in	in	ADP
ejpam-6073	176	15	ω×	ω×	PROPN
ejpam-6073	176	16	(	(	PUNCT
ejpam-6073	176	17	0,∞	0,∞	NUM
ejpam-6073	176	18	)	)	PUNCT
ejpam-6073	176	19	,	,	PUNCT
ejpam-6073	176	20	z(0	z(0	PROPN
ejpam-6073	176	21	,	,	PUNCT
ejpam-6073	176	22	t	t	PROPN
ejpam-6073	176	23	)	)	PUNCT
ejpam-6073	176	24	=	=	SYM
ejpam-6073	177	1	z(1	z(1	PROPN
ejpam-6073	177	2	,	,	PUNCT
ejpam-6073	177	3	t	t	PROPN
ejpam-6073	177	4	)	)	PUNCT
ejpam-6073	177	5	=	=	SYM
ejpam-6073	178	1	u(0	u(0	PROPN
ejpam-6073	178	2	,	,	PUNCT
ejpam-6073	178	3	t	t	PROPN
ejpam-6073	178	4	)	)	PUNCT
ejpam-6073	178	5	=	=	SYM
ejpam-6073	179	1	u(1	u(1	PROPN
ejpam-6073	179	2	,	,	PUNCT
ejpam-6073	179	3	t	t	PROPN
ejpam-6073	179	4	)	)	PUNCT
ejpam-6073	179	5	=	=	SYM
ejpam-6073	179	6	0	0	NUM
ejpam-6073	179	7	t	t	PROPN
ejpam-6073	179	8	≥	≥	NOUN
ejpam-6073	179	9	0	0	NUM
ejpam-6073	179	10	,	,	PUNCT
ejpam-6073	179	11	(	(	PUNCT
ejpam-6073	179	12	z(0	z(0	CCONJ
ejpam-6073	179	13	)	)	PUNCT
ejpam-6073	179	14	,	,	PUNCT
ejpam-6073	179	15	u(0	u(0	NOUN
ejpam-6073	179	16	)	)	PUNCT
ejpam-6073	179	17	)	)	PUNCT
ejpam-6073	180	1	=	=	PRON
ejpam-6073	180	2	(	(	PUNCT
ejpam-6073	180	3	z0	z0	PROPN
ejpam-6073	180	4	,	,	PUNCT
ejpam-6073	180	5	u0	u0	ADJ
ejpam-6073	180	6	)	)	PUNCT
ejpam-6073	180	7	,	,	PUNCT
ejpam-6073	180	8	(	(	PUNCT
ejpam-6073	180	9	zt(0	zt(0	NOUN
ejpam-6073	180	10	)	)	PUNCT
ejpam-6073	180	11	,	,	PUNCT
ejpam-6073	180	12	ut(0	ut(0	PROPN
ejpam-6073	180	13	)	)	PUNCT
ejpam-6073	180	14	)	)	PUNCT
ejpam-6073	180	15	=	=	SYM
ejpam-6073	180	16	(	(	PUNCT
ejpam-6073	180	17	z1	z1	NOUN
ejpam-6073	180	18	,	,	PUNCT
ejpam-6073	180	19	u1	u1	NOUN
ejpam-6073	180	20	)	)	PUNCT
ejpam-6073	180	21	,	,	PUNCT
ejpam-6073	180	22	in	in	ADP
ejpam-6073	180	23	ω	ω	PROPN
ejpam-6073	180	24	.	.	PUNCT
ejpam-6073	180	25	a.	a.	PROPN
ejpam-6073	180	26	m.	m.	PROPN
ejpam-6073	180	27	al	al	PROPN
ejpam-6073	180	28	-	-	PROPN
ejpam-6073	180	29	mahdi	mahdi	PROPN
ejpam-6073	180	30	et	et	PROPN
ejpam-6073	180	31	al	al	PROPN
ejpam-6073	180	32	.	.	PUNCT
ejpam-6073	180	33	/	/	SYM
ejpam-6073	180	34	eur	eur	PROPN
ejpam-6073	180	35	.	.	PUNCT
ejpam-6073	181	1	j.	j.	PROPN
ejpam-6073	181	2	pure	pure	PROPN
ejpam-6073	181	3	appl	appl	PROPN
ejpam-6073	181	4	.	.	PROPN
ejpam-6073	181	5	math	math	PROPN
ejpam-6073	181	6	,	,	PUNCT
ejpam-6073	181	7	18	18	NUM
ejpam-6073	181	8	(	(	PUNCT
ejpam-6073	181	9	3	3	NUM
ejpam-6073	181	10	)	)	PUNCT
ejpam-6073	181	11	(	(	PUNCT
ejpam-6073	181	12	2025	2025	NUM
ejpam-6073	181	13	)	)	PUNCT
ejpam-6073	181	14	,	,	PUNCT
ejpam-6073	181	15	6073	6073	NUM
ejpam-6073	181	16	9	9	NUM
ejpam-6073	181	17	of	of	ADP
ejpam-6073	181	18	29	29	NUM
ejpam-6073	181	19	multiplying	multiply	VERB
ejpam-6073	181	20	the	the	DET
ejpam-6073	181	21	first	first	ADJ
ejpam-6073	181	22	differential	differential	ADJ
ejpam-6073	181	23	equation	equation	NOUN
ejpam-6073	181	24	by	by	ADP
ejpam-6073	181	25	zt	zt	PROPN
ejpam-6073	181	26	and	and	CCONJ
ejpam-6073	181	27	the	the	DET
ejpam-6073	181	28	second	second	ADJ
ejpam-6073	181	29	by	by	ADP
ejpam-6073	181	30	ut	ut	PROPN
ejpam-6073	181	31	and	and	CCONJ
ejpam-6073	181	32	then	then	ADV
ejpam-6073	181	33	integrating	integrate	VERB
ejpam-6073	181	34	the	the	DET
ejpam-6073	181	35	result	result	NOUN
ejpam-6073	181	36	over	over	ADP
ejpam-6073	181	37	ω	ω	PROPN
ejpam-6073	181	38	,	,	PUNCT
ejpam-6073	181	39	we	we	PRON
ejpam-6073	181	40	obtain	obtain	VERB
ejpam-6073	181	41	d	d	X
ejpam-6073	181	42	dt	dt	X
ejpam-6073	182	1	[	[	PUNCT
ejpam-6073	182	2	ρz	ρz	NOUN
ejpam-6073	182	3	2	2	NUM
ejpam-6073	182	4	||zt||22	||zt||22	NOUN
ejpam-6073	182	5	+	+	CCONJ
ejpam-6073	182	6	ρu	ρu	PROPN
ejpam-6073	182	7	2	2	NUM
ejpam-6073	182	8	||ut||22	||ut||22	NOUN
ejpam-6073	182	9	+	+	CCONJ
ejpam-6073	182	10	a1	a1	NOUN
ejpam-6073	182	11	2	2	NUM
ejpam-6073	182	12	||zx||22	||zx||22	NOUN
ejpam-6073	182	13	+	+	NOUN
ejpam-6073	182	14	a3	a3	NOUN
ejpam-6073	182	15	2	2	NUM
ejpam-6073	182	16	||ux||22	||ux||22	NOUN
ejpam-6073	182	17	+	+	CCONJ
ejpam-6073	182	18	a2	a2	PROPN
ejpam-6073	182	19	∫	∫	PROPN
ejpam-6073	182	20	ω	ω	PROPN
ejpam-6073	182	21	uxzxdx	uxzxdx	PROPN
ejpam-6073	182	22	]	]	X
ejpam-6073	182	23	+	+	CCONJ
ejpam-6073	182	24	γ	γ	PROPN
ejpam-6073	182	25	∫	∫	PROPN
ejpam-6073	182	26	ω	ω	PROPN
ejpam-6073	182	27	(	(	PUNCT
ejpam-6073	182	28	|z1t|p(x)−2	|z1t|p(x)−2	PROPN
ejpam-6073	182	29	z1	z1	PROPN
ejpam-6073	182	30	t	t	PROPN
ejpam-6073	182	31	−	−	NOUN
ejpam-6073	182	32	|z2t|p(x)−2	|z2t|p(x)−2	VERB
ejpam-6073	182	33	z2	z2	PROPN
ejpam-6073	182	34	t	t	PROPN
ejpam-6073	182	35	)	)	PUNCT
ejpam-6073	182	36	(	(	PUNCT
ejpam-6073	182	37	z1	z1	NOUN
ejpam-6073	182	38	t	t	NOUN
ejpam-6073	182	39	−	−	PROPN
ejpam-6073	182	40	z2t)dx	z2t)dx	NOUN
ejpam-6073	182	41	+	+	CCONJ
ejpam-6073	182	42	β	β	X
ejpam-6073	182	43	∫	∫	PROPN
ejpam-6073	182	44	ω	ω	PROPN
ejpam-6073	182	45	(	(	PUNCT
ejpam-6073	182	46	|u1t|q(x)−2	|u1t|q(x)−2	INTJ
ejpam-6073	182	47	u1	u1	NOUN
ejpam-6073	182	48	t	t	NOUN
ejpam-6073	182	49	−	−	PROPN
ejpam-6073	182	50	|u2t|q(x)−2	|u2t|q(x)−2	PROPN
ejpam-6073	182	51	u2	u2	PROPN
ejpam-6073	182	52	t	t	PROPN
ejpam-6073	182	53	)	)	PUNCT
ejpam-6073	182	54	(	(	PUNCT
ejpam-6073	182	55	u1	u1	PROPN
ejpam-6073	182	56	t	t	PROPN
ejpam-6073	182	57	−	−	PROPN
ejpam-6073	182	58	u2t)dx	u2t)dx	VERB
ejpam-6073	182	59	=	=	NOUN
ejpam-6073	182	60	0	0	NUM
ejpam-6073	182	61	.	.	PUNCT
ejpam-6073	183	1	(	(	PUNCT
ejpam-6073	183	2	20	20	NUM
ejpam-6073	183	3	)	)	PUNCT
ejpam-6073	183	4	integrating	integrating	NOUN
ejpam-6073	183	5	(	(	PUNCT
ejpam-6073	183	6	20	20	NUM
ejpam-6073	183	7	)	)	PUNCT
ejpam-6073	183	8	over	over	ADP
ejpam-6073	183	9	(	(	PUNCT
ejpam-6073	183	10	0	0	NUM
ejpam-6073	183	11	,	,	PUNCT
ejpam-6073	183	12	t	t	PROPN
ejpam-6073	183	13	)	)	PUNCT
ejpam-6073	183	14	,	,	PUNCT
ejpam-6073	183	15	to	to	PART
ejpam-6073	183	16	get	get	VERB
ejpam-6073	183	17	ρz	ρz	NOUN
ejpam-6073	183	18	2	2	NUM
ejpam-6073	183	19	||zt||22	||zt||22	NOUN
ejpam-6073	184	1	+	+	CCONJ
ejpam-6073	184	2	ρu	ρu	PROPN
ejpam-6073	184	3	2	2	NUM
ejpam-6073	184	4	||ut||22	||ut||22	NOUN
ejpam-6073	184	5	+	+	CCONJ
ejpam-6073	184	6	a1	a1	NOUN
ejpam-6073	184	7	2	2	NUM
ejpam-6073	184	8	||zx||22	||zx||22	NOUN
ejpam-6073	184	9	+	+	NOUN
ejpam-6073	184	10	a3	a3	NOUN
ejpam-6073	184	11	2	2	NUM
ejpam-6073	184	12	||ux||22	||ux||22	NOUN
ejpam-6073	184	13	+	+	CCONJ
ejpam-6073	185	1	a2	a2	PROPN
ejpam-6073	185	2	∫	∫	PROPN
ejpam-6073	185	3	ω	ω	PROPN
ejpam-6073	185	4	uxzxdx	uxzxdx	NOUN
ejpam-6073	185	5	+	+	CCONJ
ejpam-6073	185	6	γ	γ	PROPN
ejpam-6073	185	7	∫	∫	PROPN
ejpam-6073	185	8	t	t	PROPN
ejpam-6073	185	9	0	0	NUM
ejpam-6073	185	10	∫	∫	PROPN
ejpam-6073	185	11	ω	ω	PROPN
ejpam-6073	185	12	(	(	PUNCT
ejpam-6073	185	13	|z1t|p(x)−2	|z1t|p(x)−2	PROPN
ejpam-6073	185	14	z1	z1	PROPN
ejpam-6073	185	15	t	t	PROPN
ejpam-6073	185	16	−	−	NOUN
ejpam-6073	185	17	|z2t|p(x)−2	|z2t|p(x)−2	VERB
ejpam-6073	185	18	z2	z2	PROPN
ejpam-6073	185	19	t	t	PROPN
ejpam-6073	185	20	)	)	PUNCT
ejpam-6073	185	21	(	(	PUNCT
ejpam-6073	185	22	z1	z1	PROPN
ejpam-6073	185	23	t	t	PROPN
ejpam-6073	185	24	−	−	PROPN
ejpam-6073	185	25	z2t)dxds	z2t)dxds	NOUN
ejpam-6073	185	26	+	+	CCONJ
ejpam-6073	185	27	β	β	X
ejpam-6073	185	28	∫	∫	PROPN
ejpam-6073	186	1	t	t	PROPN
ejpam-6073	186	2	0	0	NUM
ejpam-6073	186	3	∫	∫	PROPN
ejpam-6073	187	1	ω	ω	PROPN
ejpam-6073	187	2	(	(	PUNCT
ejpam-6073	187	3	|u1t|q(x)−2	|u1t|q(x)−2	INTJ
ejpam-6073	187	4	u1	u1	NOUN
ejpam-6073	187	5	t	t	NOUN
ejpam-6073	187	6	−	−	PROPN
ejpam-6073	187	7	|u2t|q(x)−2	|u2t|q(x)−2	PROPN
ejpam-6073	187	8	u2	u2	PROPN
ejpam-6073	187	9	t	t	PROPN
ejpam-6073	187	10	)	)	PUNCT
ejpam-6073	187	11	(	(	PUNCT
ejpam-6073	187	12	u1	u1	NOUN
ejpam-6073	187	13	t	t	PROPN
ejpam-6073	187	14	−	−	NUM
ejpam-6073	187	15	u2t)dxds	u2t)dxds	PROPN
ejpam-6073	187	16	=	=	NOUN
ejpam-6073	187	17	0	0	NUM
ejpam-6073	187	18	.	.	PUNCT
ejpam-6073	187	19	(	(	PUNCT
ejpam-6073	187	20	21	21	NUM
ejpam-6073	187	21	)	)	PUNCT
ejpam-6073	187	22	by	by	ADP
ejpam-6073	187	23	using	use	VERB
ejpam-6073	187	24	the	the	DET
ejpam-6073	187	25	following	follow	VERB
ejpam-6073	187	26	inequality	inequality	NOUN
ejpam-6073	187	27	[	[	PUNCT
ejpam-6073	187	28	|y	|y	NOUN
ejpam-6073	187	29	|b(x)−2y	|b(x)−2y	DET
ejpam-6073	187	30	−	−	NOUN
ejpam-6073	187	31	|z|b(x)−2z	|z|b(x)−2z	X
ejpam-6073	187	32	]	]	PUNCT
ejpam-6073	188	1	(	(	PUNCT
ejpam-6073	188	2	y	y	PROPN
ejpam-6073	188	3	−	−	PROPN
ejpam-6073	188	4	z	z	PROPN
ejpam-6073	188	5	)	)	PUNCT
ejpam-6073	188	6	≥	≥	NOUN
ejpam-6073	188	7	0	0	NUM
ejpam-6073	188	8	,	,	PUNCT
ejpam-6073	188	9	b(x	b(x	NOUN
ejpam-6073	188	10	)	)	PUNCT
ejpam-6073	188	11	≥	≥	NOUN
ejpam-6073	188	12	2	2	NUM
ejpam-6073	188	13	,	,	PUNCT
ejpam-6073	188	14	(	(	PUNCT
ejpam-6073	188	15	22	22	NUM
ejpam-6073	188	16	)	)	PUNCT
ejpam-6073	188	17	for	for	ADP
ejpam-6073	188	18	all	all	DET
ejpam-6073	188	19	x	x	SYM
ejpam-6073	188	20	∈	∈	PROPN
ejpam-6073	188	21	ω	ω	PROPN
ejpam-6073	188	22	and	and	CCONJ
ejpam-6073	188	23	y	y	PROPN
ejpam-6073	188	24	,	,	PUNCT
ejpam-6073	188	25	z	z	NOUN
ejpam-6073	188	26	∈	∈	PROPN
ejpam-6073	188	27	r	r	NOUN
ejpam-6073	188	28	,	,	PUNCT
ejpam-6073	188	29	we	we	PRON
ejpam-6073	188	30	have	have	VERB
ejpam-6073	188	31	ρz	ρz	NUM
ejpam-6073	188	32	2	2	NUM
ejpam-6073	188	33	||zt||22	||zt||22	NOUN
ejpam-6073	188	34	+	+	CCONJ
ejpam-6073	188	35	ρu	ρu	PROPN
ejpam-6073	188	36	2	2	NUM
ejpam-6073	188	37	||ut||22	||ut||22	NOUN
ejpam-6073	188	38	+	+	CCONJ
ejpam-6073	188	39	a1	a1	NOUN
ejpam-6073	188	40	2	2	NUM
ejpam-6073	188	41	||zx||22	||zx||22	NOUN
ejpam-6073	188	42	+	+	NOUN
ejpam-6073	188	43	a3	a3	NOUN
ejpam-6073	188	44	2	2	NUM
ejpam-6073	188	45	||ux||22	||ux||22	NOUN
ejpam-6073	188	46	+	+	CCONJ
ejpam-6073	189	1	a2	a2	PROPN
ejpam-6073	189	2	∫	∫	PROPN
ejpam-6073	189	3	ω	ω	PROPN
ejpam-6073	189	4	uxzxdx	uxzxdx	PROPN
ejpam-6073	189	5	≤	≤	NOUN
ejpam-6073	189	6	0	0	NUM
ejpam-6073	189	7	.	.	PUNCT
ejpam-6073	190	1	(	(	PUNCT
ejpam-6073	190	2	23	23	NUM
ejpam-6073	190	3	)	)	PUNCT
ejpam-6073	190	4	applying	apply	VERB
ejpam-6073	190	5	the	the	DET
ejpam-6073	190	6	following	follow	VERB
ejpam-6073	190	7	cauchy	cauchy	PROPN
ejpam-6073	190	8	-	-	PUNCT
ejpam-6073	190	9	schwarz	schwarz	NOUN
ejpam-6073	190	10	’	'	PUNCT
ejpam-6073	190	11	inequality	inequality	NOUN
ejpam-6073	190	12	:	:	PUNCT
ejpam-6073	191	1	|	|	ADV
ejpam-6073	191	2	⟨v1	⟨v1	PROPN
ejpam-6073	191	3	,	,	PUNCT
ejpam-6073	191	4	v2⟩	v2⟩	X
ejpam-6073	191	5	|	|	ADV
ejpam-6073	191	6	≤	≤	NOUN
ejpam-6073	191	7	∥v1∥∥v2∥	∥v1∥∥v2∥	PROPN
ejpam-6073	191	8	,	,	PUNCT
ejpam-6073	191	9	∀v1	∀v1	PROPN
ejpam-6073	191	10	,	,	PUNCT
ejpam-6073	191	11	v2	v2	PROPN
ejpam-6073	191	12	∈	∈	PROPN
ejpam-6073	191	13	l2(0	l2(0	NOUN
ejpam-6073	191	14	,	,	PUNCT
ejpam-6073	191	15	1	1	NUM
ejpam-6073	191	16	)	)	PUNCT
ejpam-6073	191	17	,	,	PUNCT
ejpam-6073	191	18	(	(	PUNCT
ejpam-6073	191	19	24	24	NUM
ejpam-6073	191	20	)	)	PUNCT
ejpam-6073	191	21	and	and	CCONJ
ejpam-6073	191	22	the	the	DET
ejpam-6073	191	23	following	follow	VERB
ejpam-6073	191	24	young	young	ADJ
ejpam-6073	191	25	inequality	inequality	NOUN
ejpam-6073	191	26	:	:	PUNCT
ejpam-6073	191	27	|ab|	|ab|	VERB
ejpam-6073	191	28	≤	≤	NUM
ejpam-6073	191	29	1	1	NUM
ejpam-6073	191	30	2	2	NUM
ejpam-6073	191	31	(	(	PUNCT
ejpam-6073	191	32	ϵa2	ϵa2	NOUN
ejpam-6073	192	1	+	+	CCONJ
ejpam-6073	192	2	1	1	NUM
ejpam-6073	192	3	ϵ	ϵ	NOUN
ejpam-6073	192	4	b2	b2	NOUN
ejpam-6073	192	5	)	)	PUNCT
ejpam-6073	192	6	,	,	PUNCT
ejpam-6073	192	7	∀a	∀a	X
ejpam-6073	192	8	,	,	PUNCT
ejpam-6073	192	9	b	b	X
ejpam-6073	192	10	∈	∈	PROPN
ejpam-6073	192	11	r	r	NOUN
ejpam-6073	192	12	,	,	PUNCT
ejpam-6073	192	13	∀ϵ	∀ϵ	NOUN
ejpam-6073	192	14	>	>	X
ejpam-6073	192	15	0	0	NUM
ejpam-6073	192	16	,	,	PUNCT
ejpam-6073	192	17	(	(	PUNCT
ejpam-6073	192	18	25	25	NUM
ejpam-6073	192	19	)	)	PUNCT
ejpam-6073	192	20	we	we	PRON
ejpam-6073	192	21	see	see	VERB
ejpam-6073	192	22	that	that	SCONJ
ejpam-6073	192	23	,	,	PUNCT
ejpam-6073	192	24	for	for	ADP
ejpam-6073	192	25	any	any	PRON
ejpam-6073	192	26	ϵ	ϵ	PROPN
ejpam-6073	192	27	>	>	X
ejpam-6073	192	28	0	0	PROPN
ejpam-6073	192	29	,	,	PUNCT
ejpam-6073	192	30	a3	a3	VERB
ejpam-6073	192	31	∥ux∥2	∥ux∥2	PUNCT
ejpam-6073	193	1	+	+	CCONJ
ejpam-6073	193	2	a1	a1	VERB
ejpam-6073	193	3	∥zx∥2	∥zx∥2	NOUN
ejpam-6073	193	4	+	+	CCONJ
ejpam-6073	193	5	2a2	2a2	NUM
ejpam-6073	193	6	∫	∫	PROPN
ejpam-6073	193	7	ω	ω	PROPN
ejpam-6073	193	8	uxzxdx	uxzxdx	PROPN
ejpam-6073	193	9	≥	≥	PROPN
ejpam-6073	193	10	(	(	PUNCT
ejpam-6073	193	11	a3	a3	NOUN
ejpam-6073	193	12	−	−	PROPN
ejpam-6073	193	13	|a2|	|a2|	NOUN
ejpam-6073	193	14	ϵ	ϵ	X
ejpam-6073	193	15	)	)	PUNCT
ejpam-6073	193	16	∥ux∥2	∥ux∥2	PUNCT
ejpam-6073	194	1	+	+	CCONJ
ejpam-6073	194	2	(	(	PUNCT
ejpam-6073	194	3	a1	a1	NOUN
ejpam-6073	194	4	−	−	PROPN
ejpam-6073	194	5	|a2|ϵ	|a2|ϵ	PROPN
ejpam-6073	194	6	)	)	PUNCT
ejpam-6073	194	7	∥zx∥2	∥zx∥2	NOUN
ejpam-6073	194	8	,	,	PUNCT
ejpam-6073	194	9	by	by	ADP
ejpam-6073	194	10	choosing	choose	VERB
ejpam-6073	194	11	ϵ	ϵ	X
ejpam-6073	194	12	=	=	SYM
ejpam-6073	194	13	1	1	NUM
ejpam-6073	194	14	2|a0|	2|a0|	NUM
ejpam-6073	194	15	(	(	PUNCT
ejpam-6073	194	16	a2	a2	NOUN
ejpam-6073	194	17	−	−	PROPN
ejpam-6073	194	18	a1	a1	NOUN
ejpam-6073	194	19	+	+	CCONJ
ejpam-6073	194	20	√	√	PROPN
ejpam-6073	194	21	(	(	PUNCT
ejpam-6073	194	22	a1	a1	NOUN
ejpam-6073	194	23	−	−	PROPN
ejpam-6073	194	24	a3)2	a3)2	PROPN
ejpam-6073	194	25	+	+	NUM
ejpam-6073	194	26	4a22	4a22	NUM
ejpam-6073	194	27	)	)	PUNCT
ejpam-6073	194	28	(	(	PUNCT
ejpam-6073	194	29	ϵ	ϵ	X
ejpam-6073	194	30	is	be	AUX
ejpam-6073	194	31	well	well	ADV
ejpam-6073	194	32	defined	define	VERB
ejpam-6073	194	33	and	and	CCONJ
ejpam-6073	194	34	positive	positive	ADJ
ejpam-6073	194	35	,	,	PUNCT
ejpam-6073	194	36	since	since	SCONJ
ejpam-6073	194	37	a2	a2	PROPN
ejpam-6073	194	38	̸=	̸=	PROPN
ejpam-6073	194	39	0	0	NUM
ejpam-6073	194	40	)	)	PUNCT
ejpam-6073	194	41	,	,	PUNCT
ejpam-6073	194	42	we	we	PRON
ejpam-6073	194	43	obtain	obtain	VERB
ejpam-6073	194	44	a3	a3	NOUN
ejpam-6073	194	45	∥ux∥2	∥ux∥2	PUNCT
ejpam-6073	195	1	+	+	CCONJ
ejpam-6073	195	2	a1	a1	VERB
ejpam-6073	195	3	∥zx∥2	∥zx∥2	NOUN
ejpam-6073	195	4	+	+	CCONJ
ejpam-6073	195	5	2a2	2a2	NUM
ejpam-6073	195	6	∫	∫	PROPN
ejpam-6073	195	7	ω	ω	PROPN
ejpam-6073	195	8	uxzxdx	uxzxdx	PROPN
ejpam-6073	195	9	≥	≥	NOUN
ejpam-6073	195	10	c̃	c̃	PROPN
ejpam-6073	195	11	(	(	PUNCT
ejpam-6073	195	12	∥ux∥2	∥ux∥2	NUM
ejpam-6073	195	13	+	+	NUM
ejpam-6073	195	14	∥zx∥2	∥zx∥2	PRON
ejpam-6073	195	15	)	)	PUNCT
ejpam-6073	195	16	,	,	PUNCT
ejpam-6073	195	17	(	(	PUNCT
ejpam-6073	195	18	26	26	NUM
ejpam-6073	195	19	)	)	PUNCT
ejpam-6073	195	20	a.	a.	NOUN
ejpam-6073	195	21	m.	m.	PROPN
ejpam-6073	195	22	al	al	PROPN
ejpam-6073	195	23	-	-	PROPN
ejpam-6073	195	24	mahdi	mahdi	PROPN
ejpam-6073	195	25	et	et	PROPN
ejpam-6073	195	26	al	al	PROPN
ejpam-6073	195	27	.	.	PUNCT
ejpam-6073	195	28	/	/	SYM
ejpam-6073	195	29	eur	eur	PROPN
ejpam-6073	195	30	.	.	PUNCT
ejpam-6073	196	1	j.	j.	PROPN
ejpam-6073	196	2	pure	pure	PROPN
ejpam-6073	196	3	appl	appl	PROPN
ejpam-6073	196	4	.	.	PROPN
ejpam-6073	196	5	math	math	PROPN
ejpam-6073	196	6	,	,	PUNCT
ejpam-6073	196	7	18	18	NUM
ejpam-6073	196	8	(	(	PUNCT
ejpam-6073	196	9	3	3	NUM
ejpam-6073	196	10	)	)	PUNCT
ejpam-6073	196	11	(	(	PUNCT
ejpam-6073	196	12	2025	2025	NUM
ejpam-6073	196	13	)	)	PUNCT
ejpam-6073	196	14	,	,	PUNCT
ejpam-6073	196	15	6073	6073	NUM
ejpam-6073	196	16	10	10	NUM
ejpam-6073	196	17	of	of	ADP
ejpam-6073	196	18	29	29	NUM
ejpam-6073	197	1	where	where	SCONJ
ejpam-6073	197	2	c̃	c̃	PROPN
ejpam-6073	197	3	:	:	PUNCT
ejpam-6073	197	4	=	=	SYM
ejpam-6073	197	5	1	1	NUM
ejpam-6073	197	6	2	2	NUM
ejpam-6073	197	7	(	(	PUNCT
ejpam-6073	197	8	a1	a1	NOUN
ejpam-6073	197	9	+	+	CCONJ
ejpam-6073	197	10	a3	a3	NOUN
ejpam-6073	197	11	−	−	NOUN
ejpam-6073	197	12	√	√	NUM
ejpam-6073	197	13	(	(	PUNCT
ejpam-6073	197	14	a1	a1	NOUN
ejpam-6073	197	15	−	−	PROPN
ejpam-6073	197	16	a3)2	a3)2	PROPN
ejpam-6073	197	17	+	+	NUM
ejpam-6073	197	18	4a22	4a22	NUM
ejpam-6073	197	19	)	)	PUNCT
ejpam-6073	197	20	.	.	PUNCT
ejpam-6073	198	1	combining	combine	VERB
ejpam-6073	198	2	(	(	PUNCT
ejpam-6073	198	3	23	23	NUM
ejpam-6073	198	4	)	)	PUNCT
ejpam-6073	198	5	and	and	CCONJ
ejpam-6073	198	6	(	(	PUNCT
ejpam-6073	198	7	26	26	NUM
ejpam-6073	198	8	)	)	PUNCT
ejpam-6073	198	9	,	,	PUNCT
ejpam-6073	198	10	we	we	PRON
ejpam-6073	198	11	find	find	VERB
ejpam-6073	198	12	ρz	ρz	NOUN
ejpam-6073	198	13	∥zt∥22	∥zt∥22	ADJ
ejpam-6073	198	14	+	+	CCONJ
ejpam-6073	198	15	a1	a1	NOUN
ejpam-6073	198	16	∥zx∥22	∥zx∥22	PROPN
ejpam-6073	198	17	=	=	SYM
ejpam-6073	198	18	0	0	X
ejpam-6073	198	19	.	.	PUNCT
ejpam-6073	199	1	similarly	similarly	ADV
ejpam-6073	199	2	,	,	PUNCT
ejpam-6073	199	3	we	we	PRON
ejpam-6073	199	4	obtain	obtain	VERB
ejpam-6073	199	5	ρu	ρu	ADP
ejpam-6073	199	6	∥ut∥22	∥ut∥22	PROPN
ejpam-6073	199	7	+	+	NUM
ejpam-6073	199	8	a3	a3	NOUN
ejpam-6073	199	9	∥ux∥22	∥ux∥22	PROPN
ejpam-6073	199	10	=	=	SYM
ejpam-6073	200	1	0	0	X
ejpam-6073	200	2	.	.	PUNCT
ejpam-6073	201	1	therefore	therefore	ADV
ejpam-6073	201	2	,	,	PUNCT
ejpam-6073	201	3	zt(x	zt(x	NUM
ejpam-6073	201	4	,	,	PUNCT
ejpam-6073	201	5	.	.	PUNCT
ejpam-6073	201	6	)	)	PUNCT
ejpam-6073	202	1	=	=	PUNCT
ejpam-6073	202	2	ut(x	ut(x	NOUN
ejpam-6073	202	3	,	,	PUNCT
ejpam-6073	202	4	.	.	PUNCT
ejpam-6073	202	5	)	)	PUNCT
ejpam-6073	203	1	=	=	PUNCT
ejpam-6073	203	2	0	0	NUM
ejpam-6073	204	1	on	on	ADP
ejpam-6073	204	2	ω	ω	PROPN
ejpam-6073	204	3	and	and	CCONJ
ejpam-6073	204	4	ux	ux	PROPN
ejpam-6073	204	5	(	(	PUNCT
ejpam-6073	204	6	.	.	NUM
ejpam-6073	204	7	,	,	PUNCT
ejpam-6073	204	8	t	t	PROPN
ejpam-6073	204	9	)	)	PUNCT
ejpam-6073	204	10	=	=	SYM
ejpam-6073	204	11	zx	zx	NUM
ejpam-6073	204	12	(	(	PUNCT
ejpam-6073	204	13	.	.	NUM
ejpam-6073	204	14	,	,	PUNCT
ejpam-6073	204	15	t	t	PROPN
ejpam-6073	204	16	)	)	PUNCT
ejpam-6073	204	17	=	=	SYM
ejpam-6073	204	18	0	0	NUM
ejpam-6073	204	19	,	,	PUNCT
ejpam-6073	204	20	for	for	ADP
ejpam-6073	204	21	a.e	a.e	PROPN
ejpam-6073	204	22	t	t	PROPN
ejpam-6073	204	23	∈	∈	PROPN
ejpam-6073	204	24	(	(	PUNCT
ejpam-6073	204	25	0	0	NUM
ejpam-6073	204	26	,	,	PUNCT
ejpam-6073	204	27	t	t	NOUN
ejpam-6073	204	28	)	)	PUNCT
ejpam-6073	204	29	.	.	PUNCT
ejpam-6073	205	1	this	this	PRON
ejpam-6073	205	2	implies	imply	VERB
ejpam-6073	205	3	u	u	NOUN
ejpam-6073	205	4	=	=	NOUN
ejpam-6073	205	5	z	z	NOUN
ejpam-6073	205	6	=	=	SYM
ejpam-6073	205	7	0	0	NUM
ejpam-6073	205	8	on	on	ADP
ejpam-6073	205	9	ω×(0	ω×(0	PROPN
ejpam-6073	205	10	,	,	PUNCT
ejpam-6073	205	11	t	t	PROPN
ejpam-6073	205	12	)	)	PUNCT
ejpam-6073	205	13	,	,	PUNCT
ejpam-6073	205	14	since	since	SCONJ
ejpam-6073	205	15	u	u	NOUN
ejpam-6073	205	16	=	=	NOUN
ejpam-6073	205	17	z	z	NOUN
ejpam-6073	205	18	=	=	SYM
ejpam-6073	205	19	0	0	NUM
ejpam-6073	205	20	on	on	ADP
ejpam-6073	205	21	∂ω×(0	∂ω×(0	PROPN
ejpam-6073	205	22	,	,	PUNCT
ejpam-6073	205	23	t	t	PROPN
ejpam-6073	205	24	)	)	PUNCT
ejpam-6073	205	25	.	.	PUNCT
ejpam-6073	206	1	this	this	PRON
ejpam-6073	206	2	proves	prove	VERB
ejpam-6073	206	3	the	the	DET
ejpam-6073	206	4	uniqueness	uniqueness	NOUN
ejpam-6073	206	5	.	.	PUNCT
ejpam-6073	207	1	existence	existence	NOUN
ejpam-6073	207	2	:	:	PUNCT
ejpam-6073	207	3	the	the	DET
ejpam-6073	207	4	proof	proof	NOUN
ejpam-6073	207	5	of	of	ADP
ejpam-6073	207	6	the	the	DET
ejpam-6073	207	7	existence	existence	NOUN
ejpam-6073	207	8	of	of	ADP
ejpam-6073	207	9	a	a	DET
ejpam-6073	207	10	weak	weak	ADJ
ejpam-6073	207	11	solution	solution	NOUN
ejpam-6073	207	12	of	of	ADP
ejpam-6073	207	13	(	(	PUNCT
ejpam-6073	207	14	q	q	NOUN
ejpam-6073	207	15	)	)	PUNCT
ejpam-6073	207	16	consists	consist	VERB
ejpam-6073	207	17	of	of	ADP
ejpam-6073	207	18	four	four	NUM
ejpam-6073	207	19	steps	step	NOUN
ejpam-6073	207	20	:	:	PUNCT
ejpam-6073	207	21	step	step	NOUN
ejpam-6073	207	22	1	1	NUM
ejpam-6073	207	23	.	.	PUNCT
ejpam-6073	207	24	approximate	approximate	ADJ
ejpam-6073	207	25	problem	problem	NOUN
ejpam-6073	207	26	:	:	PUNCT
ejpam-6073	207	27	in	in	ADP
ejpam-6073	207	28	this	this	DET
ejpam-6073	207	29	step	step	NOUN
ejpam-6073	207	30	,	,	PUNCT
ejpam-6073	207	31	we	we	PRON
ejpam-6073	207	32	consider	consider	VERB
ejpam-6073	207	33	{	{	PUNCT
ejpam-6073	207	34	wj}∞j=1	wj}∞j=1	PRON
ejpam-6073	207	35	an	an	DET
ejpam-6073	207	36	orthogonal	orthogonal	ADJ
ejpam-6073	207	37	basis	basis	NOUN
ejpam-6073	207	38	of	of	ADP
ejpam-6073	207	39	h1	h1	PROPN
ejpam-6073	207	40	0	0	NUM
ejpam-6073	207	41	(	(	PUNCT
ejpam-6073	207	42	ω	ω	NOUN
ejpam-6073	207	43	)	)	PUNCT
ejpam-6073	207	44	and	and	CCONJ
ejpam-6073	207	45	define	define	VERB
ejpam-6073	207	46	,	,	PUNCT
ejpam-6073	207	47	for	for	ADP
ejpam-6073	207	48	all	all	DET
ejpam-6073	207	49	k	k	PROPN
ejpam-6073	207	50	≥	≥	NUM
ejpam-6073	207	51	1	1	NUM
ejpam-6073	207	52	,	,	PUNCT
ejpam-6073	207	53	(	(	PUNCT
ejpam-6073	207	54	zk	zk	PROPN
ejpam-6073	207	55	,	,	PUNCT
ejpam-6073	207	56	uk	uk	PROPN
ejpam-6073	207	57	)	)	PUNCT
ejpam-6073	207	58	a	a	DET
ejpam-6073	207	59	sequence	sequence	NOUN
ejpam-6073	207	60	in	in	ADP
ejpam-6073	207	61	the	the	DET
ejpam-6073	207	62	finite	finite	ADJ
ejpam-6073	207	63	dimensional	dimensional	ADJ
ejpam-6073	207	64	subspace	subspace	NOUN
ejpam-6073	207	65	(	(	PUNCT
ejpam-6073	207	66	vk	vk	VERB
ejpam-6073	207	67	×	×	PROPN
ejpam-6073	207	68	vk	vk	NOUN
ejpam-6073	207	69	)	)	PUNCT
ejpam-6073	207	70	,	,	PUNCT
ejpam-6073	207	71	where	where	SCONJ
ejpam-6073	207	72	vk	vk	NOUN
ejpam-6073	207	73	=	=	SYM
ejpam-6073	207	74	span{w1	span{w1	PROPN
ejpam-6073	207	75	,	,	PUNCT
ejpam-6073	207	76	w2	w2	NOUN
ejpam-6073	207	77	,	,	PUNCT
ejpam-6073	207	78	...	...	PUNCT
ejpam-6073	207	79	,	,	PUNCT
ejpam-6073	207	80	wk	wk	PROPN
ejpam-6073	207	81	}	}	PUNCT
ejpam-6073	207	82	,	,	PUNCT
ejpam-6073	207	83	as	as	SCONJ
ejpam-6073	207	84	follows	follow	VERB
ejpam-6073	207	85	:	:	PUNCT
ejpam-6073	207	86	zk(x	zk(x	NUM
ejpam-6073	207	87	,	,	PUNCT
ejpam-6073	207	88	t	t	PROPN
ejpam-6073	207	89	)	)	PUNCT
ejpam-6073	207	90	=	=	PUNCT
ejpam-6073	208	1	k∑	k∑	PROPN
ejpam-6073	209	1	j=1	j=1	PROPN
ejpam-6073	209	2	aj(t)wj	aj(t)wj	PROPN
ejpam-6073	209	3	,	,	PUNCT
ejpam-6073	209	4	uk(x	uk(x	PROPN
ejpam-6073	209	5	,	,	PUNCT
ejpam-6073	209	6	t	t	PROPN
ejpam-6073	209	7	)	)	PUNCT
ejpam-6073	209	8	=	=	PUNCT
ejpam-6073	209	9	k∑	k∑	PROPN
ejpam-6073	210	1	j=1	j=1	PROPN
ejpam-6073	210	2	bj(t)wj	bj(t)wj	PROPN
ejpam-6073	210	3	,	,	PUNCT
ejpam-6073	210	4	for	for	ADP
ejpam-6073	210	5	all	all	DET
ejpam-6073	210	6	x	x	SYM
ejpam-6073	210	7	∈	∈	PROPN
ejpam-6073	210	8	ω	ω	NOUN
ejpam-6073	210	9	and	and	CCONJ
ejpam-6073	210	10	t	t	PROPN
ejpam-6073	210	11	∈	∈	PROPN
ejpam-6073	210	12	(	(	PUNCT
ejpam-6073	210	13	0	0	NUM
ejpam-6073	210	14	,	,	PUNCT
ejpam-6073	210	15	t	t	NOUN
ejpam-6073	210	16	)	)	PUNCT
ejpam-6073	210	17	satisfying	satisfy	VERB
ejpam-6073	210	18	the	the	DET
ejpam-6073	210	19	following	follow	VERB
ejpam-6073	210	20	approximate	approximate	ADJ
ejpam-6073	210	21	problem:	problem:	PROPN
ejpam-6073	210	22	ρz⟨zktt	ρz⟨zktt	PROPN
ejpam-6073	210	23	,	,	PUNCT
ejpam-6073	210	24	wj⟩l2(ω	wj⟩l2(ω	ADV
ejpam-6073	210	25	)	)	PUNCT
ejpam-6073	211	1	+	+	CCONJ
ejpam-6073	211	2	a1⟨zxk	a1⟨zxk	PROPN
ejpam-6073	211	3	,	,	PUNCT
ejpam-6073	211	4	wjx⟩l2(ω	wjx⟩l2(ω	ADJ
ejpam-6073	211	5	)	)	PUNCT
ejpam-6073	211	6	+	+	CCONJ
ejpam-6073	211	7	a2⟨ukx	a2⟨ukx	NUM
ejpam-6073	211	8	,	,	PUNCT
ejpam-6073	211	9	wjx⟩l2(ω	wjx⟩l2(ω	ADJ
ejpam-6073	211	10	)	)	PUNCT
ejpam-6073	212	1	+	+	CCONJ
ejpam-6073	213	1	γ⟨|zkt	γ⟨|zkt	PROPN
ejpam-6073	213	2	|	|	ADV
ejpam-6073	213	3	p(x)−2	p(x)−2	ADJ
ejpam-6073	213	4	zkt	zkt	NOUN
ejpam-6073	213	5	,	,	PUNCT
ejpam-6073	213	6	wj⟩l2(ω	wj⟩l2(ω	ADV
ejpam-6073	213	7	)	)	PUNCT
ejpam-6073	213	8	=	=	SYM
ejpam-6073	213	9	⟨f(x	⟨f(x	PROPN
ejpam-6073	213	10	,	,	PUNCT
ejpam-6073	213	11	t	t	PROPN
ejpam-6073	213	12	)	)	PUNCT
ejpam-6073	213	13	,	,	PUNCT
ejpam-6073	213	14	wj⟩l2(ω	wj⟩l2(ω	ADV
ejpam-6073	213	15	)	)	PUNCT
ejpam-6073	213	16	,	,	PUNCT
ejpam-6073	213	17	j	j	PROPN
ejpam-6073	213	18	=	=	SYM
ejpam-6073	213	19	1	1	NUM
ejpam-6073	213	20	,	,	PUNCT
ejpam-6073	213	21	2	2	NUM
ejpam-6073	213	22	,	,	PUNCT
ejpam-6073	213	23	...	...	PUNCT
ejpam-6073	213	24	,	,	PUNCT
ejpam-6073	213	25	k	k	NOUN
ejpam-6073	213	26	,	,	PUNCT
ejpam-6073	213	27	ρu⟨uktt	ρu⟨uktt	ADJ
ejpam-6073	213	28	,	,	PUNCT
ejpam-6073	213	29	wj⟩l2(ω	wj⟩l2(ω	ADV
ejpam-6073	213	30	)	)	PUNCT
ejpam-6073	213	31	+	+	CCONJ
ejpam-6073	213	32	a3⟨uxk	a3⟨uxk	ADJ
ejpam-6073	213	33	,	,	PUNCT
ejpam-6073	213	34	wjx⟩l2(ω	wjx⟩l2(ω	ADJ
ejpam-6073	213	35	)	)	PUNCT
ejpam-6073	214	1	+	+	CCONJ
ejpam-6073	214	2	a2⟨zkx	a2⟨zkx	PROPN
ejpam-6073	214	3	,	,	PUNCT
ejpam-6073	214	4	wjx⟩l2(ω	wjx⟩l2(ω	ADJ
ejpam-6073	214	5	)	)	PUNCT
ejpam-6073	215	1	+	+	CCONJ
ejpam-6073	215	2	β⟨|ukt	β⟨|ukt	PROPN
ejpam-6073	215	3	|	|	ADV
ejpam-6073	215	4	q(x)−2	q(x)−2	ADV
ejpam-6073	215	5	ukt	ukt	ADJ
ejpam-6073	215	6	,	,	PUNCT
ejpam-6073	215	7	wj⟩l2(ω	wj⟩l2(ω	ADV
ejpam-6073	215	8	)	)	PUNCT
ejpam-6073	215	9	=	=	SYM
ejpam-6073	216	1	⟨g(x	⟨g(x	PROPN
ejpam-6073	216	2	,	,	PUNCT
ejpam-6073	216	3	t	t	PROPN
ejpam-6073	216	4	)	)	PUNCT
ejpam-6073	216	5	,	,	PUNCT
ejpam-6073	216	6	wj⟩l2(ω	wj⟩l2(ω	ADV
ejpam-6073	216	7	)	)	PUNCT
ejpam-6073	216	8	,	,	PUNCT
ejpam-6073	216	9	j	j	PROPN
ejpam-6073	216	10	=	=	SYM
ejpam-6073	216	11	1	1	NUM
ejpam-6073	216	12	,	,	PUNCT
ejpam-6073	216	13	2	2	NUM
ejpam-6073	216	14	,	,	PUNCT
ejpam-6073	216	15	...	...	PUNCT
ejpam-6073	216	16	,	,	PUNCT
ejpam-6073	216	17	k	k	PROPN
ejpam-6073	216	18	,	,	PUNCT
ejpam-6073	216	19	zk(0	zk(0	PROPN
ejpam-6073	216	20	)	)	PUNCT
ejpam-6073	216	21	=	=	SYM
ejpam-6073	216	22	zk0	zk0	NOUN
ejpam-6073	216	23	,	,	PUNCT
ejpam-6073	216	24	z	z	PROPN
ejpam-6073	216	25	k	k	PROPN
ejpam-6073	216	26	t	t	PROPN
ejpam-6073	216	27	(	(	PUNCT
ejpam-6073	216	28	0	0	NUM
ejpam-6073	216	29	)	)	PUNCT
ejpam-6073	216	30	=	=	VERB
ejpam-6073	217	1	zk1	zk1	NOUN
ejpam-6073	217	2	,	,	PUNCT
ejpam-6073	217	3	u	u	PROPN
ejpam-6073	217	4	k(0	k(0	PROPN
ejpam-6073	217	5	)	)	PUNCT
ejpam-6073	217	6	=	=	SYM
ejpam-6073	218	1	uk0	uk0	ADJ
ejpam-6073	218	2	,	,	PUNCT
ejpam-6073	218	3	u	u	PROPN
ejpam-6073	218	4	k	k	PROPN
ejpam-6073	218	5	t	t	PROPN
ejpam-6073	218	6	(	(	PUNCT
ejpam-6073	218	7	0	0	NUM
ejpam-6073	218	8	)	)	PUNCT
ejpam-6073	218	9	=	=	SYM
ejpam-6073	218	10	uk1	uk1	PROPN
ejpam-6073	218	11	,	,	PUNCT
ejpam-6073	218	12	(	(	PUNCT
ejpam-6073	218	13	27	27	NUM
ejpam-6073	218	14	)	)	PUNCT
ejpam-6073	218	15	where	where	SCONJ
ejpam-6073	218	16	⟨	⟨	NOUN
ejpam-6073	218	17	,	,	PUNCT
ejpam-6073	218	18	⟩	⟩	NOUN
ejpam-6073	218	19	is	be	AUX
ejpam-6073	218	20	the	the	DET
ejpam-6073	218	21	inner	inner	ADJ
ejpam-6073	218	22	product	product	NOUN
ejpam-6073	218	23	in	in	ADP
ejpam-6073	218	24	l2(ω	l2(ω	PROPN
ejpam-6073	218	25	)	)	PUNCT
ejpam-6073	218	26	and	and	CCONJ
ejpam-6073	218	27	zk0	zk0	NOUN
ejpam-6073	218	28	=	=	SYM
ejpam-6073	218	29	k∑	k∑	PROPN
ejpam-6073	219	1	i=1	i=1	PROPN
ejpam-6073	219	2	⟨z0	⟨z0	PROPN
ejpam-6073	219	3	,	,	PUNCT
ejpam-6073	219	4	wi⟩wi	wi⟩wi	AUX
ejpam-6073	219	5	,	,	PUNCT
ejpam-6073	219	6	u	u	NOUN
ejpam-6073	219	7	k	k	PROPN
ejpam-6073	219	8	0	0	X
ejpam-6073	220	1	=	=	PUNCT
ejpam-6073	220	2	k∑	k∑	PROPN
ejpam-6073	220	3	i=1	i=1	PROPN
ejpam-6073	221	1	⟨u0	⟨u0	PROPN
ejpam-6073	221	2	,	,	PUNCT
ejpam-6073	221	3	wi⟩wi	wi⟩wi	AUX
ejpam-6073	221	4	,	,	PUNCT
ejpam-6073	221	5	z	z	PROPN
ejpam-6073	221	6	k	k	NOUN
ejpam-6073	222	1	1	1	X
ejpam-6073	222	2	=	=	SYM
ejpam-6073	222	3	k∑	k∑	PROPN
ejpam-6073	222	4	i=1	i=1	PROPN
ejpam-6073	223	1	⟨z1	⟨z1	PROPN
ejpam-6073	223	2	,	,	PUNCT
ejpam-6073	223	3	wi⟩wi	wi⟩wi	AUX
ejpam-6073	223	4	,	,	PUNCT
ejpam-6073	223	5	u	u	NOUN
ejpam-6073	223	6	k	k	PROPN
ejpam-6073	223	7	1	1	X
ejpam-6073	223	8	=	=	SYM
ejpam-6073	223	9	k∑	k∑	PROPN
ejpam-6073	223	10	i=1	i=1	PROPN
ejpam-6073	223	11	⟨u1	⟨u1	PROPN
ejpam-6073	223	12	,	,	PUNCT
ejpam-6073	223	13	wi⟩wi	wi⟩wi	X
ejpam-6073	223	14	.	.	PUNCT
ejpam-6073	224	1	by	by	ADP
ejpam-6073	224	2	the	the	DET
ejpam-6073	224	3	projection	projection	NOUN
ejpam-6073	224	4	theorem	theorem	NOUN
ejpam-6073	224	5	in	in	ADP
ejpam-6073	224	6	hilbert	hilbert	PROPN
ejpam-6073	224	7	spaces	space	NOUN
ejpam-6073	224	8	,	,	PUNCT
ejpam-6073	224	9	the	the	DET
ejpam-6073	224	10	approximated	approximated	ADJ
ejpam-6073	224	11	initial	initial	ADJ
ejpam-6073	224	12	data	datum	NOUN
ejpam-6073	224	13	zk0	zk0	NOUN
ejpam-6073	224	14	,	,	PUNCT
ejpam-6073	224	15	u	u	NOUN
ejpam-6073	224	16	k	k	PROPN
ejpam-6073	224	17	0	0	PROPN
ejpam-6073	224	18	,	,	PUNCT
ejpam-6073	224	19	z	z	PROPN
ejpam-6073	224	20	k	k	NOUN
ejpam-6073	224	21	1	1	NUM
ejpam-6073	224	22	,	,	PUNCT
ejpam-6073	224	23	u	u	NOUN
ejpam-6073	224	24	k	k	PROPN
ejpam-6073	224	25	1	1	NUM
ejpam-6073	224	26	are	be	AUX
ejpam-6073	224	27	obtained	obtain	VERB
ejpam-6073	224	28	via	via	ADP
ejpam-6073	224	29	orthogonal	orthogonal	ADJ
ejpam-6073	224	30	projection	projection	NOUN
ejpam-6073	224	31	onto	onto	ADP
ejpam-6073	224	32	the	the	DET
ejpam-6073	224	33	finite	finite	ADJ
ejpam-6073	224	34	-	-	ADJ
ejpam-6073	224	35	dimensional	dimensional	ADJ
ejpam-6073	224	36	subspace	subspace	NOUN
ejpam-6073	224	37	vk	vk	NOUN
ejpam-6073	224	38	,	,	PUNCT
ejpam-6073	224	39	providing	provide	VERB
ejpam-6073	224	40	the	the	DET
ejpam-6073	224	41	best	good	ADJ
ejpam-6073	224	42	approximation	approximation	NOUN
ejpam-6073	224	43	in	in	ADP
ejpam-6073	224	44	the	the	DET
ejpam-6073	224	45	corresponding	corresponding	ADJ
ejpam-6073	224	46	norm	norm	NOUN
ejpam-6073	224	47	.	.	PUNCT
ejpam-6073	225	1	since	since	SCONJ
ejpam-6073	225	2	vk	vk	PROPN
ejpam-6073	225	3	is	be	AUX
ejpam-6073	225	4	dense	dense	ADJ
ejpam-6073	225	5	in	in	ADP
ejpam-6073	225	6	h1	h1	PROPN
ejpam-6073	225	7	0	0	NUM
ejpam-6073	225	8	(	(	PUNCT
ejpam-6073	225	9	ω	ω	NOUN
ejpam-6073	225	10	)	)	PUNCT
ejpam-6073	225	11	and	and	CCONJ
ejpam-6073	225	12	l2(ω	l2(ω	NOUN
ejpam-6073	225	13	)	)	PUNCT
ejpam-6073	225	14	,	,	PUNCT
ejpam-6073	225	15	and	and	CCONJ
ejpam-6073	225	16	due	due	ADP
ejpam-6073	225	17	to	to	ADP
ejpam-6073	225	18	the	the	DET
ejpam-6073	225	19	finite	finite	ADJ
ejpam-6073	225	20	-	-	ADJ
ejpam-6073	225	21	dimensional	dimensional	ADJ
ejpam-6073	225	22	approximation	approximation	NOUN
ejpam-6073	225	23	property	property	NOUN
ejpam-6073	225	24	,	,	PUNCT
ejpam-6073	225	25	the	the	DET
ejpam-6073	225	26	projections	projection	NOUN
ejpam-6073	225	27	converge	converge	VERB
ejpam-6073	225	28	strongly	strongly	ADV
ejpam-6073	225	29	to	to	ADP
ejpam-6073	225	30	the	the	DET
ejpam-6073	225	31	original	original	ADJ
ejpam-6073	225	32	initial	initial	ADJ
ejpam-6073	225	33	data	datum	NOUN
ejpam-6073	225	34	.	.	PUNCT
ejpam-6073	226	1	furthermore	furthermore	ADV
ejpam-6073	226	2	,	,	PUNCT
ejpam-6073	226	3	the	the	DET
ejpam-6073	226	4	banach	banach	NOUN
ejpam-6073	226	5	–	–	PUNCT
ejpam-6073	226	6	alaoglu	alaoglu	NOUN
ejpam-6073	226	7	theorem	theorem	NOUN
ejpam-6073	226	8	guarantees	guarantee	VERB
ejpam-6073	226	9	weak	weak	ADJ
ejpam-6073	226	10	compactness	compactness	NOUN
ejpam-6073	226	11	of	of	ADP
ejpam-6073	226	12	bounded	bounded	ADJ
ejpam-6073	226	13	sequences	sequence	NOUN
ejpam-6073	226	14	,	,	PUNCT
ejpam-6073	226	15	but	but	CCONJ
ejpam-6073	226	16	in	in	ADP
ejpam-6073	226	17	this	this	DET
ejpam-6073	226	18	case	case	NOUN
ejpam-6073	226	19	,	,	PUNCT
ejpam-6073	226	20	weak	weak	ADJ
ejpam-6073	226	21	convergence	convergence	NOUN
ejpam-6073	226	22	implies	imply	VERB
ejpam-6073	226	23	the	the	DET
ejpam-6073	226	24	following	follow	VERB
ejpam-6073	226	25	strong	strong	ADJ
ejpam-6073	226	26	convergence,	convergence,	PROPN
ejpam-6073	226	27	zk0	zk0	PROPN
ejpam-6073	226	28	→	→	SYM
ejpam-6073	226	29	z0	z0	NOUN
ejpam-6073	226	30	and	and	CCONJ
ejpam-6073	226	31	uk0	uk0	ADJ
ejpam-6073	226	32	→	→	SYM
ejpam-6073	226	33	u0	u0	ADJ
ejpam-6073	226	34	in	in	ADP
ejpam-6073	226	35	h1	h1	PROPN
ejpam-6073	226	36	0	0	NUM
ejpam-6073	226	37	(	(	PUNCT
ejpam-6073	226	38	ω	ω	NOUN
ejpam-6073	226	39	)	)	PUNCT
ejpam-6073	226	40	and	and	CCONJ
ejpam-6073	226	41	zk1	zk1	PROPN
ejpam-6073	226	42	→	→	SYM
ejpam-6073	226	43	z1	z1	PROPN
ejpam-6073	226	44	and	and	CCONJ
ejpam-6073	226	45	uk1	uk1	NOUN
ejpam-6073	226	46	→	→	SYM
ejpam-6073	226	47	u1	u1	NOUN
ejpam-6073	226	48	in	in	ADP
ejpam-6073	226	49	l	l	NOUN
ejpam-6073	226	50	2(ω	2(ω	NUM
ejpam-6073	226	51	)	)	PUNCT
ejpam-6073	226	52	.	.	PUNCT
ejpam-6073	227	1	(	(	PUNCT
ejpam-6073	227	2	28	28	NUM
ejpam-6073	227	3	)	)	PUNCT
ejpam-6073	227	4	a.	a.	NOUN
ejpam-6073	227	5	m.	m.	PROPN
ejpam-6073	227	6	al	al	PROPN
ejpam-6073	227	7	-	-	PROPN
ejpam-6073	227	8	mahdi	mahdi	PROPN
ejpam-6073	227	9	et	et	PROPN
ejpam-6073	227	10	al	al	PROPN
ejpam-6073	227	11	.	.	PUNCT
ejpam-6073	227	12	/	/	SYM
ejpam-6073	227	13	eur	eur	PROPN
ejpam-6073	227	14	.	.	PUNCT
ejpam-6073	228	1	j.	j.	PROPN
ejpam-6073	228	2	pure	pure	PROPN
ejpam-6073	228	3	appl	appl	PROPN
ejpam-6073	228	4	.	.	PROPN
ejpam-6073	228	5	math	math	PROPN
ejpam-6073	228	6	,	,	PUNCT
ejpam-6073	228	7	18	18	NUM
ejpam-6073	228	8	(	(	PUNCT
ejpam-6073	228	9	3	3	NUM
ejpam-6073	228	10	)	)	PUNCT
ejpam-6073	228	11	(	(	PUNCT
ejpam-6073	228	12	2025	2025	NUM
ejpam-6073	228	13	)	)	PUNCT
ejpam-6073	228	14	,	,	PUNCT
ejpam-6073	228	15	6073	6073	NUM
ejpam-6073	228	16	11	11	NUM
ejpam-6073	228	17	of	of	ADP
ejpam-6073	228	18	29	29	NUM
ejpam-6073	228	19	based	base	VERB
ejpam-6073	228	20	on	on	ADP
ejpam-6073	228	21	standard	standard	ADJ
ejpam-6073	228	22	existence	existence	NOUN
ejpam-6073	228	23	theory	theory	NOUN
ejpam-6073	228	24	for	for	ADP
ejpam-6073	228	25	ordinal	ordinal	ADJ
ejpam-6073	228	26	differential	differential	ADJ
ejpam-6073	228	27	equations	equation	NOUN
ejpam-6073	228	28	,	,	PUNCT
ejpam-6073	228	29	the	the	DET
ejpam-6073	228	30	system	system	NOUN
ejpam-6073	228	31	(	(	PUNCT
ejpam-6073	228	32	27	27	NUM
ejpam-6073	228	33	)	)	PUNCT
ejpam-6073	228	34	admits	admit	VERB
ejpam-6073	228	35	a	a	DET
ejpam-6073	228	36	unique	unique	ADJ
ejpam-6073	228	37	local	local	ADJ
ejpam-6073	228	38	solution	solution	NOUN
ejpam-6073	228	39	(	(	PUNCT
ejpam-6073	228	40	zk	zk	PROPN
ejpam-6073	228	41	,	,	PUNCT
ejpam-6073	228	42	uk	uk	PROPN
ejpam-6073	228	43	)	)	PUNCT
ejpam-6073	228	44	on	on	ADP
ejpam-6073	228	45	a	a	DET
ejpam-6073	228	46	maximal	maximal	ADJ
ejpam-6073	228	47	time	time	NOUN
ejpam-6073	228	48	interval	interval	NOUN
ejpam-6073	228	49	[	[	X
ejpam-6073	228	50	0	0	NUM
ejpam-6073	228	51	,	,	PUNCT
ejpam-6073	228	52	tk	tk	PROPN
ejpam-6073	228	53	)	)	PUNCT
ejpam-6073	228	54	,	,	PUNCT
ejpam-6073	228	55	0	0	PUNCT
ejpam-6073	228	56	<	<	X
ejpam-6073	228	57	tk	tk	PROPN
ejpam-6073	228	58	<	<	X
ejpam-6073	228	59	t	t	PROPN
ejpam-6073	228	60	,	,	PUNCT
ejpam-6073	228	61	for	for	ADP
ejpam-6073	228	62	each	each	DET
ejpam-6073	228	63	k	k	PROPN
ejpam-6073	228	64	∈	∈	PROPN
ejpam-6073	228	65	n.	n.	NOUN
ejpam-6073	228	66	step	step	NOUN
ejpam-6073	228	67	2	2	NUM
ejpam-6073	228	68	.	.	PUNCT
ejpam-6073	229	1	a	a	DET
ejpam-6073	229	2	priori	priori	ADJ
ejpam-6073	229	3	estimates	estimate	NOUN
ejpam-6073	229	4	:	:	PUNCT
ejpam-6073	229	5	in	in	ADP
ejpam-6073	229	6	this	this	DET
ejpam-6073	229	7	step	step	NOUN
ejpam-6073	229	8	,	,	PUNCT
ejpam-6073	229	9	we	we	PRON
ejpam-6073	229	10	show	show	VERB
ejpam-6073	229	11	,	,	PUNCT
ejpam-6073	229	12	by	by	ADP
ejpam-6073	229	13	a	a	DET
ejpam-6073	229	14	priory	priory	NOUN
ejpam-6073	229	15	estimates	estimate	NOUN
ejpam-6073	229	16	,	,	PUNCT
ejpam-6073	229	17	that	that	SCONJ
ejpam-6073	229	18	tk	tk	PROPN
ejpam-6073	229	19	=	=	SYM
ejpam-6073	229	20	t	t	PROPN
ejpam-6073	229	21	,	,	PUNCT
ejpam-6073	229	22	for	for	ADP
ejpam-6073	229	23	each	each	DET
ejpam-6073	229	24	k	k	PROPN
ejpam-6073	229	25	∈	∈	PROPN
ejpam-6073	229	26	n.	n.	NOUN
ejpam-6073	229	27	we	we	PRON
ejpam-6073	229	28	multiply	multiply	VERB
ejpam-6073	229	29	the	the	DET
ejpam-6073	229	30	first	first	ADJ
ejpam-6073	229	31	equation	equation	NOUN
ejpam-6073	229	32	by	by	ADP
ejpam-6073	229	33	a′j(t	a′j(t	PROPN
ejpam-6073	229	34	)	)	PUNCT
ejpam-6073	229	35	and	and	CCONJ
ejpam-6073	229	36	the	the	DET
ejpam-6073	229	37	second	second	ADJ
ejpam-6073	229	38	equation	equation	NOUN
ejpam-6073	229	39	by	by	ADP
ejpam-6073	229	40	b′j(t	b′j(t	PROPN
ejpam-6073	229	41	)	)	PUNCT
ejpam-6073	229	42	in	in	ADP
ejpam-6073	229	43	(	(	PUNCT
ejpam-6073	229	44	27	27	NUM
ejpam-6073	229	45	)	)	PUNCT
ejpam-6073	229	46	,	,	PUNCT
ejpam-6073	229	47	sum	sum	VERB
ejpam-6073	229	48	over	over	ADP
ejpam-6073	229	49	j	j	PROPN
ejpam-6073	229	50	=	=	SYM
ejpam-6073	229	51	1	1	NUM
ejpam-6073	229	52	,	,	PUNCT
ejpam-6073	229	53	2	2	NUM
ejpam-6073	229	54	,	,	PUNCT
ejpam-6073	229	55	...	...	PUNCT
ejpam-6073	230	1	k	k	PROPN
ejpam-6073	230	2	and	and	CCONJ
ejpam-6073	230	3	add	add	VERB
ejpam-6073	230	4	the	the	DET
ejpam-6073	230	5	two	two	NUM
ejpam-6073	230	6	equations	equation	NOUN
ejpam-6073	230	7	to	to	PART
ejpam-6073	230	8	obtain	obtain	VERB
ejpam-6073	230	9	1	1	NUM
ejpam-6073	230	10	2	2	NUM
ejpam-6073	230	11	d	d	NOUN
ejpam-6073	230	12	dt	dt	X
ejpam-6073	230	13	[	[	PUNCT
ejpam-6073	230	14	ρz∥zkt	ρz∥zkt	X
ejpam-6073	230	15	∥22	∥22	PROPN
ejpam-6073	230	16	+	+	CCONJ
ejpam-6073	230	17	ρu∥ukt	ρu∥ukt	CCONJ
ejpam-6073	230	18	∥22	∥22	VERB
ejpam-6073	230	19	+	+	CCONJ
ejpam-6073	230	20	a1∥zkx∥22	a1∥zkx∥22	PUNCT
ejpam-6073	230	21	+	+	CCONJ
ejpam-6073	230	22	a3∥ukx∥22	a3∥ukx∥22	CCONJ
ejpam-6073	230	23	+	+	CCONJ
ejpam-6073	230	24	2a2	2a2	NUM
ejpam-6073	230	25	∫	∫	PROPN
ejpam-6073	230	26	ω	ω	NUM
ejpam-6073	230	27	ukxz	ukxz	PROPN
ejpam-6073	230	28	k	k	PROPN
ejpam-6073	230	29	xdx	xdx	PROPN
ejpam-6073	230	30	]	]	PUNCT
ejpam-6073	231	1	=	=	PUNCT
ejpam-6073	231	2	−γ	−γ	ADJ
ejpam-6073	231	3	∫	∫	PROPN
ejpam-6073	231	4	ω	ω	NUM
ejpam-6073	231	5	|zkt	|zkt	PROPN
ejpam-6073	231	6	(	(	PUNCT
ejpam-6073	231	7	x	x	X
ejpam-6073	231	8	,	,	PUNCT
ejpam-6073	231	9	t)|	t)|	NOUN
ejpam-6073	231	10	p	p	X
ejpam-6073	231	11	(	(	PUNCT
ejpam-6073	231	12	.	.	PUNCT
ejpam-6073	231	13	)	)	PUNCT
ejpam-6073	232	1	dx−	dx−	X
ejpam-6073	232	2	β	β	PROPN
ejpam-6073	232	3	∫	∫	PROPN
ejpam-6073	232	4	ω	ω	PROPN
ejpam-6073	232	5	|ukt	|ukt	PROPN
ejpam-6073	232	6	(	(	PUNCT
ejpam-6073	232	7	x	x	X
ejpam-6073	232	8	,	,	PUNCT
ejpam-6073	232	9	t)|	t)|	NOUN
ejpam-6073	232	10	q	q	NOUN
ejpam-6073	232	11	(	(	PUNCT
ejpam-6073	232	12	.	.	PUNCT
ejpam-6073	232	13	)	)	PUNCT
ejpam-6073	232	14	dx+	dx+	NOUN
ejpam-6073	232	15	∫	∫	PROPN
ejpam-6073	232	16	ω	ω	PROPN
ejpam-6073	232	17	(	(	PUNCT
ejpam-6073	232	18	zkt	zkt	PROPN
ejpam-6073	232	19	f(x	f(x	PROPN
ejpam-6073	232	20	,	,	PUNCT
ejpam-6073	232	21	t	t	PROPN
ejpam-6073	232	22	)	)	PUNCT
ejpam-6073	233	1	+	+	CCONJ
ejpam-6073	233	2	ukt	ukt	VERB
ejpam-6073	233	3	g(x	g(x	PROPN
ejpam-6073	233	4	,	,	PUNCT
ejpam-6073	233	5	t	t	PROPN
ejpam-6073	233	6	)	)	PUNCT
ejpam-6073	233	7	)	)	PUNCT
ejpam-6073	234	1	dx	dx	PROPN
ejpam-6073	234	2	.	.	PUNCT
ejpam-6073	235	1	(	(	PUNCT
ejpam-6073	235	2	29	29	NUM
ejpam-6073	235	3	)	)	PUNCT
ejpam-6073	235	4	integration	integration	NOUN
ejpam-6073	235	5	of	of	ADP
ejpam-6073	235	6	(	(	PUNCT
ejpam-6073	235	7	29	29	NUM
ejpam-6073	235	8	)	)	PUNCT
ejpam-6073	235	9	over	over	ADP
ejpam-6073	235	10	(	(	PUNCT
ejpam-6073	235	11	0	0	NUM
ejpam-6073	235	12	,	,	PUNCT
ejpam-6073	235	13	t	t	NOUN
ejpam-6073	235	14	)	)	PUNCT
ejpam-6073	235	15	leads	lead	VERB
ejpam-6073	235	16	to	to	ADP
ejpam-6073	235	17	1	1	NUM
ejpam-6073	235	18	2	2	NUM
ejpam-6073	235	19	(	(	PUNCT
ejpam-6073	235	20	ρz||zkt	ρz||zkt	NUM
ejpam-6073	235	21	||	||	NOUN
ejpam-6073	235	22	2	2	NUM
ejpam-6073	235	23	2	2	NUM
ejpam-6073	235	24	+	+	CCONJ
ejpam-6073	235	25	ρu||ukt	ρu||ukt	NUM
ejpam-6073	235	26	||	||	NUM
ejpam-6073	235	27	2	2	NUM
ejpam-6073	235	28	2	2	NUM
ejpam-6073	235	29	+	+	CCONJ
ejpam-6073	235	30	a1||zkx||	a1||zkx||	PROPN
ejpam-6073	235	31	2	2	NUM
ejpam-6073	235	32	2	2	NUM
ejpam-6073	235	33	+	+	CCONJ
ejpam-6073	235	34	a3||ukx||	a3||ukx||	ADV
ejpam-6073	235	35	2	2	NUM
ejpam-6073	235	36	2	2	NUM
ejpam-6073	235	37	+	+	SYM
ejpam-6073	235	38	2a2	2a2	NUM
ejpam-6073	235	39	∫	∫	PROPN
ejpam-6073	235	40	ω	ω	NUM
ejpam-6073	235	41	ukxz	ukxz	PROPN
ejpam-6073	235	42	k	k	PROPN
ejpam-6073	235	43	xdx	xdx	PROPN
ejpam-6073	235	44	)	)	PUNCT
ejpam-6073	236	1	+	+	CCONJ
ejpam-6073	236	2	γ	γ	PROPN
ejpam-6073	236	3	∫	∫	PROPN
ejpam-6073	236	4	t	t	PROPN
ejpam-6073	236	5	0	0	NUM
ejpam-6073	236	6	∫	∫	PROPN
ejpam-6073	236	7	ω	ω	PROPN
ejpam-6073	236	8	|zkt	|zkt	PROPN
ejpam-6073	236	9	(	(	PUNCT
ejpam-6073	236	10	s)|	s)|	NOUN
ejpam-6073	236	11	p	p	X
ejpam-6073	236	12	(	(	PUNCT
ejpam-6073	236	13	.	.	PUNCT
ejpam-6073	236	14	)	)	PUNCT
ejpam-6073	237	1	dxds+	dxds+	X
ejpam-6073	237	2	β	β	X
ejpam-6073	237	3	∫	∫	PROPN
ejpam-6073	237	4	t	t	PROPN
ejpam-6073	237	5	0	0	NUM
ejpam-6073	237	6	∫	∫	PROPN
ejpam-6073	237	7	ω	ω	PROPN
ejpam-6073	237	8	|ukt	|ukt	PROPN
ejpam-6073	237	9	(	(	PUNCT
ejpam-6073	237	10	s)|	s)|	NOUN
ejpam-6073	237	11	q	q	X
ejpam-6073	237	12	(	(	PUNCT
ejpam-6073	237	13	.	.	PUNCT
ejpam-6073	237	14	)	)	PUNCT
ejpam-6073	238	1	dxds	dxds	NOUN
ejpam-6073	238	2	=	=	SYM
ejpam-6073	238	3	1	1	NUM
ejpam-6073	238	4	2	2	NUM
ejpam-6073	238	5	(	(	PUNCT
ejpam-6073	238	6	ρz||zk1	ρz||zk1	NOUN
ejpam-6073	238	7	||	||	NOUN
ejpam-6073	238	8	2	2	NUM
ejpam-6073	238	9	2	2	NUM
ejpam-6073	238	10	+	+	CCONJ
ejpam-6073	238	11	ρu||uk1||	ρu||uk1||	NOUN
ejpam-6073	238	12	2	2	NUM
ejpam-6073	238	13	2	2	NUM
ejpam-6073	238	14	+	+	CCONJ
ejpam-6073	238	15	ρz||zk0x||	ρz||zk0x||	NOUN
ejpam-6073	238	16	2	2	NUM
ejpam-6073	238	17	2	2	NUM
ejpam-6073	238	18	+	+	CCONJ
ejpam-6073	238	19	ρu||uk0x||	ρu||uk0x||	NOUN
ejpam-6073	238	20	2	2	NUM
ejpam-6073	238	21	2	2	NUM
ejpam-6073	238	22	+	+	SYM
ejpam-6073	238	23	2a2	2a2	NUM
ejpam-6073	239	1	∫	∫	PROPN
ejpam-6073	240	1	ω	ω	PROPN
ejpam-6073	241	1	zk0xu	zk0xu	PROPN
ejpam-6073	241	2	k	k	X
ejpam-6073	241	3	0xdx	0xdx	PROPN
ejpam-6073	241	4	)	)	PUNCT
ejpam-6073	242	1	+	+	CCONJ
ejpam-6073	243	1	∫	∫	PROPN
ejpam-6073	243	2	t	t	PROPN
ejpam-6073	243	3	0	0	NUM
ejpam-6073	244	1	∫	∫	PROPN
ejpam-6073	244	2	ω	ω	PROPN
ejpam-6073	244	3	(	(	PUNCT
ejpam-6073	244	4	zkt	zkt	PROPN
ejpam-6073	244	5	f(x	f(x	PROPN
ejpam-6073	244	6	,	,	PUNCT
ejpam-6073	244	7	t	t	PROPN
ejpam-6073	244	8	)	)	PUNCT
ejpam-6073	244	9	+	+	CCONJ
ejpam-6073	244	10	ukt	ukt	VERB
ejpam-6073	244	11	g(x	g(x	PROPN
ejpam-6073	244	12	,	,	PUNCT
ejpam-6073	244	13	t	t	PROPN
ejpam-6073	244	14	)	)	PUNCT
ejpam-6073	244	15	)	)	PUNCT
ejpam-6073	244	16	dxds	dxds	NOUN
ejpam-6073	244	17	,	,	PUNCT
ejpam-6073	244	18	for	for	ADP
ejpam-6073	244	19	all	all	DET
ejpam-6073	244	20	t	t	NOUN
ejpam-6073	244	21	≤	≤	NUM
ejpam-6073	244	22	tk	tk	PROPN
ejpam-6073	244	23	.	.	PUNCT
ejpam-6073	244	24	(	(	PUNCT
ejpam-6073	244	25	30	30	NUM
ejpam-6073	244	26	)	)	PUNCT
ejpam-6073	244	27	using	use	VERB
ejpam-6073	244	28	the	the	DET
ejpam-6073	244	29	identity	identity	NOUN
ejpam-6073	244	30	(	(	PUNCT
ejpam-6073	244	31	26	26	NUM
ejpam-6073	244	32	)	)	PUNCT
ejpam-6073	244	33	and	and	CCONJ
ejpam-6073	244	34	young	young	PROPN
ejpam-6073	244	35	’s	’s	PART
ejpam-6073	244	36	inequality	inequality	NOUN
ejpam-6073	244	37	on	on	ADP
ejpam-6073	244	38	the	the	DET
ejpam-6073	244	39	last	last	ADJ
ejpam-6073	244	40	two	two	NUM
ejpam-6073	244	41	terms	term	NOUN
ejpam-6073	244	42	,	,	PUNCT
ejpam-6073	244	43	eq	eq	NOUN
ejpam-6073	244	44	.	.	PUNCT
ejpam-6073	244	45	(	(	PUNCT
ejpam-6073	244	46	30	30	NUM
ejpam-6073	244	47	)	)	PUNCT
ejpam-6073	244	48	becomes	become	VERB
ejpam-6073	244	49	for	for	ADP
ejpam-6073	244	50	any	any	DET
ejpam-6073	244	51	ε	ε	PROPN
ejpam-6073	244	52	>	>	X
ejpam-6073	244	53	0	0	PROPN
ejpam-6073	244	54	,	,	PUNCT
ejpam-6073	244	55	1	1	NUM
ejpam-6073	244	56	2	2	NUM
ejpam-6073	244	57	(	(	PUNCT
ejpam-6073	244	58	ρz||zkt	ρz||zkt	NUM
ejpam-6073	244	59	||	||	NOUN
ejpam-6073	244	60	2	2	NUM
ejpam-6073	244	61	2	2	NUM
ejpam-6073	244	62	+	+	CCONJ
ejpam-6073	244	63	ρu||ukt	ρu||ukt	NUM
ejpam-6073	244	64	||	||	NUM
ejpam-6073	244	65	2	2	NUM
ejpam-6073	244	66	2	2	NUM
ejpam-6073	244	67	+	+	X
ejpam-6073	244	68	c̃	c̃	PROPN
ejpam-6073	244	69	(	(	PUNCT
ejpam-6073	244	70	∥ux∥2	∥ux∥2	NUM
ejpam-6073	244	71	+	+	NUM
ejpam-6073	244	72	∥zx∥2	∥zx∥2	NUM
ejpam-6073	244	73	)	)	PUNCT
ejpam-6073	244	74	)	)	PUNCT
ejpam-6073	245	1	+	+	CCONJ
ejpam-6073	245	2	γ	γ	PROPN
ejpam-6073	245	3	∫	∫	PROPN
ejpam-6073	245	4	tk	tk	PROPN
ejpam-6073	245	5	0	0	PROPN
ejpam-6073	245	6	∫	∫	PROPN
ejpam-6073	245	7	ω	ω	PROPN
ejpam-6073	245	8	|zkt	|zkt	PROPN
ejpam-6073	245	9	(	(	PUNCT
ejpam-6073	245	10	s)|	s)|	NOUN
ejpam-6073	245	11	p	p	X
ejpam-6073	245	12	(	(	PUNCT
ejpam-6073	245	13	.	.	PUNCT
ejpam-6073	245	14	)	)	PUNCT
ejpam-6073	246	1	dxds+	dxds+	X
ejpam-6073	246	2	β	β	X
ejpam-6073	246	3	∫	∫	PROPN
ejpam-6073	246	4	tk	tk	PROPN
ejpam-6073	246	5	0	0	NUM
ejpam-6073	246	6	∫	∫	PROPN
ejpam-6073	246	7	ω	ω	PROPN
ejpam-6073	246	8	|ukt	|ukt	PROPN
ejpam-6073	246	9	(	(	PUNCT
ejpam-6073	246	10	s)|	s)|	NOUN
ejpam-6073	246	11	q	q	X
ejpam-6073	246	12	(	(	PUNCT
ejpam-6073	246	13	.	.	PUNCT
ejpam-6073	246	14	)	)	PUNCT
ejpam-6073	247	1	dxds	dxds	VERB
ejpam-6073	247	2	≤	≤	NUM
ejpam-6073	247	3	1	1	NUM
ejpam-6073	247	4	2	2	NUM
ejpam-6073	247	5	(	(	PUNCT
ejpam-6073	247	6	ρz||zk1	ρz||zk1	NOUN
ejpam-6073	247	7	||	||	NOUN
ejpam-6073	247	8	2	2	NUM
ejpam-6073	247	9	2	2	NUM
ejpam-6073	247	10	+	+	CCONJ
ejpam-6073	247	11	ρu||uk1||	ρu||uk1||	NOUN
ejpam-6073	247	12	2	2	NUM
ejpam-6073	247	13	2	2	NUM
ejpam-6073	247	14	+	+	CCONJ
ejpam-6073	247	15	ρz||zk0x||	ρz||zk0x||	NOUN
ejpam-6073	247	16	2	2	NUM
ejpam-6073	247	17	2	2	NUM
ejpam-6073	247	18	+	+	CCONJ
ejpam-6073	247	19	ρu||uk0x||	ρu||uk0x||	NOUN
ejpam-6073	247	20	2	2	NUM
ejpam-6073	247	21	2	2	NUM
ejpam-6073	247	22	)	)	PUNCT
ejpam-6073	248	1	+	+	CCONJ
ejpam-6073	248	2	c	c	X
ejpam-6073	248	3	(	(	PUNCT
ejpam-6073	248	4	||zk0x||	||zk0x||	ADV
ejpam-6073	248	5	2	2	NUM
ejpam-6073	248	6	2	2	NUM
ejpam-6073	248	7	+	+	NUM
ejpam-6073	248	8	||uk0x||	||uk0x||	PRON
ejpam-6073	248	9	2	2	NUM
ejpam-6073	248	10	2	2	NUM
ejpam-6073	248	11	)	)	PUNCT
ejpam-6073	249	1	+	+	CCONJ
ejpam-6073	249	2	ε	ε	PROPN
ejpam-6073	249	3	∫	∫	PROPN
ejpam-6073	249	4	tk	tk	PROPN
ejpam-6073	249	5	0	0	PROPN
ejpam-6073	250	1	(	(	PUNCT
ejpam-6073	250	2	ρu	ρu	INTJ
ejpam-6073	250	3	∥∥∥ukt	∥∥∥ukt	ADV
ejpam-6073	250	4	∥∥∥2	∥∥∥2	NOUN
ejpam-6073	250	5	2	2	NUM
ejpam-6073	250	6	+	+	NUM
ejpam-6073	250	7	ρz	ρz	NOUN
ejpam-6073	250	8	∥∥∥zkt	∥∥∥zkt	X
ejpam-6073	250	9	∥∥∥2	∥∥∥2	NOUN
ejpam-6073	250	10	2	2	NUM
ejpam-6073	250	11	)	)	PUNCT
ejpam-6073	250	12	ds+	ds+	PROPN
ejpam-6073	251	1	cε	cε	PROPN
ejpam-6073	251	2	∫	∫	PROPN
ejpam-6073	252	1	tk	tk	PROPN
ejpam-6073	252	2	0	0	PROPN
ejpam-6073	252	3	∫	∫	PROPN
ejpam-6073	252	4	ω	ω	PROPN
ejpam-6073	252	5	(	(	PUNCT
ejpam-6073	252	6	|f(x	|f(x	PROPN
ejpam-6073	252	7	,	,	PUNCT
ejpam-6073	252	8	t)|2	t)|2	NOUN
ejpam-6073	252	9	+	+	CCONJ
ejpam-6073	252	10	|g(x	|g(x	NOUN
ejpam-6073	252	11	,	,	PUNCT
ejpam-6073	252	12	t)|2	t)|2	ADJ
ejpam-6073	252	13	)	)	PUNCT
ejpam-6073	252	14	dxds	dxds	NOUN
ejpam-6073	252	15	.	.	PUNCT
ejpam-6073	253	1	(	(	PUNCT
ejpam-6073	253	2	31	31	NUM
ejpam-6073	253	3	)	)	PUNCT
ejpam-6073	253	4	using	use	VERB
ejpam-6073	253	5	(	(	PUNCT
ejpam-6073	253	6	22	22	NUM
ejpam-6073	253	7	)	)	PUNCT
ejpam-6073	253	8	and	and	CCONJ
ejpam-6073	253	9	recalling	recall	VERB
ejpam-6073	253	10	that	that	PRON
ejpam-6073	253	11	f	f	NOUN
ejpam-6073	253	12	,	,	PUNCT
ejpam-6073	253	13	g	g	PROPN
ejpam-6073	253	14	∈	∈	PROPN
ejpam-6073	253	15	l2(ω×	l2(ω×	NOUN
ejpam-6073	253	16	(	(	PUNCT
ejpam-6073	253	17	0	0	NUM
ejpam-6073	253	18	,	,	PUNCT
ejpam-6073	253	19	t	t	NOUN
ejpam-6073	253	20	)	)	PUNCT
ejpam-6073	253	21	)	)	PUNCT
ejpam-6073	253	22	,	,	PUNCT
ejpam-6073	253	23	we	we	PRON
ejpam-6073	253	24	have	have	VERB
ejpam-6073	253	25	zk0	zk0	NOUN
ejpam-6073	253	26	−→	−→	ADJ
ejpam-6073	253	27	z0	z0	NOUN
ejpam-6073	253	28	and	and	CCONJ
ejpam-6073	253	29	uk0	uk0	ADJ
ejpam-6073	253	30	−→	−→	NOUN
ejpam-6073	253	31	u0	u0	ADJ
ejpam-6073	253	32	in	in	ADP
ejpam-6073	253	33	h1	h1	PROPN
ejpam-6073	253	34	0	0	NUM
ejpam-6073	253	35	(	(	PUNCT
ejpam-6073	253	36	ω	ω	NOUN
ejpam-6073	253	37	)	)	PUNCT
ejpam-6073	253	38	,	,	PUNCT
ejpam-6073	253	39	zk1	zk1	X
ejpam-6073	253	40	−→	−→	NOUN
ejpam-6073	253	41	z1	z1	NOUN
ejpam-6073	253	42	and	and	CCONJ
ejpam-6073	253	43	uk1	uk1	NOUN
ejpam-6073	253	44	−→	−→	ADJ
ejpam-6073	253	45	u1	u1	NOUN
ejpam-6073	253	46	in	in	ADP
ejpam-6073	253	47	l2(ω	l2(ω	PROPN
ejpam-6073	253	48	)	)	PUNCT
ejpam-6073	253	49	and	and	CCONJ
ejpam-6073	253	50	appling	apple	VERB
ejpam-6073	253	51	gronwall	gronwall	PROPN
ejpam-6073	253	52	’s	’s	PART
ejpam-6073	253	53	lemma	lemma	PROPN
ejpam-6073	253	54	,	,	PUNCT
ejpam-6073	253	55	estimate	estimate	NOUN
ejpam-6073	253	56	(	(	PUNCT
ejpam-6073	253	57	31	31	NUM
ejpam-6073	253	58	)	)	PUNCT
ejpam-6073	253	59	becomes	become	VERB
ejpam-6073	253	60	,	,	PUNCT
ejpam-6073	253	61	for	for	ADP
ejpam-6073	253	62	some	some	DET
ejpam-6073	253	63	c	c	PROPN
ejpam-6073	253	64	>	>	X
ejpam-6073	253	65	0	0	PROPN
ejpam-6073	253	66	,	,	PUNCT
ejpam-6073	253	67	c	c	NOUN
ejpam-6073	253	68	sup	sup	NOUN
ejpam-6073	253	69	(	(	PUNCT
ejpam-6073	253	70	0,tk	0,tk	NOUN
ejpam-6073	253	71	)	)	PUNCT
ejpam-6073	253	72	[	[	PUNCT
ejpam-6073	253	73	||zkt	||zkt	NOUN
ejpam-6073	253	74	||	||	NOUN
ejpam-6073	253	75	2	2	NUM
ejpam-6073	253	76	2	2	NUM
ejpam-6073	253	77	+	+	CCONJ
ejpam-6073	253	78	||ukt	||ukt	ADV
ejpam-6073	253	79	||	||	NOUN
ejpam-6073	253	80	2	2	NUM
ejpam-6073	253	81	2	2	NUM
ejpam-6073	253	82	+	+	CCONJ
ejpam-6073	253	83	||zkx||	||zkx||	X
ejpam-6073	253	84	2	2	NUM
ejpam-6073	253	85	2	2	NUM
ejpam-6073	253	86	+	+	CCONJ
ejpam-6073	253	87	||ukx||	||ukx||	NUM
ejpam-6073	253	88	2	2	NUM
ejpam-6073	253	89	2	2	NUM
ejpam-6073	253	90	]	]	PUNCT
ejpam-6073	253	91	a.	a.	NOUN
ejpam-6073	253	92	m.	m.	PROPN
ejpam-6073	253	93	al	al	PROPN
ejpam-6073	253	94	-	-	PROPN
ejpam-6073	253	95	mahdi	mahdi	PROPN
ejpam-6073	253	96	et	et	PROPN
ejpam-6073	253	97	al	al	PROPN
ejpam-6073	253	98	.	.	PUNCT
ejpam-6073	253	99	/	/	SYM
ejpam-6073	253	100	eur	eur	PROPN
ejpam-6073	253	101	.	.	PUNCT
ejpam-6073	254	1	j.	j.	PROPN
ejpam-6073	254	2	pure	pure	PROPN
ejpam-6073	254	3	appl	appl	PROPN
ejpam-6073	254	4	.	.	PROPN
ejpam-6073	254	5	math	math	PROPN
ejpam-6073	254	6	,	,	PUNCT
ejpam-6073	254	7	18	18	NUM
ejpam-6073	254	8	(	(	PUNCT
ejpam-6073	254	9	3	3	NUM
ejpam-6073	254	10	)	)	PUNCT
ejpam-6073	254	11	(	(	PUNCT
ejpam-6073	254	12	2025	2025	NUM
ejpam-6073	254	13	)	)	PUNCT
ejpam-6073	254	14	,	,	PUNCT
ejpam-6073	254	15	6073	6073	NUM
ejpam-6073	254	16	12	12	NUM
ejpam-6073	254	17	of	of	ADP
ejpam-6073	254	18	29	29	NUM
ejpam-6073	254	19	+	+	CCONJ
ejpam-6073	254	20	∫	∫	PROPN
ejpam-6073	254	21	tk	tk	PROPN
ejpam-6073	254	22	0	0	PROPN
ejpam-6073	254	23	∫	∫	PROPN
ejpam-6073	254	24	ω	ω	PROPN
ejpam-6073	254	25	(	(	PUNCT
ejpam-6073	254	26	γ	γ	X
ejpam-6073	254	27	∣∣∣zkt	∣∣∣zkt	PROPN
ejpam-6073	254	28	(	(	PUNCT
ejpam-6073	254	29	x	x	X
ejpam-6073	254	30	,	,	PUNCT
ejpam-6073	254	31	t)∣∣∣p(x	t)∣∣∣p(x	PROPN
ejpam-6073	254	32	)	)	PUNCT
ejpam-6073	255	1	+	+	CCONJ
ejpam-6073	255	2	β	β	X
ejpam-6073	255	3	∣∣∣ukt	∣∣∣ukt	PROPN
ejpam-6073	255	4	(	(	PUNCT
ejpam-6073	255	5	x	x	X
ejpam-6073	255	6	,	,	PUNCT
ejpam-6073	255	7	t)∣∣∣q(x	t)∣∣∣q(x	PROPN
ejpam-6073	255	8	)	)	PUNCT
ejpam-6073	255	9	)	)	PUNCT
ejpam-6073	256	1	dxds	dxds	NOUN
ejpam-6073	256	2	≤	≤	NUM
ejpam-6073	256	3	cε	cε	VERB
ejpam-6073	257	1	+	+	CCONJ
ejpam-6073	257	2	εt	εt	INTJ
ejpam-6073	257	3	sup	sup	PROPN
ejpam-6073	257	4	(	(	PUNCT
ejpam-6073	257	5	0,tk	0,tk	NOUN
ejpam-6073	257	6	)	)	PUNCT
ejpam-6073	257	7	(	(	PUNCT
ejpam-6073	257	8	ρu	ρu	ADV
ejpam-6073	257	9	∥∥∥ukt	∥∥∥ukt	ADV
ejpam-6073	257	10	∥∥∥2	∥∥∥2	NOUN
ejpam-6073	257	11	2	2	NUM
ejpam-6073	257	12	+	+	NUM
ejpam-6073	257	13	ρz	ρz	NOUN
ejpam-6073	257	14	∥∥∥zkt	∥∥∥zkt	X
ejpam-6073	257	15	∥∥∥2	∥∥∥2	NOUN
ejpam-6073	257	16	2	2	NUM
ejpam-6073	257	17	)	)	PUNCT
ejpam-6073	257	18	∀tk	∀tk	PROPN
ejpam-6073	257	19	≤	≤	PROPN
ejpam-6073	257	20	t	t	PROPN
ejpam-6073	257	21	,	,	PUNCT
ejpam-6073	257	22	k	k	PROPN
ejpam-6073	257	23	≥	≥	NUM
ejpam-6073	257	24	1	1	X
ejpam-6073	257	25	.	.	PUNCT
ejpam-6073	257	26	choosing	choose	VERB
ejpam-6073	257	27	ε	ε	PROPN
ejpam-6073	257	28	=	=	SYM
ejpam-6073	257	29	1	1	NUM
ejpam-6073	257	30	4	4	NUM
ejpam-6073	257	31	t	t	NOUN
ejpam-6073	257	32	,	,	PUNCT
ejpam-6073	257	33	we	we	PRON
ejpam-6073	257	34	find	find	VERB
ejpam-6073	257	35	sup	sup	NOUN
ejpam-6073	257	36	(	(	PUNCT
ejpam-6073	257	37	0,tk	0,tk	NOUN
ejpam-6073	257	38	)	)	PUNCT
ejpam-6073	257	39	[	[	PUNCT
ejpam-6073	257	40	||zkt	||zkt	NOUN
ejpam-6073	257	41	||	||	NOUN
ejpam-6073	257	42	2	2	NUM
ejpam-6073	257	43	2	2	NUM
ejpam-6073	257	44	+	+	CCONJ
ejpam-6073	257	45	||ukt	||ukt	ADV
ejpam-6073	257	46	||	||	NOUN
ejpam-6073	257	47	2	2	NUM
ejpam-6073	257	48	2	2	NUM
ejpam-6073	257	49	+	+	CCONJ
ejpam-6073	257	50	||zkx||	||zkx||	X
ejpam-6073	257	51	2	2	NUM
ejpam-6073	257	52	2	2	NUM
ejpam-6073	257	53	+	+	CCONJ
ejpam-6073	257	54	||ukx||	||ukx||	NUM
ejpam-6073	257	55	2	2	NUM
ejpam-6073	257	56	2	2	NUM
ejpam-6073	257	57	]	]	PUNCT
ejpam-6073	257	58	≤	≤	NUM
ejpam-6073	257	59	c.	c.	NOUN
ejpam-6073	257	60	therefore	therefore	ADV
ejpam-6073	257	61	,	,	PUNCT
ejpam-6073	257	62	the	the	DET
ejpam-6073	257	63	local	local	ADJ
ejpam-6073	257	64	solution	solution	NOUN
ejpam-6073	257	65	(	(	PUNCT
ejpam-6073	257	66	zk	zk	PROPN
ejpam-6073	257	67	,	,	PUNCT
ejpam-6073	257	68	uk	uk	PROPN
ejpam-6073	257	69	)	)	PUNCT
ejpam-6073	257	70	of	of	ADP
ejpam-6073	257	71	system	system	NOUN
ejpam-6073	257	72	(	(	PUNCT
ejpam-6073	257	73	27	27	NUM
ejpam-6073	257	74	)	)	PUNCT
ejpam-6073	257	75	can	can	AUX
ejpam-6073	257	76	be	be	AUX
ejpam-6073	257	77	extended	extend	VERB
ejpam-6073	257	78	to	to	ADP
ejpam-6073	257	79	(	(	PUNCT
ejpam-6073	257	80	0	0	NUM
ejpam-6073	257	81	,	,	PUNCT
ejpam-6073	257	82	t	t	NOUN
ejpam-6073	257	83	)	)	PUNCT
ejpam-6073	257	84	,	,	PUNCT
ejpam-6073	257	85	for	for	ADP
ejpam-6073	257	86	all	all	DET
ejpam-6073	257	87	k	k	PROPN
ejpam-6073	257	88	≥	≥	NUM
ejpam-6073	257	89	1	1	NUM
ejpam-6073	257	90	.	.	PUNCT
ejpam-6073	258	1	furthermore	furthermore	ADV
ejpam-6073	258	2	,	,	PUNCT
ejpam-6073	258	3	we	we	PRON
ejpam-6073	258	4	have	have	VERB
ejpam-6073	258	5	(	(	PUNCT
ejpam-6073	258	6	zk	zk	PROPN
ejpam-6073	258	7	)	)	PUNCT
ejpam-6073	258	8	,	,	PUNCT
ejpam-6073	258	9	(	(	PUNCT
ejpam-6073	258	10	uk	uk	PROPN
ejpam-6073	258	11	)	)	PUNCT
ejpam-6073	258	12	are	be	AUX
ejpam-6073	258	13	bounded	bound	VERB
ejpam-6073	258	14	in	in	ADP
ejpam-6073	258	15	l∞((0	l∞((0	PROPN
ejpam-6073	258	16	,	,	PUNCT
ejpam-6073	258	17	t	t	PROPN
ejpam-6073	258	18	)	)	PUNCT
ejpam-6073	258	19	,	,	PUNCT
ejpam-6073	258	20	h1	h1	PROPN
ejpam-6073	258	21	0	0	NUM
ejpam-6073	258	22	(	(	PUNCT
ejpam-6073	258	23	ω	ω	NOUN
ejpam-6073	258	24	)	)	PUNCT
ejpam-6073	258	25	)	)	PUNCT
ejpam-6073	258	26	,	,	PUNCT
ejpam-6073	258	27	(	(	PUNCT
ejpam-6073	258	28	zkt	zkt	PROPN
ejpam-6073	258	29	)	)	PUNCT
ejpam-6073	258	30	is	be	AUX
ejpam-6073	258	31	bounded	bound	VERB
ejpam-6073	258	32	in	in	ADP
ejpam-6073	258	33	l∞((0	l∞((0	PROPN
ejpam-6073	258	34	,	,	PUNCT
ejpam-6073	258	35	t	t	PROPN
ejpam-6073	258	36	)	)	PUNCT
ejpam-6073	258	37	,	,	PUNCT
ejpam-6073	258	38	l2(ω	l2(ω	NOUN
ejpam-6073	258	39	)	)	PUNCT
ejpam-6073	258	40	)	)	PUNCT
ejpam-6073	258	41	∩	∩	NOUN
ejpam-6073	258	42	lp(.)(ω×	lp(.)(ω×	PROPN
ejpam-6073	258	43	(	(	PUNCT
ejpam-6073	258	44	0	0	NUM
ejpam-6073	258	45	,	,	PUNCT
ejpam-6073	258	46	t	t	NOUN
ejpam-6073	258	47	)	)	PUNCT
ejpam-6073	258	48	)	)	PUNCT
ejpam-6073	258	49	,	,	PUNCT
ejpam-6073	258	50	(	(	PUNCT
ejpam-6073	258	51	ukt	ukt	VERB
ejpam-6073	258	52	)	)	PUNCT
ejpam-6073	258	53	is	be	AUX
ejpam-6073	258	54	bounded	bound	VERB
ejpam-6073	258	55	in	in	ADP
ejpam-6073	258	56	l∞((0	l∞((0	PROPN
ejpam-6073	258	57	,	,	PUNCT
ejpam-6073	258	58	t	t	PROPN
ejpam-6073	258	59	)	)	PUNCT
ejpam-6073	258	60	,	,	PUNCT
ejpam-6073	258	61	l2(ω	l2(ω	NOUN
ejpam-6073	258	62	)	)	PUNCT
ejpam-6073	258	63	)	)	PUNCT
ejpam-6073	258	64	∩	∩	NOUN
ejpam-6073	258	65	lq(.)(ω×	lq(.)(ω×	PROPN
ejpam-6073	258	66	(	(	PUNCT
ejpam-6073	258	67	0	0	NUM
ejpam-6073	258	68	,	,	PUNCT
ejpam-6073	258	69	t	t	NOUN
ejpam-6073	258	70	)	)	PUNCT
ejpam-6073	258	71	)	)	PUNCT
ejpam-6073	258	72	.	.	PUNCT
ejpam-6073	259	1	consequently	consequently	ADV
ejpam-6073	259	2	,	,	PUNCT
ejpam-6073	259	3	we	we	PRON
ejpam-6073	259	4	have	have	AUX
ejpam-6073	259	5	,	,	PUNCT
ejpam-6073	259	6	up	up	ADP
ejpam-6073	259	7	to	to	PART
ejpam-6073	259	8	two	two	NUM
ejpam-6073	259	9	subsequences	subsequence	NOUN
ejpam-6073	259	10	,	,	PUNCT
ejpam-6073	259	11	zk	zk	PROPN
ejpam-6073	259	12	→	→	SYM
ejpam-6073	259	13	z	z	PROPN
ejpam-6073	259	14	and	and	CCONJ
ejpam-6073	259	15	uk	uk	PROPN
ejpam-6073	259	16	→	→	SYM
ejpam-6073	259	17	u	u	NOUN
ejpam-6073	259	18	weakly	weakly	ADJ
ejpam-6073	259	19	*	*	PUNCT
ejpam-6073	259	20	in	in	ADP
ejpam-6073	259	21	l∞((0	l∞((0	PROPN
ejpam-6073	259	22	,	,	PUNCT
ejpam-6073	259	23	t	t	PROPN
ejpam-6073	259	24	)	)	PUNCT
ejpam-6073	259	25	,	,	PUNCT
ejpam-6073	259	26	h1	h1	PROPN
ejpam-6073	259	27	0	0	NUM
ejpam-6073	259	28	(	(	PUNCT
ejpam-6073	259	29	ω	ω	NOUN
ejpam-6073	259	30	)	)	PUNCT
ejpam-6073	259	31	)	)	PUNCT
ejpam-6073	259	32	,	,	PUNCT
ejpam-6073	259	33	zkt	zkt	PROPN
ejpam-6073	259	34	→	→	SYM
ejpam-6073	259	35	zt	zt	PROPN
ejpam-6073	259	36	weakly	weakly	ADV
ejpam-6073	259	37	*	*	PUNCT
ejpam-6073	259	38	in	in	ADP
ejpam-6073	259	39	l∞((0	l∞((0	PROPN
ejpam-6073	259	40	,	,	PUNCT
ejpam-6073	259	41	t	t	PROPN
ejpam-6073	259	42	)	)	PUNCT
ejpam-6073	259	43	,	,	PUNCT
ejpam-6073	259	44	l2(ω	l2(ω	NOUN
ejpam-6073	259	45	)	)	PUNCT
ejpam-6073	259	46	)	)	PUNCT
ejpam-6073	259	47	and	and	CCONJ
ejpam-6073	259	48	weakly	weakly	ADV
ejpam-6073	259	49	in	in	ADP
ejpam-6073	259	50	lp(.)(ω×	lp(.)(ω×	PROPN
ejpam-6073	259	51	(	(	PUNCT
ejpam-6073	259	52	0	0	NUM
ejpam-6073	259	53	,	,	PUNCT
ejpam-6073	259	54	t	t	NOUN
ejpam-6073	259	55	)	)	PUNCT
ejpam-6073	259	56	)	)	PUNCT
ejpam-6073	259	57	,	,	PUNCT
ejpam-6073	259	58	ukt	ukt	VERB
ejpam-6073	259	59	→	→	SYM
ejpam-6073	259	60	ut	ut	X
ejpam-6073	259	61	weakly	weakly	ADJ
ejpam-6073	259	62	*	*	PUNCT
ejpam-6073	259	63	in	in	ADP
ejpam-6073	259	64	l∞((0	l∞((0	PROPN
ejpam-6073	259	65	,	,	PUNCT
ejpam-6073	259	66	t	t	PROPN
ejpam-6073	259	67	)	)	PUNCT
ejpam-6073	259	68	,	,	PUNCT
ejpam-6073	259	69	l2(ω	l2(ω	NOUN
ejpam-6073	259	70	)	)	PUNCT
ejpam-6073	259	71	)	)	PUNCT
ejpam-6073	259	72	and	and	CCONJ
ejpam-6073	259	73	weakly	weakly	ADV
ejpam-6073	259	74	in	in	ADP
ejpam-6073	259	75	lq(.)(ω×	lq(.)(ω×	PROPN
ejpam-6073	259	76	(	(	PUNCT
ejpam-6073	259	77	0	0	NUM
ejpam-6073	259	78	,	,	PUNCT
ejpam-6073	259	79	t	t	NOUN
ejpam-6073	259	80	)	)	PUNCT
ejpam-6073	259	81	)	)	PUNCT
ejpam-6073	259	82	.	.	PUNCT
ejpam-6073	260	1	step	step	NOUN
ejpam-6073	260	2	3	3	NUM
ejpam-6073	260	3	.	.	PUNCT
ejpam-6073	261	1	the	the	DET
ejpam-6073	261	2	nonlinear	nonlinear	ADJ
ejpam-6073	261	3	terms	term	NOUN
ejpam-6073	261	4	:	:	PUNCT
ejpam-6073	261	5	in	in	ADP
ejpam-6073	261	6	this	this	DET
ejpam-6073	261	7	step	step	NOUN
ejpam-6073	261	8	,	,	PUNCT
ejpam-6073	261	9	we	we	PRON
ejpam-6073	261	10	show	show	VERB
ejpam-6073	261	11	that	that	SCONJ
ejpam-6073	261	12	|	|	ADV
ejpam-6073	261	13	zkt	zkt	X
ejpam-6073	261	14	|p(.)−2	|p(.)−2	NOUN
ejpam-6073	261	15	zkt	zkt	NOUN
ejpam-6073	261	16	→	→	PUNCT
ejpam-6073	261	17	|	|	ADV
ejpam-6073	261	18	zt	zt	PROPN
ejpam-6073	261	19	|p(.)−2	|p(.)−2	NOUN
ejpam-6073	261	20	zt	zt	X
ejpam-6073	261	21	weakly	weakly	ADJ
ejpam-6073	261	22	in	in	ADP
ejpam-6073	261	23	l	l	PROPN
ejpam-6073	261	24	p	p	X
ejpam-6073	261	25	(	(	PUNCT
ejpam-6073	261	26	.	.	PUNCT
ejpam-6073	261	27	)	)	PUNCT
ejpam-6073	261	28	p(.)−1	p(.)−1	NOUN
ejpam-6073	261	29	(	(	PUNCT
ejpam-6073	261	30	ω×	ω×	X
ejpam-6073	261	31	(	(	PUNCT
ejpam-6073	261	32	0	0	NUM
ejpam-6073	261	33	,	,	PUNCT
ejpam-6073	261	34	t	t	NOUN
ejpam-6073	261	35	)	)	PUNCT
ejpam-6073	261	36	)	)	PUNCT
ejpam-6073	261	37	,	,	PUNCT
ejpam-6073	261	38	|	|	ADV
ejpam-6073	261	39	ukt	ukt	VERB
ejpam-6073	261	40	|q(.)−2	|q(.)−2	ADV
ejpam-6073	261	41	ukt	ukt	ADJ
ejpam-6073	261	42	→	→	SYM
ejpam-6073	261	43	|	|	ADV
ejpam-6073	261	44	ut	ut	PROPN
ejpam-6073	261	45	|q(.)−2	|q(.)−2	PROPN
ejpam-6073	261	46	ut	ut	X
ejpam-6073	261	47	weakly	weakly	ADV
ejpam-6073	261	48	in	in	ADP
ejpam-6073	261	49	l	l	PROPN
ejpam-6073	261	50	q	q	X
ejpam-6073	261	51	(	(	PUNCT
ejpam-6073	261	52	.	.	PUNCT
ejpam-6073	261	53	)	)	PUNCT
ejpam-6073	262	1	q(.)−1	q(.)−1	PROPN
ejpam-6073	262	2	(	(	PUNCT
ejpam-6073	262	3	ω×	ω×	X
ejpam-6073	262	4	(	(	PUNCT
ejpam-6073	262	5	0	0	NUM
ejpam-6073	262	6	,	,	PUNCT
ejpam-6073	262	7	t	t	NOUN
ejpam-6073	262	8	)	)	PUNCT
ejpam-6073	262	9	)	)	PUNCT
ejpam-6073	262	10	and	and	CCONJ
ejpam-6073	262	11	that	that	SCONJ
ejpam-6073	262	12	(	(	PUNCT
ejpam-6073	262	13	z	z	X
ejpam-6073	262	14	,	,	PUNCT
ejpam-6073	262	15	u	u	NOUN
ejpam-6073	262	16	)	)	PUNCT
ejpam-6073	262	17	satisfies	satisfy	VERB
ejpam-6073	262	18	the	the	DET
ejpam-6073	262	19	partial	partial	ADJ
ejpam-6073	262	20	differential	differential	ADJ
ejpam-6073	262	21	equations	equation	NOUN
ejpam-6073	262	22	of	of	ADP
ejpam-6073	262	23	(	(	PUNCT
ejpam-6073	262	24	q	q	NOUN
ejpam-6073	262	25	)	)	PUNCT
ejpam-6073	262	26	on	on	ADP
ejpam-6073	262	27	ω×	ω×	PROPN
ejpam-6073	262	28	(	(	PUNCT
ejpam-6073	262	29	0	0	NUM
ejpam-6073	262	30	,	,	PUNCT
ejpam-6073	262	31	t	t	NOUN
ejpam-6073	262	32	)	)	PUNCT
ejpam-6073	262	33	.	.	PUNCT
ejpam-6073	263	1	since	since	SCONJ
ejpam-6073	263	2	(	(	PUNCT
ejpam-6073	263	3	zkt	zkt	PROPN
ejpam-6073	263	4	)	)	PUNCT
ejpam-6073	263	5	is	be	AUX
ejpam-6073	263	6	bounded	bound	VERB
ejpam-6073	263	7	in	in	ADP
ejpam-6073	263	8	lp(.)(ω	lp(.)(ω	PROPN
ejpam-6073	263	9	×	×	NOUN
ejpam-6073	263	10	(	(	PUNCT
ejpam-6073	263	11	0	0	NUM
ejpam-6073	263	12	,	,	PUNCT
ejpam-6073	263	13	t	t	NOUN
ejpam-6073	263	14	)	)	PUNCT
ejpam-6073	263	15	)	)	PUNCT
ejpam-6073	263	16	,	,	PUNCT
ejpam-6073	263	17	then	then	ADV
ejpam-6073	263	18	(	(	PUNCT
ejpam-6073	263	19	|zkt	|zkt	INTJ
ejpam-6073	263	20	|	|	ADV
ejpam-6073	263	21	p(.)−2	p(.)−2	VERB
ejpam-6073	263	22	zkt	zkt	NOUN
ejpam-6073	263	23	)	)	PUNCT
ejpam-6073	263	24	is	be	AUX
ejpam-6073	263	25	bounded	bound	VERB
ejpam-6073	263	26	in	in	ADP
ejpam-6073	263	27	l	l	PROPN
ejpam-6073	263	28	p	p	X
ejpam-6073	263	29	(	(	PUNCT
ejpam-6073	263	30	.	.	PUNCT
ejpam-6073	263	31	)	)	PUNCT
ejpam-6073	263	32	p(.)−1	p(.)−1	NOUN
ejpam-6073	263	33	(	(	PUNCT
ejpam-6073	263	34	ω	ω	NUM
ejpam-6073	263	35	×	×	NOUN
ejpam-6073	263	36	(	(	PUNCT
ejpam-6073	263	37	0	0	NUM
ejpam-6073	263	38	,	,	PUNCT
ejpam-6073	263	39	t	t	NOUN
ejpam-6073	263	40	)	)	PUNCT
ejpam-6073	263	41	)	)	PUNCT
ejpam-6073	263	42	.	.	PUNCT
ejpam-6073	264	1	hence	hence	ADV
ejpam-6073	264	2	,	,	PUNCT
ejpam-6073	264	3	up	up	ADP
ejpam-6073	264	4	to	to	ADP
ejpam-6073	264	5	a	a	DET
ejpam-6073	264	6	subsequence	subsequence	NOUN
ejpam-6073	264	7	,	,	PUNCT
ejpam-6073	264	8	|zkt	|zkt	PUNCT
ejpam-6073	264	9	|	|	ADV
ejpam-6073	264	10	p(.)−2	p(.)−2	VERB
ejpam-6073	264	11	zkt	zkt	NOUN
ejpam-6073	264	12	⇀	⇀	SYM
ejpam-6073	264	13	χ1	χ1	NOUN
ejpam-6073	264	14	in	in	ADP
ejpam-6073	264	15	l	l	NOUN
ejpam-6073	264	16	p	p	X
ejpam-6073	264	17	(	(	PUNCT
ejpam-6073	264	18	.	.	PUNCT
ejpam-6073	264	19	)	)	PUNCT
ejpam-6073	265	1	p(.)−1	p(.)−1	NOUN
ejpam-6073	265	2	(	(	PUNCT
ejpam-6073	265	3	ω×	ω×	X
ejpam-6073	265	4	(	(	PUNCT
ejpam-6073	265	5	0	0	NUM
ejpam-6073	265	6	,	,	PUNCT
ejpam-6073	265	7	t	t	NOUN
ejpam-6073	265	8	)	)	PUNCT
ejpam-6073	265	9	)	)	PUNCT
ejpam-6073	265	10	.	.	PUNCT
ejpam-6073	266	1	(	(	PUNCT
ejpam-6073	266	2	32	32	NUM
ejpam-6073	266	3	)	)	PUNCT
ejpam-6073	266	4	similarly	similarly	ADV
ejpam-6073	266	5	,	,	PUNCT
ejpam-6073	266	6	we	we	PRON
ejpam-6073	266	7	have	have	VERB
ejpam-6073	266	8	|ukt	|ukt	ADV
ejpam-6073	266	9	|	|	ADV
ejpam-6073	266	10	q(.)−2	q(.)−2	ADV
ejpam-6073	266	11	ukt	ukt	VERB
ejpam-6073	266	12	⇀	⇀	VERB
ejpam-6073	266	13	χ2	χ2	NOUN
ejpam-6073	266	14	in	in	ADP
ejpam-6073	266	15	l	l	PROPN
ejpam-6073	266	16	q	q	PROPN
ejpam-6073	266	17	(	(	PUNCT
ejpam-6073	266	18	.	.	PUNCT
ejpam-6073	266	19	)	)	PUNCT
ejpam-6073	267	1	q(.)−1	q(.)−1	PROPN
ejpam-6073	267	2	(	(	PUNCT
ejpam-6073	267	3	ω×	ω×	X
ejpam-6073	267	4	(	(	PUNCT
ejpam-6073	267	5	0	0	NUM
ejpam-6073	267	6	,	,	PUNCT
ejpam-6073	267	7	t	t	NOUN
ejpam-6073	267	8	)	)	PUNCT
ejpam-6073	267	9	)	)	PUNCT
ejpam-6073	267	10	.	.	PUNCT
ejpam-6073	268	1	(	(	PUNCT
ejpam-6073	268	2	33	33	NUM
ejpam-6073	268	3	)	)	PUNCT
ejpam-6073	268	4	a.	a.	NOUN
ejpam-6073	268	5	m.	m.	PROPN
ejpam-6073	268	6	al	al	PROPN
ejpam-6073	268	7	-	-	PROPN
ejpam-6073	268	8	mahdi	mahdi	PROPN
ejpam-6073	268	9	et	et	PROPN
ejpam-6073	268	10	al	al	PROPN
ejpam-6073	268	11	.	.	PUNCT
ejpam-6073	268	12	/	/	SYM
ejpam-6073	268	13	eur	eur	PROPN
ejpam-6073	268	14	.	.	PUNCT
ejpam-6073	269	1	j.	j.	PROPN
ejpam-6073	269	2	pure	pure	PROPN
ejpam-6073	269	3	appl	appl	PROPN
ejpam-6073	269	4	.	.	PROPN
ejpam-6073	269	5	math	math	PROPN
ejpam-6073	269	6	,	,	PUNCT
ejpam-6073	269	7	18	18	NUM
ejpam-6073	269	8	(	(	PUNCT
ejpam-6073	269	9	3	3	NUM
ejpam-6073	269	10	)	)	PUNCT
ejpam-6073	269	11	(	(	PUNCT
ejpam-6073	269	12	2025	2025	NUM
ejpam-6073	269	13	)	)	PUNCT
ejpam-6073	269	14	,	,	PUNCT
ejpam-6073	269	15	6073	6073	NUM
ejpam-6073	269	16	13	13	NUM
ejpam-6073	269	17	of	of	ADP
ejpam-6073	269	18	29	29	NUM
ejpam-6073	269	19	we	we	PRON
ejpam-6073	269	20	can	can	AUX
ejpam-6073	269	21	show	show	VERB
ejpam-6073	269	22	that	that	DET
ejpam-6073	269	23	χ1	χ1	NOUN
ejpam-6073	269	24	=	=	SYM
ejpam-6073	269	25	|zt|p(.)−2zt	|zt|p(.)−2zt	PROPN
ejpam-6073	269	26	and	and	CCONJ
ejpam-6073	269	27	χ2	χ2	NOUN
ejpam-6073	269	28	=	=	SYM
ejpam-6073	269	29	|ut|q(.)−2ut	|ut|q(.)−2ut	PROPN
ejpam-6073	269	30	by	by	ADP
ejpam-6073	269	31	following	follow	VERB
ejpam-6073	269	32	the	the	DET
ejpam-6073	269	33	same	same	ADJ
ejpam-6073	269	34	steps	step	NOUN
ejpam-6073	269	35	as	as	ADP
ejpam-6073	269	36	in	in	ADP
ejpam-6073	269	37	[	[	X
ejpam-6073	269	38	34	34	NUM
ejpam-6073	269	39	]	]	PUNCT
ejpam-6073	269	40	.	.	PUNCT
ejpam-6073	270	1	now	now	ADV
ejpam-6073	270	2	,	,	PUNCT
ejpam-6073	270	3	integrate	integrate	VERB
ejpam-6073	270	4	(	(	PUNCT
ejpam-6073	270	5	27	27	NUM
ejpam-6073	270	6	)	)	PUNCT
ejpam-6073	270	7	on	on	ADP
ejpam-6073	270	8	(	(	PUNCT
ejpam-6073	270	9	0	0	NUM
ejpam-6073	270	10	,	,	PUNCT
ejpam-6073	270	11	t	t	PROPN
ejpam-6073	270	12	)	)	PUNCT
ejpam-6073	270	13	to	to	PART
ejpam-6073	270	14	obtain	obtain	VERB
ejpam-6073	270	15	∀j	∀j	NOUN
ejpam-6073	270	16	<	<	X
ejpam-6073	270	17	k,∫	k,∫	NOUN
ejpam-6073	270	18	ω	ω	NUM
ejpam-6073	270	19	zkt	zkt	PROPN
ejpam-6073	271	1	wj(x)dx−	wj(x)dx−	PROPN
ejpam-6073	271	2	∫	∫	PROPN
ejpam-6073	271	3	ω	ω	PROPN
ejpam-6073	271	4	zk1wj(x)dx+	zk1wj(x)dx+	PROPN
ejpam-6073	271	5	a1	a1	PROPN
ejpam-6073	271	6	∫	∫	PROPN
ejpam-6073	271	7	t	t	PROPN
ejpam-6073	271	8	0	0	NUM
ejpam-6073	271	9	∫	∫	PROPN
ejpam-6073	271	10	ω	ω	PROPN
ejpam-6073	271	11	zkxwjx(x)dxds+	zkxwjx(x)dxds+	PROPN
ejpam-6073	271	12	a2	a2	PROPN
ejpam-6073	271	13	∫	∫	PROPN
ejpam-6073	271	14	t	t	PROPN
ejpam-6073	271	15	0	0	NUM
ejpam-6073	271	16	∫	∫	PROPN
ejpam-6073	271	17	ω	ω	NUM
ejpam-6073	271	18	ukxwjx(x)dxds	ukxwjx(x)dxds	PUNCT
ejpam-6073	271	19	+	+	CCONJ
ejpam-6073	271	20	γ	γ	PROPN
ejpam-6073	271	21	∫	∫	PROPN
ejpam-6073	271	22	t	t	PROPN
ejpam-6073	271	23	0	0	NUM
ejpam-6073	271	24	∫	∫	PROPN
ejpam-6073	271	25	ω	ω	NUM
ejpam-6073	271	26	|zkt	|zkt	PROPN
ejpam-6073	271	27	|	|	ADV
ejpam-6073	271	28	p(.)−2	p(.)−2	ADV
ejpam-6073	271	29	zkt	zkt	NOUN
ejpam-6073	271	30	wj(x)dxds	wj(x)dxds	X
ejpam-6073	272	1	=	=	SYM
ejpam-6073	272	2	∫	∫	PROPN
ejpam-6073	272	3	t	t	PROPN
ejpam-6073	272	4	0	0	NUM
ejpam-6073	272	5	∫	∫	PROPN
ejpam-6073	272	6	ω	ω	PROPN
ejpam-6073	272	7	wjf(x	wjf(x	PROPN
ejpam-6073	272	8	,	,	PUNCT
ejpam-6073	272	9	t)dxds,∫	t)dxds,∫	PUNCT
ejpam-6073	272	10	ω	ω	NOUN
ejpam-6073	272	11	uktwj(x)dx−	uktwj(x)dx−	NUM
ejpam-6073	272	12	∫	∫	PROPN
ejpam-6073	272	13	ω	ω	PROPN
ejpam-6073	272	14	uk1wj(x)dx+	uk1wj(x)dx+	PROPN
ejpam-6073	272	15	a3	a3	PROPN
ejpam-6073	272	16	∫	∫	PROPN
ejpam-6073	272	17	t	t	PROPN
ejpam-6073	272	18	0	0	NUM
ejpam-6073	273	1	∫	∫	PROPN
ejpam-6073	273	2	ω	ω	NUM
ejpam-6073	273	3	ukxwjx(x)dxds+	ukxwjx(x)dxds+	PROPN
ejpam-6073	273	4	a2	a2	PROPN
ejpam-6073	273	5	∫	∫	PROPN
ejpam-6073	273	6	t	t	PROPN
ejpam-6073	273	7	0	0	NUM
ejpam-6073	273	8	∫	∫	PROPN
ejpam-6073	273	9	ω	ω	PROPN
ejpam-6073	273	10	zkxwjx(x)dx	zkxwjx(x)dx	NUM
ejpam-6073	273	11	+	+	CCONJ
ejpam-6073	273	12	β	β	X
ejpam-6073	273	13	∫	∫	PROPN
ejpam-6073	273	14	t	t	PROPN
ejpam-6073	273	15	0	0	NUM
ejpam-6073	273	16	∫	∫	PROPN
ejpam-6073	273	17	ω	ω	PROPN
ejpam-6073	273	18	|ukt	|ukt	PROPN
ejpam-6073	273	19	|	|	ADV
ejpam-6073	273	20	q(.)−2	q(.)−2	ADJ
ejpam-6073	273	21	uktwj(x)dxds	uktwj(x)dxds	PUNCT
ejpam-6073	273	22	=	=	SYM
ejpam-6073	274	1	∫	∫	PROPN
ejpam-6073	274	2	t	t	PROPN
ejpam-6073	274	3	0	0	NUM
ejpam-6073	274	4	∫	∫	PROPN
ejpam-6073	274	5	ω	ω	NUM
ejpam-6073	274	6	wjg(x	wjg(x	PROPN
ejpam-6073	274	7	,	,	PUNCT
ejpam-6073	274	8	t)dxds	t)dxds	PROPN
ejpam-6073	274	9	.	.	PUNCT
ejpam-6073	275	1	as	as	SCONJ
ejpam-6073	275	2	k	k	PROPN
ejpam-6073	275	3	goes	go	VERB
ejpam-6073	275	4	to	to	ADP
ejpam-6073	275	5	+	+	PROPN
ejpam-6073	275	6	∞	∞	PROPN
ejpam-6073	275	7	,	,	PUNCT
ejpam-6073	275	8	we	we	PRON
ejpam-6073	275	9	easily	easily	ADV
ejpam-6073	275	10	check	check	VERB
ejpam-6073	275	11	that	that	SCONJ
ejpam-6073	275	12	∀j	∀j	NOUN
ejpam-6073	275	13	<	<	X
ejpam-6073	275	14	k	k	PROPN
ejpam-6073	275	15	,	,	PUNCT
ejpam-6073	275	16	∫	∫	PROPN
ejpam-6073	275	17	ω	ω	PROPN
ejpam-6073	275	18	ztwj(x)dx−	ztwj(x)dx−	NUM
ejpam-6073	275	19	∫	∫	PROPN
ejpam-6073	275	20	ω	ω	PROPN
ejpam-6073	275	21	z1wj(x)dx+	z1wj(x)dx+	PROPN
ejpam-6073	275	22	a1	a1	PROPN
ejpam-6073	275	23	∫	∫	PROPN
ejpam-6073	275	24	t	t	PROPN
ejpam-6073	275	25	0	0	NUM
ejpam-6073	275	26	∫	∫	PROPN
ejpam-6073	276	1	ω	ω	PROPN
ejpam-6073	276	2	zxwjx(x)dxds+	zxwjx(x)dxds+	PROPN
ejpam-6073	276	3	a2	a2	PROPN
ejpam-6073	276	4	∫	∫	PROPN
ejpam-6073	276	5	t	t	PROPN
ejpam-6073	276	6	0	0	NUM
ejpam-6073	276	7	∫	∫	PROPN
ejpam-6073	276	8	ω	ω	NUM
ejpam-6073	276	9	uxwjx(x)dxds	uxwjx(x)dxds	PROPN
ejpam-6073	276	10	+	+	CCONJ
ejpam-6073	276	11	γ	γ	PROPN
ejpam-6073	276	12	∫	∫	PROPN
ejpam-6073	276	13	t	t	PROPN
ejpam-6073	276	14	0	0	NUM
ejpam-6073	276	15	∫	∫	PROPN
ejpam-6073	276	16	ω	ω	NUM
ejpam-6073	276	17	|zt|p(.)−2ztwj(x)dxds	|zt|p(.)−2ztwj(x)dxds	NOUN
ejpam-6073	277	1	=	=	SYM
ejpam-6073	277	2	∫	∫	PROPN
ejpam-6073	277	3	t	t	PROPN
ejpam-6073	277	4	0	0	NUM
ejpam-6073	277	5	∫	∫	PROPN
ejpam-6073	277	6	ω	ω	PROPN
ejpam-6073	277	7	wjf(x	wjf(x	PROPN
ejpam-6073	277	8	,	,	PUNCT
ejpam-6073	277	9	t)dxds,∫	t)dxds,∫	PUNCT
ejpam-6073	277	10	ω	ω	NUM
ejpam-6073	277	11	utwj(x)dx−	utwj(x)dx−	NUM
ejpam-6073	277	12	∫	∫	PROPN
ejpam-6073	277	13	ω	ω	PROPN
ejpam-6073	277	14	u1wj(x)dx+	u1wj(x)dx+	PROPN
ejpam-6073	277	15	a3	a3	NOUN
ejpam-6073	277	16	∫	∫	PROPN
ejpam-6073	277	17	t	t	PROPN
ejpam-6073	277	18	0	0	NUM
ejpam-6073	278	1	∫	∫	PROPN
ejpam-6073	278	2	ω	ω	NUM
ejpam-6073	278	3	uxwjx(x)dxds+	uxwjx(x)dxds+	PROPN
ejpam-6073	278	4	a2	a2	PROPN
ejpam-6073	278	5	∫	∫	PROPN
ejpam-6073	278	6	t	t	PROPN
ejpam-6073	278	7	0	0	NUM
ejpam-6073	278	8	∫	∫	PROPN
ejpam-6073	278	9	ω	ω	NUM
ejpam-6073	278	10	zxwjx(x)dx	zxwjx(x)dx	PROPN
ejpam-6073	278	11	+	+	X
ejpam-6073	278	12	β	β	X
ejpam-6073	278	13	∫	∫	PROPN
ejpam-6073	278	14	t	t	PROPN
ejpam-6073	278	15	0	0	NUM
ejpam-6073	278	16	∫	∫	PROPN
ejpam-6073	278	17	ω	ω	PROPN
ejpam-6073	278	18	|ut|q(.)−2utwj(x)dxds	|ut|q(.)−2utwj(x)dxds	PROPN
ejpam-6073	278	19	=	=	SYM
ejpam-6073	278	20	∫	∫	PROPN
ejpam-6073	278	21	t	t	PROPN
ejpam-6073	278	22	0	0	NUM
ejpam-6073	278	23	∫	∫	PROPN
ejpam-6073	278	24	ω	ω	NUM
ejpam-6073	278	25	wjg(x	wjg(x	PROPN
ejpam-6073	278	26	,	,	PUNCT
ejpam-6073	278	27	t)dxds	t)dxds	PROPN
ejpam-6073	278	28	.	.	PUNCT
ejpam-6073	279	1	consequently	consequently	ADV
ejpam-6073	279	2	,	,	PUNCT
ejpam-6073	279	3	we	we	PRON
ejpam-6073	279	4	have	have	VERB
ejpam-6073	279	5	∀w	∀w	ADJ
ejpam-6073	279	6	∈	∈	PROPN
ejpam-6073	279	7	h1	h1	NOUN
ejpam-6073	279	8	0	0	NUM
ejpam-6073	279	9	(	(	PUNCT
ejpam-6073	279	10	ω	ω	NUM
ejpam-6073	279	11	)	)	PUNCT
ejpam-6073	279	12	∫	∫	PROPN
ejpam-6073	280	1	ω	ω	NUM
ejpam-6073	280	2	ztw(x)dx−	ztw(x)dx−	PROPN
ejpam-6073	280	3	∫	∫	PROPN
ejpam-6073	281	1	ω	ω	PROPN
ejpam-6073	281	2	z1w(x)dx+	z1w(x)dx+	PROPN
ejpam-6073	281	3	a1	a1	NOUN
ejpam-6073	281	4	∫	∫	PROPN
ejpam-6073	281	5	t	t	PROPN
ejpam-6073	281	6	0	0	NUM
ejpam-6073	281	7	∫	∫	PROPN
ejpam-6073	281	8	ω	ω	NUM
ejpam-6073	281	9	zxwx(x)dxds+	zxwx(x)dxds+	PROPN
ejpam-6073	281	10	a2	a2	PROPN
ejpam-6073	282	1	∫	∫	PROPN
ejpam-6073	282	2	t	t	PROPN
ejpam-6073	282	3	0	0	NUM
ejpam-6073	282	4	∫	∫	PROPN
ejpam-6073	282	5	ω	ω	NUM
ejpam-6073	282	6	uxwx(x)dxds	uxwx(x)dxds	PUNCT
ejpam-6073	283	1	+	+	CCONJ
ejpam-6073	283	2	γ	γ	PROPN
ejpam-6073	283	3	∫	∫	PROPN
ejpam-6073	283	4	t	t	PROPN
ejpam-6073	283	5	0	0	NUM
ejpam-6073	283	6	∫	∫	PROPN
ejpam-6073	283	7	ω	ω	PROPN
ejpam-6073	283	8	|zt|p(.)−2ztw(x)dxds	|zt|p(.)−2ztw(x)dxds	PROPN
ejpam-6073	283	9	=	=	SYM
ejpam-6073	283	10	∫	∫	PROPN
ejpam-6073	283	11	t	t	PROPN
ejpam-6073	283	12	0	0	NUM
ejpam-6073	283	13	∫	∫	PROPN
ejpam-6073	283	14	ω	ω	NUM
ejpam-6073	283	15	wf(x	wf(x	PROPN
ejpam-6073	283	16	,	,	PUNCT
ejpam-6073	283	17	t)dxds,∫	t)dxds,∫	X
ejpam-6073	283	18	ω	ω	NOUN
ejpam-6073	283	19	utw(x)dx−	utw(x)dx−	PROPN
ejpam-6073	283	20	∫	∫	PROPN
ejpam-6073	283	21	ω	ω	PROPN
ejpam-6073	283	22	u1w(x)dx+	u1w(x)dx+	PROPN
ejpam-6073	283	23	a3	a3	PROPN
ejpam-6073	284	1	∫	∫	PROPN
ejpam-6073	284	2	t	t	PROPN
ejpam-6073	284	3	0	0	NUM
ejpam-6073	285	1	∫	∫	PROPN
ejpam-6073	286	1	ω	ω	NUM
ejpam-6073	286	2	uxwx(x)dxds+	uxwx(x)dxds+	PROPN
ejpam-6073	286	3	a2	a2	PROPN
ejpam-6073	286	4	∫	∫	PROPN
ejpam-6073	286	5	t	t	PROPN
ejpam-6073	286	6	0	0	NUM
ejpam-6073	286	7	∫	∫	PROPN
ejpam-6073	286	8	ω	ω	PROPN
ejpam-6073	286	9	zxwx(x)dxds	zxwx(x)dxds	NUM
ejpam-6073	286	10	+	+	CCONJ
ejpam-6073	286	11	β	β	X
ejpam-6073	286	12	∫	∫	PROPN
ejpam-6073	286	13	t	t	PROPN
ejpam-6073	286	14	0	0	NUM
ejpam-6073	286	15	∫	∫	PROPN
ejpam-6073	286	16	ω	ω	PROPN
ejpam-6073	286	17	|ut|q(.)−2utw(x)dxds	|ut|q(.)−2utw(x)dxds	PROPN
ejpam-6073	286	18	=	=	SYM
ejpam-6073	286	19	∫	∫	PROPN
ejpam-6073	286	20	t	t	PROPN
ejpam-6073	286	21	0	0	NUM
ejpam-6073	286	22	∫	∫	PROPN
ejpam-6073	286	23	ω	ω	PROPN
ejpam-6073	286	24	wg(x	wg(x	PROPN
ejpam-6073	286	25	,	,	PUNCT
ejpam-6073	286	26	t)dxds	t)dxds	PROPN
ejpam-6073	286	27	.	.	PUNCT
ejpam-6073	287	1	all	all	DET
ejpam-6073	287	2	terms	term	NOUN
ejpam-6073	287	3	define	define	VERB
ejpam-6073	287	4	absolute	absolute	ADJ
ejpam-6073	287	5	continuous	continuous	ADJ
ejpam-6073	287	6	functions	function	NOUN
ejpam-6073	287	7	,	,	PUNCT
ejpam-6073	287	8	so	so	SCONJ
ejpam-6073	287	9	we	we	PRON
ejpam-6073	287	10	get	get	VERB
ejpam-6073	287	11	,	,	PUNCT
ejpam-6073	287	12	for	for	ADP
ejpam-6073	287	13	a.e	a.e	PROPN
ejpam-6073	287	14	.	.	PROPN
ejpam-6073	287	15	t	t	PROPN
ejpam-6073	287	16	∈	∈	PROPN
ejpam-6073	288	1	[	[	X
ejpam-6073	288	2	0	0	NUM
ejpam-6073	288	3	,	,	PUNCT
ejpam-6073	288	4	t	t	NOUN
ejpam-6073	288	5	]	]	PUNCT
ejpam-6073	288	6	and	and	CCONJ
ejpam-6073	288	7	∀w	∀w	PROPN
ejpam-6073	288	8	∈	∈	PROPN
ejpam-6073	288	9	a.	a.	NOUN
ejpam-6073	288	10	m.	m.	PROPN
ejpam-6073	289	1	al	al	PROPN
ejpam-6073	289	2	-	-	PROPN
ejpam-6073	289	3	mahdi	mahdi	PROPN
ejpam-6073	289	4	et	et	PROPN
ejpam-6073	289	5	al	al	PROPN
ejpam-6073	289	6	.	.	PUNCT
ejpam-6073	289	7	/	/	SYM
ejpam-6073	289	8	eur	eur	PROPN
ejpam-6073	289	9	.	.	PUNCT
ejpam-6073	290	1	j.	j.	PROPN
ejpam-6073	290	2	pure	pure	PROPN
ejpam-6073	290	3	appl	appl	PROPN
ejpam-6073	290	4	.	.	PROPN
ejpam-6073	290	5	math	math	PROPN
ejpam-6073	290	6	,	,	PUNCT
ejpam-6073	290	7	18	18	NUM
ejpam-6073	290	8	(	(	PUNCT
ejpam-6073	290	9	3	3	NUM
ejpam-6073	290	10	)	)	PUNCT
ejpam-6073	290	11	(	(	PUNCT
ejpam-6073	290	12	2025	2025	NUM
ejpam-6073	290	13	)	)	PUNCT
ejpam-6073	290	14	,	,	PUNCT
ejpam-6073	290	15	6073	6073	NUM
ejpam-6073	290	16	14	14	NUM
ejpam-6073	290	17	of	of	ADP
ejpam-6073	290	18	29	29	NUM
ejpam-6073	290	19	h1	h1	NOUN
ejpam-6073	290	20	0	0	NUM
ejpam-6073	290	21	(	(	PUNCT
ejpam-6073	290	22	ω),∫	ω),∫	PROPN
ejpam-6073	290	23	ω	ω	PROPN
ejpam-6073	290	24	zttw(x)dx+	zttw(x)dx+	PROPN
ejpam-6073	290	25	a1	a1	PROPN
ejpam-6073	290	26	∫	∫	PROPN
ejpam-6073	290	27	ω	ω	PROPN
ejpam-6073	290	28	zxwx(x)dx+	zxwx(x)dx+	PROPN
ejpam-6073	290	29	a2	a2	PROPN
ejpam-6073	290	30	∫	∫	PROPN
ejpam-6073	290	31	ω	ω	PROPN
ejpam-6073	290	32	uxwx(x)dx+	uxwx(x)dx+	PROPN
ejpam-6073	290	33	γ	γ	PROPN
ejpam-6073	290	34	∫	∫	PROPN
ejpam-6073	290	35	ω	ω	PROPN
ejpam-6073	290	36	|zt|p(.)−2ztw(x)dx	|zt|p(.)−2ztw(x)dx	PROPN
ejpam-6073	290	37	=	=	PUNCT
ejpam-6073	290	38	∫	∫	PROPN
ejpam-6073	290	39	ω	ω	NUM
ejpam-6073	290	40	wf(x	wf(x	PROPN
ejpam-6073	290	41	,	,	PUNCT
ejpam-6073	290	42	t)dx,∫	t)dx,∫	PROPN
ejpam-6073	290	43	ω	ω	PROPN
ejpam-6073	290	44	uttw(x)dx+	uttw(x)dx+	PROPN
ejpam-6073	290	45	a3	a3	NOUN
ejpam-6073	290	46	∫	∫	PROPN
ejpam-6073	290	47	ω	ω	PROPN
ejpam-6073	290	48	uxwx(x)dx+	uxwx(x)dx+	PROPN
ejpam-6073	290	49	a2	a2	PROPN
ejpam-6073	290	50	∫	∫	PROPN
ejpam-6073	291	1	ω	ω	PROPN
ejpam-6073	291	2	zxwx(x)dx+	zxwx(x)dx+	PROPN
ejpam-6073	291	3	β	β	SYM
ejpam-6073	291	4	∫	∫	PROPN
ejpam-6073	291	5	ω	ω	NUM
ejpam-6073	291	6	|ut|q(.)−2utw(x)dx	|ut|q(.)−2utw(x)dx	NOUN
ejpam-6073	291	7	=	=	PUNCT
ejpam-6073	291	8	∫	∫	PROPN
ejpam-6073	291	9	ω	ω	PROPN
ejpam-6073	291	10	wg(x	wg(x	PROPN
ejpam-6073	291	11	,	,	PUNCT
ejpam-6073	291	12	t)dx	t)dx	PROPN
ejpam-6073	291	13	.	.	PUNCT
ejpam-6073	292	1	this	this	PRON
ejpam-6073	292	2	implies	imply	VERB
ejpam-6073	292	3	that	that	SCONJ
ejpam-6073	292	4	ρzztt	ρzztt	VERB
ejpam-6073	292	5	−	−	PROPN
ejpam-6073	292	6	a1zxx	a1zxx	NOUN
ejpam-6073	292	7	−	−	PROPN
ejpam-6073	292	8	a2uxx	a2uxx	PROPN
ejpam-6073	292	9	+	+	CCONJ
ejpam-6073	292	10	γ|zt|p(·)−2zt	γ|zt|p(·)−2zt	NOUN
ejpam-6073	292	11	=	=	SYM
ejpam-6073	292	12	f	f	X
ejpam-6073	292	13	,	,	PUNCT
ejpam-6073	292	14	in	in	ADP
ejpam-6073	292	15	d′(ω×	d′(ω×	PROPN
ejpam-6073	292	16	(	(	PUNCT
ejpam-6073	292	17	0	0	NUM
ejpam-6073	292	18	,	,	PUNCT
ejpam-6073	292	19	t	t	NOUN
ejpam-6073	292	20	)	)	PUNCT
ejpam-6073	292	21	)	)	PUNCT
ejpam-6073	292	22	ρuutt	ρuutt	NOUN
ejpam-6073	292	23	−	−	NOUN
ejpam-6073	292	24	a3uxx	a3uxx	NUM
ejpam-6073	292	25	−	−	PROPN
ejpam-6073	293	1	a2zxx	a2zxx	NOUN
ejpam-6073	294	1	+	+	NUM
ejpam-6073	294	2	β|ut|q(·)−2ut	β|ut|q(·)−2ut	NOUN
ejpam-6073	294	3	=	=	SYM
ejpam-6073	294	4	g	g	NOUN
ejpam-6073	294	5	,	,	PUNCT
ejpam-6073	294	6	in	in	ADP
ejpam-6073	294	7	d′(ω×	d′(ω×	PROPN
ejpam-6073	294	8	(	(	PUNCT
ejpam-6073	294	9	0	0	NUM
ejpam-6073	294	10	,	,	PUNCT
ejpam-6073	294	11	t	t	NOUN
ejpam-6073	294	12	)	)	PUNCT
ejpam-6073	294	13	)	)	PUNCT
ejpam-6073	294	14	.	.	PUNCT
ejpam-6073	295	1	this	this	PRON
ejpam-6073	295	2	implies	imply	VERB
ejpam-6073	295	3	that	that	SCONJ
ejpam-6073	295	4	(	(	PUNCT
ejpam-6073	295	5	z	z	NOUN
ejpam-6073	295	6	,	,	PUNCT
ejpam-6073	295	7	u	u	NOUN
ejpam-6073	295	8	)	)	PUNCT
ejpam-6073	295	9	satisfies	satisfy	VERB
ejpam-6073	295	10	the	the	DET
ejpam-6073	295	11	two	two	NUM
ejpam-6073	295	12	differential	differential	ADJ
ejpam-6073	295	13	equations	equation	NOUN
ejpam-6073	295	14	in	in	ADP
ejpam-6073	295	15	(	(	PUNCT
ejpam-6073	295	16	q	q	NOUN
ejpam-6073	295	17	)	)	PUNCT
ejpam-6073	295	18	,	,	PUNCT
ejpam-6073	295	19	on	on	ADP
ejpam-6073	295	20	ω×	ω×	PROPN
ejpam-6073	295	21	(	(	PUNCT
ejpam-6073	295	22	0	0	NUM
ejpam-6073	295	23	,	,	PUNCT
ejpam-6073	295	24	t	t	NOUN
ejpam-6073	295	25	)	)	PUNCT
ejpam-6073	295	26	.	.	PUNCT
ejpam-6073	296	1	step	step	NOUN
ejpam-6073	296	2	4	4	NUM
ejpam-6073	296	3	.	.	PUNCT
ejpam-6073	297	1	the	the	DET
ejpam-6073	297	2	initial	initial	ADJ
ejpam-6073	297	3	conditions	condition	NOUN
ejpam-6073	297	4	:	:	PUNCT
ejpam-6073	297	5	we	we	PRON
ejpam-6073	297	6	can	can	AUX
ejpam-6073	297	7	handle	handle	VERB
ejpam-6073	297	8	the	the	DET
ejpam-6073	297	9	initial	initial	ADJ
ejpam-6073	297	10	conditions	condition	NOUN
ejpam-6073	297	11	like	like	ADP
ejpam-6073	297	12	the	the	DET
ejpam-6073	297	13	one	one	NUM
ejpam-6073	297	14	in	in	ADP
ejpam-6073	297	15	[	[	X
ejpam-6073	297	16	34	34	NUM
ejpam-6073	297	17	]	]	PUNCT
ejpam-6073	297	18	.	.	PUNCT
ejpam-6073	298	1	hence	hence	ADV
ejpam-6073	298	2	,	,	PUNCT
ejpam-6073	298	3	we	we	PRON
ejpam-6073	298	4	deduce	deduce	VERB
ejpam-6073	298	5	that	that	SCONJ
ejpam-6073	298	6	(	(	PUNCT
ejpam-6073	298	7	z	z	X
ejpam-6073	298	8	,	,	PUNCT
ejpam-6073	298	9	u	u	NOUN
ejpam-6073	298	10	)	)	PUNCT
ejpam-6073	298	11	is	be	AUX
ejpam-6073	298	12	the	the	DET
ejpam-6073	298	13	unique	unique	ADJ
ejpam-6073	298	14	local	local	ADJ
ejpam-6073	298	15	solution	solution	NOUN
ejpam-6073	298	16	of	of	ADP
ejpam-6073	298	17	(	(	PUNCT
ejpam-6073	298	18	q	q	NOUN
ejpam-6073	298	19	)	)	PUNCT
ejpam-6073	298	20	.	.	PUNCT
ejpam-6073	299	1	this	this	PRON
ejpam-6073	299	2	completes	complete	VERB
ejpam-6073	299	3	the	the	DET
ejpam-6073	299	4	proof	proof	NOUN
ejpam-6073	299	5	of	of	ADP
ejpam-6073	299	6	theorem	theorem	NOUN
ejpam-6073	299	7	1	1	NUM
ejpam-6073	299	8	.	.	PUNCT
ejpam-6073	300	1	now	now	ADV
ejpam-6073	300	2	,	,	PUNCT
ejpam-6073	300	3	we	we	PRON
ejpam-6073	300	4	proceed	proceed	VERB
ejpam-6073	300	5	to	to	PART
ejpam-6073	300	6	establish	establish	VERB
ejpam-6073	300	7	the	the	DET
ejpam-6073	300	8	local	local	ADJ
ejpam-6073	300	9	existence	existence	NOUN
ejpam-6073	300	10	result	result	NOUN
ejpam-6073	300	11	for	for	ADP
ejpam-6073	300	12	problem	problem	NOUN
ejpam-6073	300	13	(	(	PUNCT
ejpam-6073	300	14	p	p	NOUN
ejpam-6073	300	15	)	)	PUNCT
ejpam-6073	300	16	,	,	PUNCT
ejpam-6073	300	17	we	we	PRON
ejpam-6073	300	18	first	first	ADV
ejpam-6073	300	19	recall	recall	VERB
ejpam-6073	300	20	the	the	DET
ejpam-6073	300	21	following	follow	VERB
ejpam-6073	300	22	elementary	elementary	NOUN
ejpam-6073	300	23	inequalities:∣∣∣|a|k	inequalities:∣∣∣|a|k	PROPN
ejpam-6073	300	24	−	−	PROPN
ejpam-6073	301	1	|b|k	|b|k	NOUN
ejpam-6073	301	2	∣∣∣	∣∣∣	ADJ
ejpam-6073	301	3	≤	≤	NUM
ejpam-6073	301	4	c	c	NOUN
ejpam-6073	301	5	|a−	|a−	PROPN
ejpam-6073	301	6	b|	b|	PROPN
ejpam-6073	301	7	(	(	PUNCT
ejpam-6073	301	8	|a|k−1	|a|k−1	NUM
ejpam-6073	301	9	+	+	NUM
ejpam-6073	301	10	|b|k−1	|b|k−1	NUM
ejpam-6073	301	11	)	)	PUNCT
ejpam-6073	301	12	,	,	PUNCT
ejpam-6073	301	13	(	(	PUNCT
ejpam-6073	301	14	34	34	NUM
ejpam-6073	301	15	)	)	PUNCT
ejpam-6073	301	16	for	for	ADP
ejpam-6073	301	17	some	some	DET
ejpam-6073	301	18	constant	constant	ADJ
ejpam-6073	301	19	c	c	NOUN
ejpam-6073	301	20	>	>	X
ejpam-6073	301	21	0	0	PROPN
ejpam-6073	301	22	,	,	PUNCT
ejpam-6073	301	23	all	all	PRON
ejpam-6073	301	24	k	k	PROPN
ejpam-6073	301	25	≥	≥	NUM
ejpam-6073	301	26	1	1	NUM
ejpam-6073	301	27	and	and	CCONJ
ejpam-6073	301	28	all	all	DET
ejpam-6073	301	29	a	a	PRON
ejpam-6073	301	30	,	,	PUNCT
ejpam-6073	301	31	b	b	X
ejpam-6073	301	32	∈	∈	PROPN
ejpam-6073	301	33	r.	r.	PROPN
ejpam-6073	301	34	also∣∣∣|a|k0	also∣∣∣|a|k0	PROPN
ejpam-6073	301	35	a−	a−	PROPN
ejpam-6073	301	36	|b|k0	|b|k0	VERB
ejpam-6073	301	37	b	b	PROPN
ejpam-6073	301	38	∣∣∣	∣∣∣	ADJ
ejpam-6073	301	39	≤	≤	NUM
ejpam-6073	301	40	c	c	NOUN
ejpam-6073	301	41	|a−	|a−	NOUN
ejpam-6073	301	42	b|	b|	PROPN
ejpam-6073	301	43	(	(	PUNCT
ejpam-6073	301	44	|a|k0	|a|k0	NOUN
ejpam-6073	301	45	+	+	NUM
ejpam-6073	301	46	|b|k0	|b|k0	NOUN
ejpam-6073	301	47	)	)	PUNCT
ejpam-6073	301	48	,	,	PUNCT
ejpam-6073	301	49	(	(	PUNCT
ejpam-6073	301	50	35	35	NUM
ejpam-6073	301	51	)	)	PUNCT
ejpam-6073	301	52	for	for	ADP
ejpam-6073	301	53	some	some	DET
ejpam-6073	301	54	constant	constant	ADJ
ejpam-6073	301	55	c	c	NOUN
ejpam-6073	301	56	>	>	X
ejpam-6073	301	57	0	0	PROPN
ejpam-6073	301	58	,	,	PUNCT
ejpam-6073	301	59	all	all	DET
ejpam-6073	301	60	k0	k0	PROPN
ejpam-6073	301	61	≥	≥	NUM
ejpam-6073	301	62	0	0	NUM
ejpam-6073	301	63	and	and	CCONJ
ejpam-6073	301	64	all	all	DET
ejpam-6073	301	65	a	a	DET
ejpam-6073	301	66	,	,	PUNCT
ejpam-6073	301	67	b	b	X
ejpam-6073	301	68	∈	∈	PROPN
ejpam-6073	301	69	r.	r.	PROPN
ejpam-6073	301	70	remark	remark	NOUN
ejpam-6073	301	71	1	1	NUM
ejpam-6073	301	72	.	.	PUNCT
ejpam-6073	301	73	for	for	ADP
ejpam-6073	301	74	a.e	a.e	PROPN
ejpam-6073	301	75	.	.	PUNCT
ejpam-6073	301	76	x	x	PUNCT
ejpam-6073	301	77	∈	∈	PROPN
ejpam-6073	301	78	ω	ω	PROPN
ejpam-6073	301	79	and	and	CCONJ
ejpam-6073	301	80	m(x	m(x	NOUN
ejpam-6073	301	81	)	)	PUNCT
ejpam-6073	301	82	and	and	CCONJ
ejpam-6073	301	83	ℓ(x	ℓ(x	PROPN
ejpam-6073	301	84	)	)	PUNCT
ejpam-6073	301	85	satisfying	satisfying	NOUN
ejpam-6073	301	86	(	(	PUNCT
ejpam-6073	301	87	a1	a1	NOUN
ejpam-6073	301	88	)	)	PUNCT
ejpam-6073	301	89	,	,	PUNCT
ejpam-6073	301	90	the	the	DET
ejpam-6073	301	91	functions	function	NOUN
ejpam-6073	301	92	h1(s	h1(s	NUM
ejpam-6073	301	93	)	)	PUNCT
ejpam-6073	301	94	=	=	SYM
ejpam-6073	301	95	c|s|m(x)−2	c|s|m(x)−2	PROPN
ejpam-6073	301	96	and	and	CCONJ
ejpam-6073	301	97	h2(s	h2(s	ADJ
ejpam-6073	301	98	)	)	PUNCT
ejpam-6073	301	99	=	=	PUNCT
ejpam-6073	302	1	d|s|ℓ(x)−2	d|s|ℓ(x)−2	NOUN
ejpam-6073	302	2	are	be	AUX
ejpam-6073	302	3	differentiable	differentiable	ADJ
ejpam-6073	302	4	and	and	CCONJ
ejpam-6073	302	5	|h′1(s)|	|h′1(s)|	X
ejpam-6073	302	6	=	=	PROPN
ejpam-6073	302	7	|c||m(x	|c||m(x	NUM
ejpam-6073	302	8	)	)	PUNCT
ejpam-6073	302	9	−	−	NOUN
ejpam-6073	302	10	1||s|m(x)−2	1||s|m(x)−2	NUM
ejpam-6073	302	11	,	,	PUNCT
ejpam-6073	302	12	|h′2(s)|	|h′2(s)|	PUNCT
ejpam-6073	302	13	=	=	SYM
ejpam-6073	302	14	|d||ℓ(x)−	|d||ℓ(x)−	NOUN
ejpam-6073	302	15	1||s|ℓ(x)−2	1||s|ℓ(x)−2	NOUN
ejpam-6073	302	16	.	.	PUNCT
ejpam-6073	303	1	theorem	theorem	NOUN
ejpam-6073	303	2	2	2	NUM
ejpam-6073	303	3	.	.	PUNCT
ejpam-6073	304	1	let	let	VERB
ejpam-6073	304	2	(	(	PUNCT
ejpam-6073	304	3	u0	u0	ADJ
ejpam-6073	304	4	,	,	PUNCT
ejpam-6073	304	5	u1	u1	NOUN
ejpam-6073	304	6	)	)	PUNCT
ejpam-6073	304	7	,	,	PUNCT
ejpam-6073	304	8	(	(	PUNCT
ejpam-6073	304	9	v0	v0	NOUN
ejpam-6073	304	10	,	,	PUNCT
ejpam-6073	304	11	v1	v1	NOUN
ejpam-6073	304	12	)	)	PUNCT
ejpam-6073	304	13	∈	∈	PROPN
ejpam-6073	304	14	h1	h1	NOUN
ejpam-6073	304	15	0	0	NUM
ejpam-6073	304	16	(	(	PUNCT
ejpam-6073	304	17	ω	ω	NOUN
ejpam-6073	304	18	)	)	PUNCT
ejpam-6073	304	19	×	×	PROPN
ejpam-6073	304	20	l2(ω	l2(ω	NOUN
ejpam-6073	304	21	)	)	PUNCT
ejpam-6073	304	22	be	be	AUX
ejpam-6073	304	23	given	give	VERB
ejpam-6073	304	24	.	.	PUNCT
ejpam-6073	305	1	assume	assume	VERB
ejpam-6073	305	2	that	that	SCONJ
ejpam-6073	305	3	(	(	PUNCT
ejpam-6073	305	4	a1)-(a2	a1)-(a2	PROPN
ejpam-6073	305	5	)	)	PUNCT
ejpam-6073	305	6	hold	hold	NOUN
ejpam-6073	305	7	.	.	PUNCT
ejpam-6073	306	1	then	then	ADV
ejpam-6073	306	2	,	,	PUNCT
ejpam-6073	306	3	problem	problem	NOUN
ejpam-6073	306	4	(	(	PUNCT
ejpam-6073	306	5	p	p	NOUN
ejpam-6073	306	6	)	)	PUNCT
ejpam-6073	306	7	has	have	VERB
ejpam-6073	306	8	a	a	DET
ejpam-6073	306	9	unique	unique	ADJ
ejpam-6073	306	10	weak	weak	ADJ
ejpam-6073	306	11	local	local	ADJ
ejpam-6073	306	12	solution	solution	NOUN
ejpam-6073	306	13	(	(	PUNCT
ejpam-6073	306	14	z	z	NOUN
ejpam-6073	306	15	,	,	PUNCT
ejpam-6073	306	16	u	u	NOUN
ejpam-6073	306	17	)	)	PUNCT
ejpam-6073	306	18	on	on	ADP
ejpam-6073	306	19	[	[	X
ejpam-6073	306	20	0	0	NUM
ejpam-6073	306	21	,	,	PUNCT
ejpam-6073	306	22	t	t	NOUN
ejpam-6073	306	23	)	)	PUNCT
ejpam-6073	306	24	,	,	PUNCT
ejpam-6073	306	25	in	in	ADP
ejpam-6073	306	26	the	the	DET
ejpam-6073	306	27	sense	sense	NOUN
ejpam-6073	306	28	of	of	ADP
ejpam-6073	306	29	definition	definition	NOUN
ejpam-6073	306	30	1	1	NUM
ejpam-6073	306	31	,	,	PUNCT
ejpam-6073	306	32	for	for	ADP
ejpam-6073	306	33	some	some	DET
ejpam-6073	306	34	t	t	NOUN
ejpam-6073	306	35	>	>	X
ejpam-6073	306	36	0	0	X
ejpam-6073	306	37	.	.	PUNCT
ejpam-6073	307	1	proof	proof	NOUN
ejpam-6073	307	2	.	.	PUNCT
ejpam-6073	308	1	existence	existence	NOUN
ejpam-6073	308	2	:	:	PUNCT
ejpam-6073	308	3	let	let	VERB
ejpam-6073	308	4	v1	v1	NOUN
ejpam-6073	308	5	,	,	PUNCT
ejpam-6073	308	6	v2	v2	PROPN
ejpam-6073	308	7	∈	∈	PROPN
ejpam-6073	308	8	l∞	l∞	NOUN
ejpam-6073	308	9	(	(	PUNCT
ejpam-6073	308	10	[	[	X
ejpam-6073	308	11	0	0	NUM
ejpam-6073	308	12	,	,	PUNCT
ejpam-6073	308	13	t	t	NOUN
ejpam-6073	308	14	)	)	PUNCT
ejpam-6073	308	15	,	,	PUNCT
ejpam-6073	308	16	h1	h1	PROPN
ejpam-6073	308	17	0	0	NUM
ejpam-6073	308	18	(	(	PUNCT
ejpam-6073	308	19	ω	ω	NOUN
ejpam-6073	308	20	)	)	PUNCT
ejpam-6073	308	21	)	)	PUNCT
ejpam-6073	308	22	.	.	PUNCT
ejpam-6073	309	1	using	use	VERB
ejpam-6073	309	2	lemma	lemma	PROPN
ejpam-6073	309	3	15	15	NUM
ejpam-6073	309	4	and	and	CCONJ
ejpam-6073	309	5	the	the	DET
ejpam-6073	309	6	embedding	embed	VERB
ejpam-6073	309	7	property	property	NOUN
ejpam-6073	309	8	,	,	PUNCT
ejpam-6073	309	9	we	we	PRON
ejpam-6073	309	10	have	have	VERB
ejpam-6073	309	11	||h1(v1)||22	||h1(v1)||22	NOUN
ejpam-6073	309	12	=	=	SYM
ejpam-6073	309	13	∫	∫	PROPN
ejpam-6073	309	14	ω	ω	PROPN
ejpam-6073	309	15	|v1|2(m(x)−1)dx	|v1|2(m(x)−1)dx	PROPN
ejpam-6073	309	16	≤	≤	PROPN
ejpam-6073	309	17	|c|	|c|	PROPN
ejpam-6073	309	18	(	(	PUNCT
ejpam-6073	309	19	∫	∫	PROPN
ejpam-6073	309	20	ω	ω	PROPN
ejpam-6073	309	21	|v1|2(m2−1)dx+	|v1|2(m2−1)dx+	ADJ
ejpam-6073	309	22	∫	∫	PROPN
ejpam-6073	309	23	ω	ω	PROPN
ejpam-6073	309	24	|v1|2(m1−1)dx	|v1|2(m1−1)dx	PROPN
ejpam-6073	309	25	)	)	PUNCT
ejpam-6073	309	26	<	<	X
ejpam-6073	310	1	+	+	NOUN
ejpam-6073	310	2	∞	∞	NOUN
ejpam-6073	310	3	||h2(v2)||22	||h2(v2)||22	PRON
ejpam-6073	310	4	=	=	PUNCT
ejpam-6073	310	5	∫	∫	PROPN
ejpam-6073	310	6	ω	ω	PROPN
ejpam-6073	310	7	|v2|2(ℓ(x)−1)dx	|v2|2(ℓ(x)−1)dx	ADJ
ejpam-6073	310	8	≤	≤	PROPN
ejpam-6073	310	9	|d|	|d|	PROPN
ejpam-6073	310	10	(	(	PUNCT
ejpam-6073	310	11	∫	∫	PROPN
ejpam-6073	310	12	ω	ω	PROPN
ejpam-6073	310	13	|v2|2(ℓ2−1)dx+	|v2|2(ℓ2−1)dx+	PROPN
ejpam-6073	310	14	∫	∫	PROPN
ejpam-6073	310	15	ω	ω	PROPN
ejpam-6073	310	16	|v2|2(ℓ1−1)dx	|v2|2(ℓ1−1)dx	PROPN
ejpam-6073	310	17	)	)	PUNCT
ejpam-6073	310	18	<	<	X
ejpam-6073	311	1	+	+	PROPN
ejpam-6073	311	2	∞.	∞.	PROPN
ejpam-6073	311	3	(	(	PUNCT
ejpam-6073	311	4	36	36	NUM
ejpam-6073	311	5	)	)	PUNCT
ejpam-6073	311	6	a.	a.	NOUN
ejpam-6073	311	7	m.	m.	PROPN
ejpam-6073	311	8	al	al	PROPN
ejpam-6073	311	9	-	-	PROPN
ejpam-6073	311	10	mahdi	mahdi	PROPN
ejpam-6073	311	11	et	et	PROPN
ejpam-6073	311	12	al	al	PROPN
ejpam-6073	311	13	.	.	PUNCT
ejpam-6073	311	14	/	/	SYM
ejpam-6073	311	15	eur	eur	PROPN
ejpam-6073	311	16	.	.	PUNCT
ejpam-6073	312	1	j.	j.	PROPN
ejpam-6073	312	2	pure	pure	PROPN
ejpam-6073	312	3	appl	appl	PROPN
ejpam-6073	312	4	.	.	PROPN
ejpam-6073	312	5	math	math	PROPN
ejpam-6073	312	6	,	,	PUNCT
ejpam-6073	312	7	18	18	NUM
ejpam-6073	312	8	(	(	PUNCT
ejpam-6073	312	9	3	3	NUM
ejpam-6073	312	10	)	)	PUNCT
ejpam-6073	312	11	(	(	PUNCT
ejpam-6073	312	12	2025	2025	NUM
ejpam-6073	312	13	)	)	PUNCT
ejpam-6073	312	14	,	,	PUNCT
ejpam-6073	312	15	6073	6073	NUM
ejpam-6073	312	16	15	15	NUM
ejpam-6073	312	17	of	of	ADP
ejpam-6073	312	18	29	29	NUM
ejpam-6073	312	19	hence	hence	ADV
ejpam-6073	312	20	,	,	PUNCT
ejpam-6073	312	21	h1(v1	h1(v1	NOUN
ejpam-6073	312	22	)	)	PUNCT
ejpam-6073	312	23	,	,	PUNCT
ejpam-6073	312	24	h2(v2	h2(v2	PROPN
ejpam-6073	312	25	)	)	PUNCT
ejpam-6073	312	26	∈	∈	PROPN
ejpam-6073	312	27	l∞([0	l∞([0	PROPN
ejpam-6073	312	28	,	,	PUNCT
ejpam-6073	312	29	t	t	PROPN
ejpam-6073	312	30	)	)	PUNCT
ejpam-6073	312	31	,	,	PUNCT
ejpam-6073	312	32	l2(ω	l2(ω	NOUN
ejpam-6073	312	33	)	)	PUNCT
ejpam-6073	312	34	)	)	PUNCT
ejpam-6073	313	1	⊂	⊂	PROPN
ejpam-6073	313	2	l2(ω×	l2(ω×	PROPN
ejpam-6073	313	3	(	(	PUNCT
ejpam-6073	313	4	0	0	NUM
ejpam-6073	313	5	,	,	PUNCT
ejpam-6073	313	6	t	t	NOUN
ejpam-6073	313	7	)	)	PUNCT
ejpam-6073	313	8	)	)	PUNCT
ejpam-6073	313	9	.	.	PUNCT
ejpam-6073	314	1	therefore	therefore	ADV
ejpam-6073	314	2	,	,	PUNCT
ejpam-6073	314	3	for	for	ADP
ejpam-6073	314	4	each	each	DET
ejpam-6073	314	5	v1	v1	NOUN
ejpam-6073	314	6	,	,	PUNCT
ejpam-6073	314	7	v2	v2	PROPN
ejpam-6073	314	8	∈	∈	PROPN
ejpam-6073	314	9	l∞([0	l∞([0	PROPN
ejpam-6073	314	10	,	,	PUNCT
ejpam-6073	314	11	t	t	PROPN
ejpam-6073	314	12	)	)	PUNCT
ejpam-6073	314	13	,	,	PUNCT
ejpam-6073	314	14	h1	h1	PROPN
ejpam-6073	314	15	0	0	NUM
ejpam-6073	314	16	(	(	PUNCT
ejpam-6073	314	17	ω	ω	NOUN
ejpam-6073	314	18	)	)	PUNCT
ejpam-6073	314	19	)	)	PUNCT
ejpam-6073	314	20	,	,	PUNCT
ejpam-6073	314	21	there	there	PRON
ejpam-6073	314	22	exists	exist	VERB
ejpam-6073	314	23	a	a	DET
ejpam-6073	314	24	unique	unique	ADJ
ejpam-6073	314	25	solution	solution	NOUN
ejpam-6073	314	26	(	(	PUNCT
ejpam-6073	314	27	z	z	NOUN
ejpam-6073	314	28	,	,	PUNCT
ejpam-6073	314	29	u	u	NOUN
ejpam-6073	314	30	)	)	PUNCT
ejpam-6073	314	31	∈	∈	PROPN
ejpam-6073	314	32	l∞([0	l∞([0	PROPN
ejpam-6073	314	33	,	,	PUNCT
ejpam-6073	314	34	t	t	PROPN
ejpam-6073	314	35	)	)	PUNCT
ejpam-6073	314	36	,	,	PUNCT
ejpam-6073	314	37	h1	h1	PROPN
ejpam-6073	314	38	0	0	NUM
ejpam-6073	314	39	(	(	PUNCT
ejpam-6073	314	40	ω	ω	NOUN
ejpam-6073	314	41	)	)	PUNCT
ejpam-6073	314	42	)	)	PUNCT
ejpam-6073	314	43	,	,	PUNCT
ejpam-6073	314	44	zt	zt	PROPN
ejpam-6073	314	45	∈	∈	PROPN
ejpam-6073	314	46	l∞([0	l∞([0	PROPN
ejpam-6073	314	47	,	,	PUNCT
ejpam-6073	314	48	t	t	PROPN
ejpam-6073	314	49	)	)	PUNCT
ejpam-6073	314	50	,	,	PUNCT
ejpam-6073	314	51	l2(ω	l2(ω	NOUN
ejpam-6073	314	52	)	)	PUNCT
ejpam-6073	314	53	)	)	PUNCT
ejpam-6073	315	1	∩	∩	NOUN
ejpam-6073	315	2	lp(ω×	lp(ω×	PROPN
ejpam-6073	315	3	(	(	PUNCT
ejpam-6073	315	4	0	0	NUM
ejpam-6073	315	5	,	,	PUNCT
ejpam-6073	315	6	t	t	NOUN
ejpam-6073	315	7	)	)	PUNCT
ejpam-6073	315	8	)	)	PUNCT
ejpam-6073	315	9	and	and	CCONJ
ejpam-6073	315	10	ut	ut	PROPN
ejpam-6073	315	11	∈	∈	PROPN
ejpam-6073	315	12	l∞([0	l∞([0	PROPN
ejpam-6073	315	13	,	,	PUNCT
ejpam-6073	315	14	t	t	PROPN
ejpam-6073	315	15	)	)	PUNCT
ejpam-6073	315	16	,	,	PUNCT
ejpam-6073	315	17	l2(ω	l2(ω	NOUN
ejpam-6073	315	18	)	)	PUNCT
ejpam-6073	315	19	)	)	PUNCT
ejpam-6073	315	20	∩	∩	ADJ
ejpam-6073	315	21	lq(ω×	lq(ω×	NOUN
ejpam-6073	315	22	(	(	PUNCT
ejpam-6073	315	23	0	0	NUM
ejpam-6073	315	24	,	,	PUNCT
ejpam-6073	315	25	t	t	NOUN
ejpam-6073	315	26	)	)	PUNCT
ejpam-6073	315	27	)	)	PUNCT
ejpam-6073	316	1	satisfying	satisfy	VERB
ejpam-6073	316	2	the	the	DET
ejpam-6073	316	3	following	follow	VERB
ejpam-6073	316	4	nonlinear	nonlinear	ADJ
ejpam-6073	316	5	problem	problem	PROPN
ejpam-6073	316	6	ρzztt	ρzztt	NOUN
ejpam-6073	316	7	−	−	PROPN
ejpam-6073	316	8	a1zxx	a1zxx	NOUN
ejpam-6073	316	9	−	−	PROPN
ejpam-6073	316	10	a2uxx	a2uxx	NOUN
ejpam-6073	316	11	+	+	CCONJ
ejpam-6073	316	12	γ	γ	X
ejpam-6073	316	13	|zt|p(x)−2	|zt|p(x)−2	ADJ
ejpam-6073	316	14	zt	zt	PROPN
ejpam-6073	316	15	=	=	SYM
ejpam-6073	316	16	h1(v1	h1(v1	NOUN
ejpam-6073	316	17	)	)	PUNCT
ejpam-6073	316	18	in	in	ADP
ejpam-6073	316	19	ω×	ω×	PROPN
ejpam-6073	316	20	(	(	PUNCT
ejpam-6073	316	21	0	0	NUM
ejpam-6073	316	22	,	,	PUNCT
ejpam-6073	316	23	t	t	PROPN
ejpam-6073	316	24	)	)	PUNCT
ejpam-6073	316	25	,	,	PUNCT
ejpam-6073	316	26	ρuutt	ρuutt	VERB
ejpam-6073	316	27	−	−	NOUN
ejpam-6073	316	28	a3uxx	a3uxx	NUM
ejpam-6073	316	29	−	−	PROPN
ejpam-6073	317	1	a2zxx	a2zxx	NOUN
ejpam-6073	318	1	+	+	CCONJ
ejpam-6073	318	2	β	β	X
ejpam-6073	318	3	|ut|q(x)−2	|ut|q(x)−2	ADJ
ejpam-6073	318	4	ut	ut	PROPN
ejpam-6073	319	1	=	=	PROPN
ejpam-6073	319	2	h2(v2	h2(v2	PROPN
ejpam-6073	319	3	)	)	PUNCT
ejpam-6073	319	4	in	in	ADP
ejpam-6073	319	5	ω×	ω×	PROPN
ejpam-6073	319	6	(	(	PUNCT
ejpam-6073	319	7	0	0	NUM
ejpam-6073	319	8	,	,	PUNCT
ejpam-6073	319	9	t	t	PROPN
ejpam-6073	319	10	)	)	PUNCT
ejpam-6073	319	11	,	,	PUNCT
ejpam-6073	319	12	u	u	NOUN
ejpam-6073	319	13	=	=	PUNCT
ejpam-6073	319	14	z	z	NOUN
ejpam-6073	319	15	=	=	SYM
ejpam-6073	319	16	0	0	NUM
ejpam-6073	320	1	on	on	ADP
ejpam-6073	320	2	∂ω×	∂ω×	PROPN
ejpam-6073	320	3	(	(	PUNCT
ejpam-6073	320	4	0	0	NUM
ejpam-6073	320	5	,	,	PUNCT
ejpam-6073	320	6	t	t	PROPN
ejpam-6073	320	7	)	)	PUNCT
ejpam-6073	320	8	,	,	PUNCT
ejpam-6073	320	9	u	u	NOUN
ejpam-6073	320	10	(	(	PUNCT
ejpam-6073	320	11	0	0	NUM
ejpam-6073	320	12	)	)	PUNCT
ejpam-6073	320	13	=	=	PRON
ejpam-6073	320	14	u0	u0	ADJ
ejpam-6073	320	15	and	and	CCONJ
ejpam-6073	320	16	ut	ut	PROPN
ejpam-6073	320	17	(	(	PUNCT
ejpam-6073	320	18	0	0	NUM
ejpam-6073	320	19	)	)	PUNCT
ejpam-6073	320	20	=	=	NOUN
ejpam-6073	320	21	u1	u1	PROPN
ejpam-6073	320	22	in	in	ADP
ejpam-6073	320	23	ω	ω	PROPN
ejpam-6073	320	24	,	,	PUNCT
ejpam-6073	320	25	z	z	PROPN
ejpam-6073	320	26	(	(	PUNCT
ejpam-6073	320	27	0	0	NUM
ejpam-6073	320	28	)	)	PUNCT
ejpam-6073	320	29	=	=	SYM
ejpam-6073	320	30	z0	z0	PROPN
ejpam-6073	320	31	and	and	CCONJ
ejpam-6073	320	32	zt	zt	PROPN
ejpam-6073	320	33	(	(	PUNCT
ejpam-6073	320	34	0	0	NUM
ejpam-6073	320	35	)	)	PUNCT
ejpam-6073	320	36	=	=	SYM
ejpam-6073	320	37	z1	z1	PROPN
ejpam-6073	320	38	in	in	ADP
ejpam-6073	320	39	ω	ω	PROPN
ejpam-6073	320	40	.	.	PUNCT
ejpam-6073	321	1	(	(	PUNCT
ejpam-6073	321	2	r	r	NOUN
ejpam-6073	321	3	)	)	PUNCT
ejpam-6073	321	4	now	now	ADV
ejpam-6073	321	5	,	,	PUNCT
ejpam-6073	321	6	let	let	VERB
ejpam-6073	321	7	wt	wt	NOUN
ejpam-6073	321	8	=	=	VERB
ejpam-6073	321	9	{	{	PUNCT
ejpam-6073	321	10	w	w	PROPN
ejpam-6073	321	11	∈	∈	PROPN
ejpam-6073	321	12	l∞((0	l∞((0	PROPN
ejpam-6073	321	13	,	,	PUNCT
ejpam-6073	321	14	t	t	PROPN
ejpam-6073	321	15	)	)	PUNCT
ejpam-6073	321	16	,	,	PUNCT
ejpam-6073	321	17	h1	h1	PROPN
ejpam-6073	321	18	0	0	NUM
ejpam-6073	322	1	(	(	PUNCT
ejpam-6073	322	2	ω))/wt	ω))/wt	PROPN
ejpam-6073	322	3	∈	∈	PROPN
ejpam-6073	322	4	l∞((0	l∞((0	PROPN
ejpam-6073	322	5	,	,	PUNCT
ejpam-6073	322	6	t	t	PROPN
ejpam-6073	322	7	)	)	PUNCT
ejpam-6073	322	8	,	,	PUNCT
ejpam-6073	322	9	l2(ω	l2(ω	NOUN
ejpam-6073	322	10	)	)	PUNCT
ejpam-6073	322	11	)	)	PUNCT
ejpam-6073	322	12	}	}	PUNCT
ejpam-6073	322	13	,	,	PUNCT
ejpam-6073	322	14	and	and	CCONJ
ejpam-6073	322	15	define	define	VERB
ejpam-6073	322	16	the	the	DET
ejpam-6073	322	17	map	map	NOUN
ejpam-6073	322	18	k	k	X
ejpam-6073	322	19	:	:	PUNCT
ejpam-6073	322	20	wt	wt	ADP
ejpam-6073	322	21	×wt	×wt	NOUN
ejpam-6073	322	22	−→wt	−→wt	NOUN
ejpam-6073	322	23	×wt	×wt	VERB
ejpam-6073	322	24	by	by	ADP
ejpam-6073	322	25	k(v1	k(v1	NOUN
ejpam-6073	322	26	,	,	PUNCT
ejpam-6073	322	27	v2	v2	NOUN
ejpam-6073	322	28	)	)	PUNCT
ejpam-6073	322	29	=	=	PUNCT
ejpam-6073	322	30	(	(	PUNCT
ejpam-6073	322	31	z	z	NOUN
ejpam-6073	322	32	,	,	PUNCT
ejpam-6073	322	33	u	u	NOUN
ejpam-6073	322	34	)	)	PUNCT
ejpam-6073	322	35	.	.	PUNCT
ejpam-6073	323	1	we	we	PRON
ejpam-6073	323	2	note	note	VERB
ejpam-6073	323	3	that	that	SCONJ
ejpam-6073	323	4	wt	wt	PROPN
ejpam-6073	323	5	is	be	AUX
ejpam-6073	323	6	a	a	DET
ejpam-6073	323	7	banach	banach	NOUN
ejpam-6073	323	8	space	space	NOUN
ejpam-6073	323	9	with	with	ADP
ejpam-6073	323	10	respect	respect	NOUN
ejpam-6073	323	11	to	to	ADP
ejpam-6073	323	12	the	the	DET
ejpam-6073	323	13	following	following	ADJ
ejpam-6073	323	14	norm	norm	NOUN
ejpam-6073	323	15	||w||2wt	||w||2wt	PUNCT
ejpam-6073	324	1	=	=	SYM
ejpam-6073	324	2	sup	sup	INTJ
ejpam-6073	324	3	(	(	PUNCT
ejpam-6073	324	4	0,t	0,t	PROPN
ejpam-6073	324	5	)	)	PUNCT
ejpam-6073	324	6	∫	∫	PROPN
ejpam-6073	325	1	ω	ω	PROPN
ejpam-6073	325	2	|wx|2dx+	|wx|2dx+	PROPN
ejpam-6073	325	3	sup	sup	NOUN
ejpam-6073	325	4	(	(	PUNCT
ejpam-6073	325	5	0,t	0,t	PROPN
ejpam-6073	325	6	)	)	PUNCT
ejpam-6073	325	7	∫	∫	PROPN
ejpam-6073	326	1	ω	ω	PROPN
ejpam-6073	326	2	|wt|2dx	|wt|2dx	PROPN
ejpam-6073	326	3	,	,	PUNCT
ejpam-6073	326	4	and	and	CCONJ
ejpam-6073	326	5	k	k	PROPN
ejpam-6073	326	6	is	be	AUX
ejpam-6073	326	7	well	well	ADV
ejpam-6073	326	8	defined	define	VERB
ejpam-6073	326	9	by	by	ADP
ejpam-6073	326	10	virtue	virtue	NOUN
ejpam-6073	326	11	of	of	ADP
ejpam-6073	326	12	theorem	theorem	NOUN
ejpam-6073	326	13	1	1	NUM
ejpam-6073	326	14	.	.	PUNCT
ejpam-6073	327	1	in	in	ADP
ejpam-6073	327	2	what	what	PRON
ejpam-6073	327	3	follows	follow	VERB
ejpam-6073	327	4	,	,	PUNCT
ejpam-6073	327	5	we	we	PRON
ejpam-6073	327	6	prove	prove	VERB
ejpam-6073	327	7	that	that	SCONJ
ejpam-6073	327	8	k	k	PROPN
ejpam-6073	327	9	is	be	AUX
ejpam-6073	327	10	a	a	DET
ejpam-6073	327	11	contraction	contraction	NOUN
ejpam-6073	327	12	mapping	mapping	NOUN
ejpam-6073	327	13	from	from	ADP
ejpam-6073	327	14	a	a	DET
ejpam-6073	327	15	closed	closed	ADJ
ejpam-6073	327	16	bounded	bound	VERB
ejpam-6073	327	17	ball	ball	NOUN
ejpam-6073	327	18	b(0,m	b(0,m	NOUN
ejpam-6073	327	19	)	)	PUNCT
ejpam-6073	327	20	into	into	ADP
ejpam-6073	327	21	itself	itself	PRON
ejpam-6073	327	22	,	,	PUNCT
ejpam-6073	327	23	where	where	SCONJ
ejpam-6073	327	24	b(0,m	b(0,m	NOUN
ejpam-6073	327	25	)	)	PUNCT
ejpam-6073	328	1	=	=	PRON
ejpam-6073	328	2	{	{	PUNCT
ejpam-6073	328	3	(	(	PUNCT
ejpam-6073	328	4	v1	v1	NOUN
ejpam-6073	328	5	,	,	PUNCT
ejpam-6073	328	6	v2	v2	PROPN
ejpam-6073	328	7	)	)	PUNCT
ejpam-6073	328	8	∈wt	∈wt	PROPN
ejpam-6073	328	9	×wt	×wt	NOUN
ejpam-6073	328	10	/	/	SYM
ejpam-6073	328	11	∥(v1	∥(v1	PROPN
ejpam-6073	328	12	,	,	PUNCT
ejpam-6073	328	13	v2)∥wt×wt	v2)∥wt×wt	PROPN
ejpam-6073	328	14	≤m	≤m	PROPN
ejpam-6073	328	15	}	}	PUNCT
ejpam-6073	328	16	,	,	PUNCT
ejpam-6073	328	17	for	for	ADP
ejpam-6073	328	18	m	m	PROPN
ejpam-6073	328	19	>	>	X
ejpam-6073	328	20	1	1	NUM
ejpam-6073	328	21	and	and	CCONJ
ejpam-6073	328	22	t0	t0	PRON
ejpam-6073	328	23	>	>	X
ejpam-6073	328	24	0	0	PUNCT
ejpam-6073	328	25	to	to	PART
ejpam-6073	328	26	be	be	AUX
ejpam-6073	328	27	fixed	fix	VERB
ejpam-6073	328	28	later	later	ADV
ejpam-6073	328	29	.	.	PUNCT
ejpam-6073	329	1	multiplying	multiply	VERB
ejpam-6073	329	2	the	the	DET
ejpam-6073	329	3	first	first	ADJ
ejpam-6073	329	4	equation	equation	NOUN
ejpam-6073	329	5	in	in	ADP
ejpam-6073	329	6	(	(	PUNCT
ejpam-6073	329	7	r	r	NOUN
ejpam-6073	329	8	)	)	PUNCT
ejpam-6073	329	9	by	by	ADP
ejpam-6073	329	10	zt	zt	PROPN
ejpam-6073	329	11	,	,	PUNCT
ejpam-6073	329	12	the	the	DET
ejpam-6073	329	13	second	second	ADJ
ejpam-6073	329	14	one	one	NUM
ejpam-6073	329	15	by	by	ADP
ejpam-6073	329	16	ut	ut	PROPN
ejpam-6073	329	17	and	and	CCONJ
ejpam-6073	329	18	integrating	integrate	VERB
ejpam-6073	329	19	the	the	DET
ejpam-6073	329	20	two	two	NUM
ejpam-6073	329	21	results	result	NOUN
ejpam-6073	329	22	over	over	ADP
ejpam-6073	329	23	ω×	ω×	PROPN
ejpam-6073	329	24	(	(	PUNCT
ejpam-6073	329	25	0	0	NUM
ejpam-6073	329	26	,	,	PUNCT
ejpam-6073	329	27	t	t	PROPN
ejpam-6073	329	28	)	)	PUNCT
ejpam-6073	329	29	we	we	PRON
ejpam-6073	329	30	get	get	VERB
ejpam-6073	329	31	,	,	PUNCT
ejpam-6073	329	32	for	for	ADP
ejpam-6073	329	33	all	all	DET
ejpam-6073	329	34	t	t	NOUN
ejpam-6073	329	35	≤	≤	X
ejpam-6073	329	36	t	t	PROPN
ejpam-6073	329	37	,	,	PUNCT
ejpam-6073	329	38	ρu	ρu	ADV
ejpam-6073	329	39	2	2	NUM
ejpam-6073	329	40	∥ut∥22	∥ut∥22	ADV
ejpam-6073	329	41	+	+	NUM
ejpam-6073	329	42	ρz	ρz	NOUN
ejpam-6073	329	43	2	2	NUM
ejpam-6073	329	44	∥zt∥22	∥zt∥22	PROPN
ejpam-6073	329	45	+	+	NUM
ejpam-6073	329	46	a3	a3	NOUN
ejpam-6073	329	47	2	2	NUM
ejpam-6073	329	48	∥ux∥22	∥ux∥22	NOUN
ejpam-6073	329	49	+	+	CCONJ
ejpam-6073	329	50	a1	a1	NOUN
ejpam-6073	329	51	2	2	NUM
ejpam-6073	329	52	∥zx∥22	∥zx∥22	PROPN
ejpam-6073	329	53	+	+	CCONJ
ejpam-6073	329	54	a2	a2	PROPN
ejpam-6073	329	55	∫	∫	PROPN
ejpam-6073	330	1	ω	ω	PROPN
ejpam-6073	330	2	uxzxdx−	uxzxdx−	PROPN
ejpam-6073	330	3	ρu	ρu	INTJ
ejpam-6073	330	4	2	2	NUM
ejpam-6073	330	5	∥u1∥22	∥u1∥22	NOUN
ejpam-6073	330	6	−	−	ADP
ejpam-6073	330	7	ρz	ρz	NOUN
ejpam-6073	330	8	2	2	NUM
ejpam-6073	330	9	∥z1∥22	∥z1∥22	NOUN
ejpam-6073	330	10	−	−	PROPN
ejpam-6073	330	11	ρu	ρu	INTJ
ejpam-6073	330	12	2	2	NUM
ejpam-6073	330	13	∥u0x∥22	∥u0x∥22	PROPN
ejpam-6073	330	14	−	−	ADP
ejpam-6073	331	1	ρz	ρz	NOUN
ejpam-6073	331	2	2	2	NUM
ejpam-6073	331	3	∥z0x∥22	∥z0x∥22	PROPN
ejpam-6073	331	4	−	−	PROPN
ejpam-6073	332	1	a2	a2	PROPN
ejpam-6073	332	2	∫	∫	PROPN
ejpam-6073	332	3	ω	ω	NUM
ejpam-6073	332	4	u0xz0xdx+	u0xz0xdx+	PROPN
ejpam-6073	332	5	γ	γ	PROPN
ejpam-6073	332	6	∫	∫	PROPN
ejpam-6073	332	7	t	t	PROPN
ejpam-6073	332	8	0	0	NUM
ejpam-6073	333	1	∫	∫	PROPN
ejpam-6073	333	2	ω	ω	NUM
ejpam-6073	333	3	|zt|p(x	|zt|p(x	PROPN
ejpam-6073	333	4	)	)	PUNCT
ejpam-6073	333	5	dxds+	dxds+	PROPN
ejpam-6073	334	1	β	β	X
ejpam-6073	334	2	∫	∫	PROPN
ejpam-6073	334	3	t	t	PROPN
ejpam-6073	334	4	0	0	NUM
ejpam-6073	334	5	∫	∫	PROPN
ejpam-6073	334	6	ω	ω	NUM
ejpam-6073	334	7	|ut|q(x	|ut|q(x	PROPN
ejpam-6073	334	8	)	)	PUNCT
ejpam-6073	334	9	dxds	dxds	NOUN
ejpam-6073	334	10	=	=	SYM
ejpam-6073	334	11	∫	∫	PROPN
ejpam-6073	334	12	t	t	PROPN
ejpam-6073	334	13	0	0	NUM
ejpam-6073	334	14	∫	∫	PROPN
ejpam-6073	335	1	ω	ω	NUM
ejpam-6073	335	2	zth1(v1)dxds+	zth1(v1)dxds+	PROPN
ejpam-6073	335	3	∫	∫	PROPN
ejpam-6073	336	1	t	t	PROPN
ejpam-6073	336	2	0	0	NUM
ejpam-6073	336	3	∫	∫	PROPN
ejpam-6073	336	4	ω	ω	PROPN
ejpam-6073	336	5	uth2(v2)dxds	uth2(v2)dxds	PROPN
ejpam-6073	336	6	.	.	PUNCT
ejpam-6073	337	1	(	(	PUNCT
ejpam-6073	337	2	37	37	NUM
ejpam-6073	337	3	)	)	PUNCT
ejpam-6073	337	4	using	use	VERB
ejpam-6073	337	5	the	the	DET
ejpam-6073	337	6	definitions	definition	NOUN
ejpam-6073	337	7	of	of	ADP
ejpam-6073	337	8	hi	hi	INTJ
ejpam-6073	337	9	,	,	PUNCT
ejpam-6073	337	10	i	i	PRON
ejpam-6073	337	11	=	=	NOUN
ejpam-6073	337	12	1	1	NUM
ejpam-6073	337	13	,	,	PUNCT
ejpam-6073	337	14	2	2	NUM
ejpam-6073	337	15	,	,	PUNCT
ejpam-6073	337	16	lemma	lemma	PROPN
ejpam-6073	337	17	15	15	NUM
ejpam-6073	337	18	and	and	CCONJ
ejpam-6073	337	19	young	young	ADJ
ejpam-6073	337	20	’s	’s	PART
ejpam-6073	337	21	and	and	CCONJ
ejpam-6073	337	22	poincaré	poincaré	PROPN
ejpam-6073	337	23	’s	’s	PART
ejpam-6073	337	24	inequalities	inequality	NOUN
ejpam-6073	337	25	,	,	PUNCT
ejpam-6073	337	26	we	we	PRON
ejpam-6073	337	27	have	have	VERB
ejpam-6073	337	28	for	for	ADP
ejpam-6073	337	29	ε	ε	PROPN
ejpam-6073	337	30	>	>	X
ejpam-6073	337	31	0,∫	0,∫	PROPN
ejpam-6073	337	32	ω	ω	PROPN
ejpam-6073	337	33	|v1|m(x)−2v1ztdx	|v1|m(x)−2v1ztdx	PROPN
ejpam-6073	337	34	≤	≤	PROPN
ejpam-6073	337	35	ερz	ερz	VERB
ejpam-6073	337	36	4	4	NUM
ejpam-6073	337	37	∫	∫	PROPN
ejpam-6073	337	38	ω	ω	PROPN
ejpam-6073	337	39	z2	z2	PROPN
ejpam-6073	337	40	t	t	PROPN
ejpam-6073	337	41	dx+	dx+	NOUN
ejpam-6073	337	42	c	c	PROPN
ejpam-6073	337	43	ε	ε	PROPN
ejpam-6073	337	44	∫	∫	PROPN
ejpam-6073	337	45	ω	ω	PROPN
ejpam-6073	337	46	|v1|2(m(x)−1)dx	|v1|2(m(x)−1)dx	PROPN
ejpam-6073	337	47	≤	≤	NUM
ejpam-6073	337	48	ερz	ερz	VERB
ejpam-6073	337	49	4	4	NUM
ejpam-6073	337	50	∫	∫	PROPN
ejpam-6073	337	51	ω	ω	PROPN
ejpam-6073	337	52	z2	z2	PROPN
ejpam-6073	337	53	t	t	PROPN
ejpam-6073	337	54	dx+	dx+	NOUN
ejpam-6073	337	55	ce	ce	PROPN
ejpam-6073	337	56	ε	ε	PROPN
ejpam-6073	337	57	[	[	PUNCT
ejpam-6073	337	58	||v1x||2m2−2	||v1x||2m2−2	ADP
ejpam-6073	337	59	2	2	NUM
ejpam-6073	337	60	+	+	CCONJ
ejpam-6073	337	61	||v1x||2m1−2	||v1x||2m1−2	PRON
ejpam-6073	337	62	2	2	NUM
ejpam-6073	337	63	]	]	PUNCT
ejpam-6073	337	64	.	.	PUNCT
ejpam-6073	338	1	(	(	PUNCT
ejpam-6073	338	2	38	38	NUM
ejpam-6073	338	3	)	)	PUNCT
ejpam-6073	338	4	a.	a.	NOUN
ejpam-6073	338	5	m.	m.	PROPN
ejpam-6073	338	6	al	al	PROPN
ejpam-6073	338	7	-	-	PROPN
ejpam-6073	338	8	mahdi	mahdi	PROPN
ejpam-6073	338	9	et	et	PROPN
ejpam-6073	338	10	al	al	PROPN
ejpam-6073	338	11	.	.	PUNCT
ejpam-6073	338	12	/	/	SYM
ejpam-6073	338	13	eur	eur	PROPN
ejpam-6073	338	14	.	.	PUNCT
ejpam-6073	339	1	j.	j.	PROPN
ejpam-6073	339	2	pure	pure	PROPN
ejpam-6073	339	3	appl	appl	PROPN
ejpam-6073	339	4	.	.	PROPN
ejpam-6073	339	5	math	math	PROPN
ejpam-6073	339	6	,	,	PUNCT
ejpam-6073	339	7	18	18	NUM
ejpam-6073	339	8	(	(	PUNCT
ejpam-6073	339	9	3	3	NUM
ejpam-6073	339	10	)	)	PUNCT
ejpam-6073	339	11	(	(	PUNCT
ejpam-6073	339	12	2025	2025	NUM
ejpam-6073	339	13	)	)	PUNCT
ejpam-6073	339	14	,	,	PUNCT
ejpam-6073	339	15	6073	6073	NUM
ejpam-6073	339	16	16	16	NUM
ejpam-6073	339	17	of	of	ADP
ejpam-6073	339	18	29	29	NUM
ejpam-6073	339	19	similarly	similarly	ADV
ejpam-6073	339	20	,	,	PUNCT
ejpam-6073	339	21	we	we	PRON
ejpam-6073	339	22	have∫	have∫	VERB
ejpam-6073	339	23	ω	ω	PROPN
ejpam-6073	339	24	|v2|ℓ(x)−2v2utdx	|v2|ℓ(x)−2v2utdx	PROPN
ejpam-6073	339	25	≤	≤	PROPN
ejpam-6073	339	26	ερu	ερu	PROPN
ejpam-6073	339	27	4	4	NUM
ejpam-6073	339	28	∫	∫	NOUN
ejpam-6073	339	29	ω	ω	NUM
ejpam-6073	340	1	u2tdx+	u2tdx+	INTJ
ejpam-6073	340	2	c	c	PROPN
ejpam-6073	340	3	ε	ε	PROPN
ejpam-6073	340	4	∫	∫	PROPN
ejpam-6073	340	5	ω	ω	PROPN
ejpam-6073	340	6	|v2|2(ℓ(x)−1)dx	|v2|2(ℓ(x)−1)dx	ADJ
ejpam-6073	340	7	≤	≤	NUM
ejpam-6073	340	8	ερu	ερu	PROPN
ejpam-6073	340	9	4	4	NUM
ejpam-6073	340	10	∫	∫	NOUN
ejpam-6073	340	11	ω	ω	X
ejpam-6073	340	12	u2tdx+	u2tdx+	PROPN
ejpam-6073	340	13	ce	ce	PROPN
ejpam-6073	340	14	ε	ε	PROPN
ejpam-6073	340	15	[	[	PUNCT
ejpam-6073	340	16	||v2x||2ℓ2−2	||v2x||2ℓ2−2	X
ejpam-6073	340	17	2	2	NUM
ejpam-6073	340	18	+	+	CCONJ
ejpam-6073	340	19	||v2x||2ℓ1−2	||v2x||2ℓ1−2	X
ejpam-6073	340	20	2	2	NUM
ejpam-6073	340	21	]	]	PUNCT
ejpam-6073	340	22	.	.	PUNCT
ejpam-6073	341	1	(	(	PUNCT
ejpam-6073	341	2	39	39	NUM
ejpam-6073	341	3	)	)	PUNCT
ejpam-6073	341	4	thus	thus	ADV
ejpam-6073	341	5	,	,	PUNCT
ejpam-6073	341	6	(	(	PUNCT
ejpam-6073	341	7	37	37	NUM
ejpam-6073	341	8	)	)	PUNCT
ejpam-6073	341	9	becomes	become	VERB
ejpam-6073	341	10	ρu	ρu	ADP
ejpam-6073	341	11	2	2	NUM
ejpam-6073	341	12	∥ut∥22	∥ut∥22	ADV
ejpam-6073	342	1	+	+	NUM
ejpam-6073	342	2	ρz	ρz	NOUN
ejpam-6073	342	3	2	2	NUM
ejpam-6073	342	4	∥zt∥22	∥zt∥22	PROPN
ejpam-6073	342	5	+	+	NUM
ejpam-6073	342	6	a3	a3	NOUN
ejpam-6073	342	7	2	2	NUM
ejpam-6073	342	8	∥ux∥22	∥ux∥22	NOUN
ejpam-6073	342	9	+	+	CCONJ
ejpam-6073	342	10	a1	a1	NOUN
ejpam-6073	342	11	2	2	NUM
ejpam-6073	342	12	∥zx∥22	∥zx∥22	PROPN
ejpam-6073	342	13	+	+	CCONJ
ejpam-6073	342	14	a2	a2	PROPN
ejpam-6073	342	15	∫	∫	PROPN
ejpam-6073	342	16	ω	ω	PROPN
ejpam-6073	342	17	uxzxdx	uxzxdx	ADJ
ejpam-6073	342	18	≤	≤	NOUN
ejpam-6073	342	19	λ0	λ0	NOUN
ejpam-6073	342	20	+	+	CCONJ
ejpam-6073	342	21	εtρz	εtρz	NOUN
ejpam-6073	342	22	4	4	NUM
ejpam-6073	342	23	sup	sup	NOUN
ejpam-6073	342	24	(	(	PUNCT
ejpam-6073	342	25	0,t	0,t	PROPN
ejpam-6073	342	26	)	)	PUNCT
ejpam-6073	342	27	∫	∫	PROPN
ejpam-6073	343	1	ω	ω	PROPN
ejpam-6073	343	2	z2	z2	PROPN
ejpam-6073	343	3	t	t	PROPN
ejpam-6073	343	4	dx+	dx+	NOUN
ejpam-6073	343	5	εtρu	εtρu	NOUN
ejpam-6073	343	6	4	4	NUM
ejpam-6073	343	7	sup	sup	NOUN
ejpam-6073	343	8	(	(	PUNCT
ejpam-6073	343	9	0,t	0,t	PROPN
ejpam-6073	343	10	)	)	PUNCT
ejpam-6073	343	11	∫	∫	PROPN
ejpam-6073	344	1	ω	ω	NUM
ejpam-6073	344	2	u2tdx	u2tdx	PROPN
ejpam-6073	344	3	+	+	CCONJ
ejpam-6073	344	4	ce	ce	PROPN
ejpam-6073	344	5	ε	ε	PROPN
ejpam-6073	344	6	[	[	PUNCT
ejpam-6073	344	7	||v1x||2m1−2	||v1x||2m1−2	NOUN
ejpam-6073	344	8	2	2	NUM
ejpam-6073	344	9	+	+	CCONJ
ejpam-6073	344	10	||v1x||2m2−2	||v1x||2m2−2	ADP
ejpam-6073	344	11	2	2	NUM
ejpam-6073	344	12	+	+	NUM
ejpam-6073	344	13	||v2x||2ℓ2−2	||v2x||2ℓ2−2	NOUN
ejpam-6073	344	14	2	2	NUM
ejpam-6073	344	15	+	+	CCONJ
ejpam-6073	344	16	||v2x||2ℓ1−2	||v2x||2ℓ1−2	X
ejpam-6073	344	17	2	2	NUM
ejpam-6073	344	18	]	]	PUNCT
ejpam-6073	344	19	,	,	PUNCT
ejpam-6073	344	20	where	where	SCONJ
ejpam-6073	344	21	,	,	PUNCT
ejpam-6073	344	22	by	by	ADP
ejpam-6073	344	23	using	use	VERB
ejpam-6073	344	24	(	(	PUNCT
ejpam-6073	344	25	26	26	NUM
ejpam-6073	344	26	)	)	PUNCT
ejpam-6073	344	27	,	,	PUNCT
ejpam-6073	344	28	λ0	λ0	NOUN
ejpam-6073	344	29	=	=	SYM
ejpam-6073	344	30	ρu	ρu	ADP
ejpam-6073	344	31	2	2	NUM
ejpam-6073	344	32	∥u1∥22	∥u1∥22	NOUN
ejpam-6073	345	1	+	+	CCONJ
ejpam-6073	345	2	ρz	ρz	NOUN
ejpam-6073	345	3	2	2	NUM
ejpam-6073	345	4	∥z1∥22	∥z1∥22	NOUN
ejpam-6073	346	1	+	+	CCONJ
ejpam-6073	346	2	ρu	ρu	PRON
ejpam-6073	346	3	2	2	NUM
ejpam-6073	346	4	∥u0x∥22	∥u0x∥22	PROPN
ejpam-6073	346	5	+	+	CCONJ
ejpam-6073	347	1	ρz	ρz	NOUN
ejpam-6073	347	2	2	2	NUM
ejpam-6073	347	3	∥z0x∥22	∥z0x∥22	PUNCT
ejpam-6073	347	4	+	+	NUM
ejpam-6073	347	5	a2	a2	PROPN
ejpam-6073	347	6	∫	∫	PROPN
ejpam-6073	347	7	ω	ω	PROPN
ejpam-6073	347	8	u0xz0xdx	u0xz0xdx	PROPN
ejpam-6073	347	9	≥	≥	PROPN
ejpam-6073	347	10	0	0	NUM
ejpam-6073	347	11	,	,	PUNCT
ejpam-6073	347	12	and	and	CCONJ
ejpam-6073	347	13	ce	ce	PROPN
ejpam-6073	347	14	is	be	AUX
ejpam-6073	347	15	the	the	DET
ejpam-6073	347	16	embedding	embed	VERB
ejpam-6073	347	17	constant	constant	ADJ
ejpam-6073	347	18	.	.	PUNCT
ejpam-6073	348	1	choosing	choose	VERB
ejpam-6073	348	2	ε	ε	PROPN
ejpam-6073	348	3	such	such	ADJ
ejpam-6073	348	4	that	that	SCONJ
ejpam-6073	348	5	εt	εt	PROPN
ejpam-6073	348	6	=	=	NOUN
ejpam-6073	348	7	1	1	NUM
ejpam-6073	348	8	,	,	PUNCT
ejpam-6073	348	9	we	we	PRON
ejpam-6073	348	10	get	get	VERB
ejpam-6073	348	11	||z||2wt	||z||2wt	PUNCT
ejpam-6073	348	12	+	+	NUM
ejpam-6073	348	13	||u||2wt	||u||2wt	PUNCT
ejpam-6073	348	14	≤	≤	ADJ
ejpam-6073	348	15	λ0	λ0	NOUN
ejpam-6073	348	16	+	+	CCONJ
ejpam-6073	348	17	tc	tc	X
ejpam-6073	348	18	(	(	PUNCT
ejpam-6073	348	19	||v1||2(m1−1	||v1||2(m1−1	PROPN
ejpam-6073	348	20	)	)	PUNCT
ejpam-6073	348	21	wt	wt	ADP
ejpam-6073	349	1	+	+	PUNCT
ejpam-6073	349	2	||v1||2(m2−1	||v1||2(m2−1	NOUN
ejpam-6073	349	3	)	)	PUNCT
ejpam-6073	349	4	wt	wt	NOUN
ejpam-6073	349	5	+	+	PUNCT
ejpam-6073	349	6	||v2||2(ℓ1−1	||v2||2(ℓ1−1	ADV
ejpam-6073	349	7	)	)	PUNCT
ejpam-6073	350	1	wt	wt	PROPN
ejpam-6073	350	2	+	+	NUM
ejpam-6073	350	3	||v2||2(ℓ2−1	||v2||2(ℓ2−1	NOUN
ejpam-6073	350	4	)	)	PUNCT
ejpam-6073	350	5	wt	wt	NOUN
ejpam-6073	350	6	)	)	PUNCT
ejpam-6073	350	7	.	.	PUNCT
ejpam-6073	351	1	suppose	suppose	VERB
ejpam-6073	351	2	that	that	SCONJ
ejpam-6073	351	3	max	max	PROPN
ejpam-6073	351	4	{	{	PUNCT
ejpam-6073	351	5	||v1||wt	||v1||wt	PROPN
ejpam-6073	351	6	,	,	PUNCT
ejpam-6073	351	7	||v2||wt	||v2||wt	PROPN
ejpam-6073	351	8	}	}	PUNCT
ejpam-6073	351	9	≤m	≤m	NOUN
ejpam-6073	351	10	,	,	PUNCT
ejpam-6073	351	11	for	for	ADP
ejpam-6073	351	12	some	some	DET
ejpam-6073	351	13	m	m	NOUN
ejpam-6073	351	14	large	large	ADJ
ejpam-6073	351	15	.	.	PUNCT
ejpam-6073	352	1	then	then	ADV
ejpam-6073	352	2	,	,	PUNCT
ejpam-6073	352	3	we	we	PRON
ejpam-6073	352	4	have	have	VERB
ejpam-6073	352	5	for	for	ADP
ejpam-6073	352	6	large	large	ADJ
ejpam-6073	352	7	m	m	PROPN
ejpam-6073	352	8	>	>	X
ejpam-6073	352	9	0	0	NUM
ejpam-6073	352	10	,	,	PUNCT
ejpam-6073	352	11	||u||2wt	||u||2wt	PUNCT
ejpam-6073	353	1	+	+	CCONJ
ejpam-6073	353	2	||z||2wt	||z||2wt	X
ejpam-6073	353	3	≤	≤	ADJ
ejpam-6073	353	4	λ0	λ0	NOUN
ejpam-6073	353	5	+	+	CCONJ
ejpam-6073	353	6	tcm̃	tcm̃	DET
ejpam-6073	353	7	≤m2	≤m2	NOUN
ejpam-6073	353	8	,	,	PUNCT
ejpam-6073	353	9	where	where	SCONJ
ejpam-6073	353	10	m̃	m̃	PROPN
ejpam-6073	353	11	=	=	SYM
ejpam-6073	353	12	max{m2(m2−1),m2(ℓ2−1	max{m2(m2−1),m2(ℓ2−1	NOUN
ejpam-6073	353	13	)	)	PUNCT
ejpam-6073	353	14	}	}	PUNCT
ejpam-6073	353	15	and	and	CCONJ
ejpam-6073	353	16	m2	m2	PROPN
ejpam-6073	353	17	>	>	X
ejpam-6073	353	18	λ0	λ0	NOUN
ejpam-6073	353	19	and	and	CCONJ
ejpam-6073	353	20	t	t	NOUN
ejpam-6073	353	21	≤	≤	NUM
ejpam-6073	353	22	t0	t0	PROPN
ejpam-6073	353	23	<	<	X
ejpam-6073	353	24	m2−λ0	m2−λ0	X
ejpam-6073	353	25	cm̃	cm̃	NOUN
ejpam-6073	353	26	.	.	PUNCT
ejpam-6073	354	1	hence	hence	ADV
ejpam-6073	354	2	,	,	PUNCT
ejpam-6073	354	3	we	we	PRON
ejpam-6073	354	4	conclude	conclude	VERB
ejpam-6073	354	5	that	that	SCONJ
ejpam-6073	354	6	that	that	SCONJ
ejpam-6073	354	7	k	k	PROPN
ejpam-6073	354	8	maps	maps	PROPN
ejpam-6073	354	9	b(0,m	b(0,m	NUM
ejpam-6073	354	10	)	)	PUNCT
ejpam-6073	354	11	into	into	ADP
ejpam-6073	354	12	b(0,m	b(0,m	NUM
ejpam-6073	354	13	)	)	PUNCT
ejpam-6073	354	14	.	.	PUNCT
ejpam-6073	355	1	next	next	ADV
ejpam-6073	355	2	,	,	PUNCT
ejpam-6073	355	3	we	we	PRON
ejpam-6073	355	4	prove	prove	VERB
ejpam-6073	355	5	,	,	PUNCT
ejpam-6073	355	6	for	for	ADP
ejpam-6073	355	7	t0(even	t0(even	NOUN
ejpam-6073	355	8	smaller	small	ADJ
ejpam-6073	355	9	)	)	PUNCT
ejpam-6073	355	10	,	,	PUNCT
ejpam-6073	355	11	k	k	PROPN
ejpam-6073	355	12	is	be	AUX
ejpam-6073	355	13	a	a	DET
ejpam-6073	355	14	contraction	contraction	NOUN
ejpam-6073	355	15	.	.	PUNCT
ejpam-6073	356	1	for	for	ADP
ejpam-6073	356	2	this	this	DET
ejpam-6073	356	3	purpose	purpose	NOUN
ejpam-6073	356	4	,	,	PUNCT
ejpam-6073	356	5	let	let	VERB
ejpam-6073	356	6	(	(	PUNCT
ejpam-6073	356	7	z1	z1	ADJ
ejpam-6073	356	8	,	,	PUNCT
ejpam-6073	356	9	u1	u1	NOUN
ejpam-6073	356	10	)	)	PUNCT
ejpam-6073	356	11	=	=	SYM
ejpam-6073	356	12	k(v1	k(v1	NOUN
ejpam-6073	356	13	,	,	PUNCT
ejpam-6073	356	14	ṽ1	ṽ1	NOUN
ejpam-6073	356	15	)	)	PUNCT
ejpam-6073	356	16	and	and	CCONJ
ejpam-6073	356	17	(	(	PUNCT
ejpam-6073	356	18	z2	z2	PROPN
ejpam-6073	356	19	,	,	PUNCT
ejpam-6073	356	20	u2	u2	NOUN
ejpam-6073	356	21	)	)	PUNCT
ejpam-6073	356	22	=	=	SYM
ejpam-6073	356	23	k(v2	k(v2	NOUN
ejpam-6073	356	24	,	,	PUNCT
ejpam-6073	356	25	ṽ2	ṽ2	PROPN
ejpam-6073	356	26	)	)	PUNCT
ejpam-6073	356	27	and	and	CCONJ
ejpam-6073	356	28	set	set	VERB
ejpam-6073	356	29	(	(	PUNCT
ejpam-6073	356	30	z	z	NOUN
ejpam-6073	356	31	,	,	PUNCT
ejpam-6073	356	32	u	u	NOUN
ejpam-6073	356	33	)	)	PUNCT
ejpam-6073	356	34	=	=	SYM
ejpam-6073	356	35	(	(	PUNCT
ejpam-6073	356	36	v1	v1	VERB
ejpam-6073	356	37	−	−	PROPN
ejpam-6073	356	38	v2	v2	PROPN
ejpam-6073	356	39	,	,	PUNCT
ejpam-6073	356	40	ṽ1	ṽ1	NOUN
ejpam-6073	357	1	−	−	PROPN
ejpam-6073	357	2	ṽ2	ṽ2	PROPN
ejpam-6073	357	3	)	)	PUNCT
ejpam-6073	357	4	then	then	ADV
ejpam-6073	357	5	(	(	PUNCT
ejpam-6073	357	6	z	z	NOUN
ejpam-6073	357	7	,	,	PUNCT
ejpam-6073	357	8	u	u	NOUN
ejpam-6073	357	9	)	)	PUNCT
ejpam-6073	357	10	satisfies	satisfy	VERB
ejpam-6073	357	11	the	the	DET
ejpam-6073	357	12	following	following	NOUN
ejpam-6073	357	13	ρzztt	ρzztt	NOUN
ejpam-6073	358	1	−	−	PROPN
ejpam-6073	358	2	a1zxx	a1zxx	PROPN
ejpam-6073	358	3	−	−	PROPN
ejpam-6073	358	4	a2uxx	a2uxx	NOUN
ejpam-6073	358	5	+	+	CCONJ
ejpam-6073	358	6	γ	γ	X
ejpam-6073	358	7	(	(	PUNCT
ejpam-6073	358	8	|v1t|p(·)−2v1	|v1t|p(·)−2v1	NOUN
ejpam-6073	358	9	t	t	NOUN
ejpam-6073	358	10	−	−	PROPN
ejpam-6073	358	11	|v2t|p(·)−2v2	|v2t|p(·)−2v2	NOUN
ejpam-6073	358	12	t	t	NOUN
ejpam-6073	358	13	)	)	PUNCT
ejpam-6073	359	1	=	=	PUNCT
ejpam-6073	359	2	c	c	X
ejpam-6073	359	3	(	(	PUNCT
ejpam-6073	359	4	|v1|m(·)−2v1	|v1|m(·)−2v1	PROPN
ejpam-6073	359	5	−	−	PROPN
ejpam-6073	359	6	|v2|m(·)−2v2	|v2|m(·)−2v2	NUM
ejpam-6073	359	7	)	)	PUNCT
ejpam-6073	359	8	,	,	PUNCT
ejpam-6073	359	9	ρuutt	ρuutt	VERB
ejpam-6073	359	10	−	−	NOUN
ejpam-6073	359	11	a3uxx	a3uxx	NUM
ejpam-6073	359	12	−	−	PROPN
ejpam-6073	360	1	a2zxx	a2zxx	PROPN
ejpam-6073	361	1	+	+	CCONJ
ejpam-6073	361	2	β	β	X
ejpam-6073	361	3	(	(	PUNCT
ejpam-6073	361	4	|ṽ1t|q(·)−2ṽ1	|ṽ1t|q(·)−2ṽ1	NOUN
ejpam-6073	361	5	t	t	NOUN
ejpam-6073	361	6	−	−	NUM
ejpam-6073	361	7	|ṽ2t|q(·)−2ṽ2	|ṽ2t|q(·)−2ṽ2	ADP
ejpam-6073	361	8	t	t	NOUN
ejpam-6073	361	9	)	)	PUNCT
ejpam-6073	362	1	=	=	PUNCT
ejpam-6073	363	1	d	d	PROPN
ejpam-6073	363	2	(	(	PUNCT
ejpam-6073	363	3	|ṽ1|ℓ(·)−2ṽ1	|ṽ1|ℓ(·)−2ṽ1	NOUN
ejpam-6073	363	4	−	−	PROPN
ejpam-6073	363	5	|ṽ2|ℓ(·)−2ṽ2	|ṽ2|ℓ(·)−2ṽ2	PROPN
ejpam-6073	363	6	)	)	PUNCT
ejpam-6073	363	7	,	,	PUNCT
ejpam-6073	363	8	u(x	u(x	PROPN
ejpam-6073	363	9	,	,	PUNCT
ejpam-6073	363	10	0	0	NUM
ejpam-6073	363	11	)	)	PUNCT
ejpam-6073	363	12	=	=	SYM
ejpam-6073	363	13	u0(x	u0(x	NOUN
ejpam-6073	363	14	)	)	PUNCT
ejpam-6073	363	15	,	,	PUNCT
ejpam-6073	363	16	ut(x	ut(x	NOUN
ejpam-6073	363	17	,	,	PUNCT
ejpam-6073	363	18	0	0	NUM
ejpam-6073	363	19	)	)	PUNCT
ejpam-6073	363	20	=	=	SYM
ejpam-6073	363	21	u1(x	u1(x	NOUN
ejpam-6073	363	22	)	)	PUNCT
ejpam-6073	363	23	,	,	PUNCT
ejpam-6073	363	24	z(x	z(x	NUM
ejpam-6073	363	25	,	,	PUNCT
ejpam-6073	363	26	0	0	NUM
ejpam-6073	363	27	)	)	PUNCT
ejpam-6073	363	28	=	=	SYM
ejpam-6073	363	29	z0(x	z0(x	NUM
ejpam-6073	363	30	)	)	PUNCT
ejpam-6073	363	31	,	,	PUNCT
ejpam-6073	363	32	zt(x	zt(x	NUM
ejpam-6073	363	33	,	,	PUNCT
ejpam-6073	363	34	0	0	NUM
ejpam-6073	363	35	)	)	PUNCT
ejpam-6073	363	36	=	=	SYM
ejpam-6073	363	37	z1(x	z1(x	NOUN
ejpam-6073	363	38	)	)	PUNCT
ejpam-6073	363	39	,	,	PUNCT
ejpam-6073	363	40	z(0	z(0	PROPN
ejpam-6073	363	41	,	,	PUNCT
ejpam-6073	363	42	t	t	PROPN
ejpam-6073	363	43	)	)	PUNCT
ejpam-6073	363	44	=	=	SYM
ejpam-6073	364	1	z(1	z(1	PROPN
ejpam-6073	364	2	,	,	PUNCT
ejpam-6073	364	3	t	t	PROPN
ejpam-6073	364	4	)	)	PUNCT
ejpam-6073	364	5	=	=	SYM
ejpam-6073	365	1	u(0	u(0	PROPN
ejpam-6073	365	2	,	,	PUNCT
ejpam-6073	365	3	t	t	PROPN
ejpam-6073	365	4	)	)	PUNCT
ejpam-6073	365	5	=	=	SYM
ejpam-6073	366	1	u(1	u(1	PROPN
ejpam-6073	366	2	,	,	PUNCT
ejpam-6073	366	3	t	t	PROPN
ejpam-6073	366	4	)	)	PUNCT
ejpam-6073	366	5	=	=	SYM
ejpam-6073	366	6	0	0	X
ejpam-6073	366	7	.	.	PUNCT
ejpam-6073	367	1	(	(	PUNCT
ejpam-6073	367	2	40	40	NUM
ejpam-6073	367	3	)	)	PUNCT
ejpam-6073	367	4	a.	a.	NOUN
ejpam-6073	367	5	m.	m.	PROPN
ejpam-6073	367	6	al	al	PROPN
ejpam-6073	367	7	-	-	PROPN
ejpam-6073	367	8	mahdi	mahdi	PROPN
ejpam-6073	367	9	et	et	PROPN
ejpam-6073	367	10	al	al	PROPN
ejpam-6073	367	11	.	.	PUNCT
ejpam-6073	367	12	/	/	SYM
ejpam-6073	367	13	eur	eur	PROPN
ejpam-6073	367	14	.	.	PUNCT
ejpam-6073	368	1	j.	j.	PROPN
ejpam-6073	368	2	pure	pure	PROPN
ejpam-6073	368	3	appl	appl	PROPN
ejpam-6073	368	4	.	.	PROPN
ejpam-6073	368	5	math	math	PROPN
ejpam-6073	368	6	,	,	PUNCT
ejpam-6073	368	7	18	18	NUM
ejpam-6073	368	8	(	(	PUNCT
ejpam-6073	368	9	3	3	NUM
ejpam-6073	368	10	)	)	PUNCT
ejpam-6073	368	11	(	(	PUNCT
ejpam-6073	368	12	2025	2025	NUM
ejpam-6073	368	13	)	)	PUNCT
ejpam-6073	368	14	,	,	PUNCT
ejpam-6073	368	15	6073	6073	NUM
ejpam-6073	368	16	17	17	NUM
ejpam-6073	368	17	of	of	ADP
ejpam-6073	368	18	29	29	NUM
ejpam-6073	368	19	multiplication	multiplication	NOUN
ejpam-6073	368	20	the	the	DET
ejpam-6073	368	21	first	first	ADJ
ejpam-6073	368	22	equation	equation	NOUN
ejpam-6073	368	23	by	by	ADP
ejpam-6073	368	24	zt	zt	PROPN
ejpam-6073	368	25	and	and	CCONJ
ejpam-6073	368	26	the	the	DET
ejpam-6073	368	27	second	second	ADJ
ejpam-6073	368	28	by	by	ADP
ejpam-6073	368	29	ut	ut	PROPN
ejpam-6073	368	30	,	,	PUNCT
ejpam-6073	368	31	integration	integration	NOUN
ejpam-6073	368	32	over	over	ADP
ejpam-6073	368	33	ω	ω	NUM
ejpam-6073	368	34	×	×	NOUN
ejpam-6073	368	35	(	(	PUNCT
ejpam-6073	368	36	0	0	NUM
ejpam-6073	368	37	,	,	PUNCT
ejpam-6073	368	38	t	t	PROPN
ejpam-6073	368	39	)	)	PUNCT
ejpam-6073	368	40	and	and	CCONJ
ejpam-6073	368	41	addition	addition	NOUN
ejpam-6073	368	42	of	of	ADP
ejpam-6073	368	43	the	the	DET
ejpam-6073	368	44	two	two	NUM
ejpam-6073	368	45	equations	equation	NOUN
ejpam-6073	368	46	yield	yield	VERB
ejpam-6073	368	47	ρu	ρu	ADV
ejpam-6073	368	48	2	2	NUM
ejpam-6073	368	49	∥ut∥22	∥ut∥22	ADV
ejpam-6073	369	1	+	+	NUM
ejpam-6073	369	2	ρz	ρz	NOUN
ejpam-6073	369	3	2	2	NUM
ejpam-6073	369	4	∥zt∥22	∥zt∥22	PROPN
ejpam-6073	369	5	+	+	NUM
ejpam-6073	369	6	a3	a3	NOUN
ejpam-6073	369	7	2	2	NUM
ejpam-6073	369	8	∥ux∥22	∥ux∥22	NOUN
ejpam-6073	369	9	+	+	CCONJ
ejpam-6073	369	10	a1	a1	NOUN
ejpam-6073	369	11	2	2	NUM
ejpam-6073	369	12	∥zx∥22	∥zx∥22	PROPN
ejpam-6073	369	13	+	+	CCONJ
ejpam-6073	370	1	a2	a2	PROPN
ejpam-6073	370	2	∫	∫	PROPN
ejpam-6073	370	3	ω	ω	PROPN
ejpam-6073	370	4	uxzxdx	uxzxdx	NOUN
ejpam-6073	370	5	+	+	CCONJ
ejpam-6073	370	6	γ	γ	PROPN
ejpam-6073	370	7	∫	∫	PROPN
ejpam-6073	370	8	t	t	PROPN
ejpam-6073	370	9	0	0	NUM
ejpam-6073	370	10	∫	∫	PROPN
ejpam-6073	370	11	ω	ω	PROPN
ejpam-6073	370	12	(	(	PUNCT
ejpam-6073	370	13	|v1t|p(·)−2v1	|v1t|p(·)−2v1	NOUN
ejpam-6073	370	14	t	t	NOUN
ejpam-6073	370	15	−	−	PROPN
ejpam-6073	370	16	|v2t|p(·)−2v2	|v2t|p(·)−2v2	NOUN
ejpam-6073	370	17	t	t	NOUN
ejpam-6073	370	18	)	)	PUNCT
ejpam-6073	370	19	ztdxds+	ztdxds+	X
ejpam-6073	371	1	β	β	X
ejpam-6073	371	2	∫	∫	PROPN
ejpam-6073	371	3	t	t	PROPN
ejpam-6073	371	4	0	0	NUM
ejpam-6073	371	5	∫	∫	PROPN
ejpam-6073	371	6	ω	ω	PROPN
ejpam-6073	371	7	(	(	PUNCT
ejpam-6073	371	8	|ṽ1t|q(·)−2ṽ1	|ṽ1t|q(·)−2ṽ1	NOUN
ejpam-6073	371	9	t	t	NOUN
ejpam-6073	371	10	−	−	NUM
ejpam-6073	371	11	|ṽ2t|q(·)−2ṽ2	|ṽ2t|q(·)−2ṽ2	ADP
ejpam-6073	371	12	t	t	NOUN
ejpam-6073	371	13	)	)	PUNCT
ejpam-6073	372	1	utdxds	utdxds	NOUN
ejpam-6073	372	2	=	=	SYM
ejpam-6073	373	1	∫	∫	PROPN
ejpam-6073	373	2	t	t	PROPN
ejpam-6073	373	3	0	0	NUM
ejpam-6073	374	1	∫	∫	PROPN
ejpam-6073	374	2	ω	ω	PROPN
ejpam-6073	374	3	(	(	PUNCT
ejpam-6073	374	4	h1(v1)−	h1(v1)−	PROPN
ejpam-6073	374	5	h1(v2))ztdxds+	h1(v2))ztdxds+	PROPN
ejpam-6073	374	6	∫	∫	PROPN
ejpam-6073	375	1	t	t	PROPN
ejpam-6073	375	2	0	0	NUM
ejpam-6073	376	1	∫	∫	PROPN
ejpam-6073	377	1	ω	ω	PROPN
ejpam-6073	378	1	(	(	PUNCT
ejpam-6073	379	1	h2(ṽ1)−	h2(ṽ1)−	PROPN
ejpam-6073	379	2	h2(ṽ2))utdxds	h2(ṽ2))utdxds	PROPN
ejpam-6073	379	3	.	.	PUNCT
ejpam-6073	380	1	hence	hence	ADV
ejpam-6073	380	2	,	,	PUNCT
ejpam-6073	380	3	we	we	PRON
ejpam-6073	380	4	have	have	VERB
ejpam-6073	380	5	ρu	ρu	ADV
ejpam-6073	380	6	2	2	NUM
ejpam-6073	380	7	∥ut∥22	∥ut∥22	ADV
ejpam-6073	381	1	+	+	NUM
ejpam-6073	381	2	ρz	ρz	NOUN
ejpam-6073	381	3	2	2	NUM
ejpam-6073	381	4	∥zt∥22	∥zt∥22	PROPN
ejpam-6073	381	5	+	+	NUM
ejpam-6073	381	6	a3	a3	NOUN
ejpam-6073	381	7	2	2	NUM
ejpam-6073	381	8	∥ux∥22	∥ux∥22	NOUN
ejpam-6073	381	9	+	+	CCONJ
ejpam-6073	381	10	a1	a1	NOUN
ejpam-6073	381	11	2	2	NUM
ejpam-6073	381	12	∥zx∥22	∥zx∥22	PROPN
ejpam-6073	381	13	+	+	CCONJ
ejpam-6073	382	1	a2	a2	PROPN
ejpam-6073	382	2	∫	∫	PROPN
ejpam-6073	382	3	ω	ω	PROPN
ejpam-6073	382	4	uxzxdx	uxzxdx	PROPN
ejpam-6073	383	1	≤	≤	NUM
ejpam-6073	383	2	∫	∫	PROPN
ejpam-6073	383	3	t	t	PROPN
ejpam-6073	383	4	0	0	NUM
ejpam-6073	383	5	∫	∫	PROPN
ejpam-6073	383	6	ω	ω	PROPN
ejpam-6073	383	7	(	(	PUNCT
ejpam-6073	383	8	h1(v2)−	h1(v2)−	NOUN
ejpam-6073	383	9	h1(v2))ztdxds+	h1(v2))ztdxds+	PROPN
ejpam-6073	383	10	∫	∫	PROPN
ejpam-6073	384	1	t	t	PROPN
ejpam-6073	384	2	0	0	NUM
ejpam-6073	384	3	∫	∫	PROPN
ejpam-6073	384	4	ω	ω	PROPN
ejpam-6073	384	5	(	(	PUNCT
ejpam-6073	384	6	h2(ṽ1)−	h2(ṽ1)−	PROPN
ejpam-6073	384	7	h2(ṽ2))utdxds	h2(ṽ2))utdxds	PROPN
ejpam-6073	384	8	.	.	PUNCT
ejpam-6073	385	1	(	(	PUNCT
ejpam-6073	385	2	41	41	NUM
ejpam-6073	385	3	)	)	PUNCT
ejpam-6073	385	4	now	now	ADV
ejpam-6073	385	5	,	,	PUNCT
ejpam-6073	385	6	we	we	PRON
ejpam-6073	385	7	evaluate	evaluate	VERB
ejpam-6073	385	8	i1	i1	PROPN
ejpam-6073	385	9	=	=	SYM
ejpam-6073	385	10	∫	∫	PROPN
ejpam-6073	385	11	ω	ω	NUM
ejpam-6073	385	12	|h1(v1)−	|h1(v1)−	NOUN
ejpam-6073	385	13	h1(v2)||zt|	h1(v2)||zt|	NOUN
ejpam-6073	385	14	and	and	CCONJ
ejpam-6073	385	15	i2	i2	PROPN
ejpam-6073	385	16	=	=	SYM
ejpam-6073	385	17	∫	∫	PROPN
ejpam-6073	385	18	ω	ω	PROPN
ejpam-6073	385	19	|h2(ṽ1)−	|h2(ṽ1)−	PROPN
ejpam-6073	385	20	h2(ṽ2)||ut|	h2(ṽ2)||ut|	PROPN
ejpam-6073	385	21	.	.	PUNCT
ejpam-6073	386	1	therefore	therefore	ADV
ejpam-6073	386	2	,	,	PUNCT
ejpam-6073	386	3	i1	i1	PROPN
ejpam-6073	386	4	=	=	SYM
ejpam-6073	386	5	∫	∫	PROPN
ejpam-6073	386	6	ω	ω	NUM
ejpam-6073	386	7	|h1(v1	|h1(v1	PROPN
ejpam-6073	386	8	)	)	PUNCT
ejpam-6073	386	9	−	−	NOUN
ejpam-6073	386	10	h1(v2)||zt|	h1(v2)||zt|	NOUN
ejpam-6073	386	11	=	=	SYM
ejpam-6073	386	12	∫	∫	PROPN
ejpam-6073	386	13	ω	ω	PROPN
ejpam-6073	386	14	|h′1(ξ)||v||zt|,where	|h′1(ξ)||v||zt|,where	ADP
ejpam-6073	386	15	v	v	NOUN
ejpam-6073	386	16	=	=	SYM
ejpam-6073	386	17	v1	v1	NOUN
ejpam-6073	386	18	−	−	PROPN
ejpam-6073	386	19	v2	v2	PROPN
ejpam-6073	386	20	and	and	CCONJ
ejpam-6073	386	21	ξ	ξ	X
ejpam-6073	386	22	=	=	SYM
ejpam-6073	386	23	αv1	αv1	PROPN
ejpam-6073	386	24	−	−	PROPN
ejpam-6073	386	25	(	(	PUNCT
ejpam-6073	386	26	1−	1−	NUM
ejpam-6073	386	27	α)v2	α)v2	PROPN
ejpam-6073	386	28	,	,	PUNCT
ejpam-6073	386	29	0	0	NUM
ejpam-6073	386	30	≤	≤	NUM
ejpam-6073	386	31	α	α	NOUN
ejpam-6073	386	32	≤	≤	NUM
ejpam-6073	386	33	1	1	NUM
ejpam-6073	386	34	.	.	PUNCT
ejpam-6073	386	35	applying	apply	VERB
ejpam-6073	386	36	young	young	PROPN
ejpam-6073	386	37	’s	’s	PART
ejpam-6073	386	38	inequality	inequality	NOUN
ejpam-6073	386	39	,	,	PUNCT
ejpam-6073	386	40	we	we	PRON
ejpam-6073	386	41	get	get	VERB
ejpam-6073	386	42	for	for	ADP
ejpam-6073	386	43	any	any	DET
ejpam-6073	386	44	δ	δ	PROPN
ejpam-6073	386	45	>	>	X
ejpam-6073	386	46	0	0	PUNCT
ejpam-6073	387	1	and	and	CCONJ
ejpam-6073	387	2	some	some	DET
ejpam-6073	387	3	positive	positive	ADJ
ejpam-6073	387	4	constant	constant	ADJ
ejpam-6073	387	5	c	c	NOUN
ejpam-6073	387	6	,	,	PUNCT
ejpam-6073	387	7	i1	i1	PROPN
ejpam-6073	387	8	≤	≤	PROPN
ejpam-6073	387	9	δ	δ	PROPN
ejpam-6073	387	10	2	2	NUM
ejpam-6073	387	11	∫	∫	PROPN
ejpam-6073	387	12	ω	ω	PROPN
ejpam-6073	387	13	z2	z2	PROPN
ejpam-6073	387	14	t	t	PROPN
ejpam-6073	387	15	dx+	dx+	NOUN
ejpam-6073	387	16	2	2	NUM
ejpam-6073	387	17	δ	δ	PROPN
ejpam-6073	387	18	∫	∫	PROPN
ejpam-6073	387	19	ω	ω	PROPN
ejpam-6073	387	20	|h′1(ξ)|2|v|2dx	|h′1(ξ)|2|v|2dx	PROPN
ejpam-6073	387	21	≤	≤	ADJ
ejpam-6073	387	22	δ	δ	PROPN
ejpam-6073	387	23	2	2	NUM
ejpam-6073	387	24	∫	∫	PROPN
ejpam-6073	387	25	ω	ω	PROPN
ejpam-6073	387	26	z2	z2	PROPN
ejpam-6073	387	27	t	t	PROPN
ejpam-6073	387	28	dx+	dx+	NOUN
ejpam-6073	387	29	c	c	PROPN
ejpam-6073	387	30	δ	δ	PROPN
ejpam-6073	387	31	∫	∫	PROPN
ejpam-6073	387	32	ω	ω	NUM
ejpam-6073	388	1	|αv1	|αv1	PROPN
ejpam-6073	388	2	−	−	PROPN
ejpam-6073	388	3	(	(	PUNCT
ejpam-6073	388	4	1−	1−	NUM
ejpam-6073	388	5	α)v2|2(m(x)−2)|v|2dx	α)v2|2(m(x)−2)|v|2dx	PROPN
ejpam-6073	388	6	≤	≤	PUNCT
ejpam-6073	388	7	δ	δ	PROPN
ejpam-6073	388	8	2	2	NUM
ejpam-6073	388	9	∫	∫	PROPN
ejpam-6073	388	10	ω	ω	PROPN
ejpam-6073	388	11	z2	z2	PROPN
ejpam-6073	388	12	t	t	PROPN
ejpam-6073	388	13	dx	dx	PROPN
ejpam-6073	389	1	+	+	CCONJ
ejpam-6073	389	2	cδ	cδ	PROPN
ejpam-6073	389	3	(	(	PUNCT
ejpam-6073	389	4	∫	∫	PROPN
ejpam-6073	389	5	ω	ω	PROPN
ejpam-6073	389	6	|v|	|v|	PROPN
ejpam-6073	389	7	2n	2n	NUM
ejpam-6073	389	8	n−2	n−2	PROPN
ejpam-6073	389	9	)	)	PUNCT
ejpam-6073	389	10	n−2	n−2	PROPN
ejpam-6073	389	11	n	n	NUM
ejpam-6073	389	12	×	×	NOUN
ejpam-6073	390	1	[	[	X
ejpam-6073	390	2	(	(	PUNCT
ejpam-6073	390	3	∫	∫	PROPN
ejpam-6073	390	4	ω	ω	PROPN
ejpam-6073	390	5	|αv1	|αv1	PROPN
ejpam-6073	390	6	+	+	CCONJ
ejpam-6073	390	7	(	(	PUNCT
ejpam-6073	390	8	1−	1−	NUM
ejpam-6073	390	9	α)v2|n(m2−2	α)v2|n(m2−2	NUM
ejpam-6073	390	10	)	)	PUNCT
ejpam-6073	390	11	)	)	PUNCT
ejpam-6073	390	12	2	2	NUM
ejpam-6073	390	13	n	n	NOUN
ejpam-6073	390	14	+	+	CCONJ
ejpam-6073	390	15	(	(	PUNCT
ejpam-6073	390	16	∫	∫	PROPN
ejpam-6073	390	17	ω	ω	NUM
ejpam-6073	390	18	|αv1	|αv1	PROPN
ejpam-6073	390	19	+	+	CCONJ
ejpam-6073	390	20	(	(	PUNCT
ejpam-6073	390	21	1−	1−	NUM
ejpam-6073	390	22	α)v2|n(m1−2	α)v2|n(m1−2	NUM
ejpam-6073	390	23	)	)	PUNCT
ejpam-6073	390	24	)	)	PUNCT
ejpam-6073	390	25	2	2	NUM
ejpam-6073	390	26	n	n	NOUN
ejpam-6073	390	27	]	]	PUNCT
ejpam-6073	390	28	.	.	PUNCT
ejpam-6073	391	1	by	by	ADP
ejpam-6073	391	2	recalling	recall	VERB
ejpam-6073	391	3	lemma	lemma	PROPN
ejpam-6073	391	4	(	(	PUNCT
ejpam-6073	391	5	15	15	NUM
ejpam-6073	391	6	)	)	PUNCT
ejpam-6073	391	7	,	,	PUNCT
ejpam-6073	391	8	we	we	PRON
ejpam-6073	391	9	arrive	arrive	VERB
ejpam-6073	391	10	at	at	ADP
ejpam-6073	391	11	i1	i1	PROPN
ejpam-6073	391	12	≤	≤	PROPN
ejpam-6073	392	1	δ	δ	PROPN
ejpam-6073	392	2	2	2	NUM
ejpam-6073	392	3	∫	∫	PROPN
ejpam-6073	392	4	ω	ω	PROPN
ejpam-6073	392	5	z2	z2	PROPN
ejpam-6073	392	6	t	t	PROPN
ejpam-6073	392	7	dx+	dx+	NOUN
ejpam-6073	392	8	cδce∥vx∥22	cδce∥vx∥22	X
ejpam-6073	392	9	(	(	PUNCT
ejpam-6073	392	10	∥v1x∥	∥v1x∥	NOUN
ejpam-6073	392	11	2(m2−2	2(m2−2	NUM
ejpam-6073	392	12	)	)	PUNCT
ejpam-6073	392	13	2	2	NUM
ejpam-6073	392	14	+	+	CCONJ
ejpam-6073	392	15	∥v1x∥	∥v1x∥	NOUN
ejpam-6073	392	16	2(m1−2	2(m1−2	NUM
ejpam-6073	392	17	)	)	PUNCT
ejpam-6073	392	18	2	2	NUM
ejpam-6073	392	19	+	+	CCONJ
ejpam-6073	392	20	∥v2x∥	∥v2x∥	ADP
ejpam-6073	392	21	2(m2−2	2(m2−2	NUM
ejpam-6073	392	22	)	)	PUNCT
ejpam-6073	392	23	2	2	NUM
ejpam-6073	393	1	+	+	CCONJ
ejpam-6073	393	2	∥v2x∥	∥v2x∥	ADP
ejpam-6073	393	3	2(m1−2	2(m1−2	NUM
ejpam-6073	393	4	)	)	PUNCT
ejpam-6073	393	5	2	2	NUM
ejpam-6073	393	6	)	)	PUNCT
ejpam-6073	393	7	≤	≤	NUM
ejpam-6073	393	8	δ	δ	PROPN
ejpam-6073	393	9	2	2	NUM
ejpam-6073	393	10	∫	∫	PROPN
ejpam-6073	393	11	ω	ω	PROPN
ejpam-6073	393	12	z2	z2	PROPN
ejpam-6073	393	13	t	t	PROPN
ejpam-6073	393	14	dx+	dx+	PROPN
ejpam-6073	393	15	cδcem̃∥vx∥22	cδcem̃∥vx∥22	PROPN
ejpam-6073	393	16	.	.	PUNCT
ejpam-6073	394	1	similarly	similarly	ADV
ejpam-6073	394	2	,	,	PUNCT
ejpam-6073	394	3	we	we	PRON
ejpam-6073	394	4	can	can	AUX
ejpam-6073	394	5	show	show	VERB
ejpam-6073	394	6	that	that	SCONJ
ejpam-6073	394	7	i2	i2	PROPN
ejpam-6073	394	8	≤	≤	PROPN
ejpam-6073	394	9	δ	δ	PROPN
ejpam-6073	394	10	2	2	NUM
ejpam-6073	394	11	∫	∫	PROPN
ejpam-6073	394	12	ω	ω	PROPN
ejpam-6073	394	13	u2	u2	PROPN
ejpam-6073	394	14	t	t	PROPN
ejpam-6073	394	15	dx+	dx+	NOUN
ejpam-6073	394	16	cδcem̃∥ṽx∥22	cδcem̃∥ṽx∥22	PROPN
ejpam-6073	394	17	,	,	PUNCT
ejpam-6073	394	18	where	where	SCONJ
ejpam-6073	394	19	ṽ	ṽ	PROPN
ejpam-6073	394	20	=	=	SYM
ejpam-6073	394	21	ṽ1	ṽ1	PROPN
ejpam-6073	394	22	−	−	PROPN
ejpam-6073	394	23	ṽ2	ṽ2	PROPN
ejpam-6073	394	24	.	.	PROPN
ejpam-6073	394	25	therefore	therefore	ADV
ejpam-6073	394	26	,	,	PUNCT
ejpam-6073	394	27	(	(	PUNCT
ejpam-6073	394	28	41	41	NUM
ejpam-6073	394	29	)	)	PUNCT
ejpam-6073	394	30	takes	take	VERB
ejpam-6073	394	31	the	the	DET
ejpam-6073	394	32	form	form	NOUN
ejpam-6073	394	33	∥(z	∥(z	VERB
ejpam-6073	394	34	,	,	PUNCT
ejpam-6073	394	35	u)∥2wt×wt	u)∥2wt×wt	VERB
ejpam-6073	394	36	≤	≤	ADJ
ejpam-6073	394	37	δ	δ	PROPN
ejpam-6073	394	38	2	2	NUM
ejpam-6073	394	39	t0c∥(z	t0c∥(z	NOUN
ejpam-6073	394	40	,	,	PUNCT
ejpam-6073	394	41	u)∥2wt×wt	u)∥2wt×wt	VERB
ejpam-6073	394	42	+	+	CCONJ
ejpam-6073	394	43	4cδm̃t0c∥(v	4cδm̃t0c∥(v	ADJ
ejpam-6073	394	44	,	,	PUNCT
ejpam-6073	394	45	ṽ)∥2wt×wt	ṽ)∥2wt×wt	NOUN
ejpam-6073	394	46	.	.	PUNCT
ejpam-6073	395	1	a.	a.	PROPN
ejpam-6073	395	2	m.	m.	PROPN
ejpam-6073	395	3	al	al	PROPN
ejpam-6073	395	4	-	-	PROPN
ejpam-6073	395	5	mahdi	mahdi	PROPN
ejpam-6073	395	6	et	et	PROPN
ejpam-6073	395	7	al	al	PROPN
ejpam-6073	395	8	.	.	PUNCT
ejpam-6073	395	9	/	/	SYM
ejpam-6073	395	10	eur	eur	PROPN
ejpam-6073	395	11	.	.	PUNCT
ejpam-6073	396	1	j.	j.	PROPN
ejpam-6073	396	2	pure	pure	PROPN
ejpam-6073	396	3	appl	appl	PROPN
ejpam-6073	396	4	.	.	PROPN
ejpam-6073	396	5	math	math	PROPN
ejpam-6073	396	6	,	,	PUNCT
ejpam-6073	396	7	18	18	NUM
ejpam-6073	396	8	(	(	PUNCT
ejpam-6073	396	9	3	3	NUM
ejpam-6073	396	10	)	)	PUNCT
ejpam-6073	396	11	(	(	PUNCT
ejpam-6073	396	12	2025	2025	NUM
ejpam-6073	396	13	)	)	PUNCT
ejpam-6073	396	14	,	,	PUNCT
ejpam-6073	396	15	6073	6073	NUM
ejpam-6073	396	16	18	18	NUM
ejpam-6073	396	17	of	of	ADP
ejpam-6073	396	18	29	29	NUM
ejpam-6073	396	19	choosing	choose	VERB
ejpam-6073	396	20	δ	δ	PROPN
ejpam-6073	396	21	small	small	ADJ
ejpam-6073	396	22	enough	enough	ADV
ejpam-6073	396	23	,	,	PUNCT
ejpam-6073	396	24	we	we	PRON
ejpam-6073	396	25	arrive	arrive	VERB
ejpam-6073	396	26	at	at	ADP
ejpam-6073	396	27	∥(z	∥(z	ADV
ejpam-6073	396	28	,	,	PUNCT
ejpam-6073	396	29	u)∥2wt×wt	u)∥2wt×wt	VERB
ejpam-6073	396	30	≤	≤	ADJ
ejpam-6073	396	31	ct0∥(v	ct0∥(v	NOUN
ejpam-6073	396	32	,	,	PUNCT
ejpam-6073	396	33	ṽ)∥2wt×wt	ṽ)∥2wt×wt	ADV
ejpam-6073	396	34	.	.	PUNCT
ejpam-6073	397	1	taking	take	VERB
ejpam-6073	397	2	t0	t0	PRON
ejpam-6073	397	3	small	small	ADJ
ejpam-6073	397	4	enough	enough	ADV
ejpam-6073	397	5	,	,	PUNCT
ejpam-6073	397	6	we	we	PRON
ejpam-6073	397	7	get	get	VERB
ejpam-6073	397	8	,	,	PUNCT
ejpam-6073	397	9	for	for	SCONJ
ejpam-6073	397	10	some	some	PRON
ejpam-6073	397	11	0	0	NUM
ejpam-6073	397	12	<	<	X
ejpam-6073	397	13	k	k	X
ejpam-6073	397	14	<	<	X
ejpam-6073	397	15	1	1	NUM
ejpam-6073	397	16	,	,	PUNCT
ejpam-6073	397	17	∥(z	∥(z	ADV
ejpam-6073	397	18	,	,	PUNCT
ejpam-6073	397	19	u)∥wt×wt	u)∥wt×wt	ADJ
ejpam-6073	397	20	≤	≤	NOUN
ejpam-6073	397	21	k∥(v	k∥(v	NOUN
ejpam-6073	397	22	,	,	PUNCT
ejpam-6073	397	23	ṽ)∥2wt×wt	ṽ)∥2wt×wt	ADV
ejpam-6073	397	24	.	.	PUNCT
ejpam-6073	398	1	thus	thus	ADV
ejpam-6073	398	2	k	k	PROPN
ejpam-6073	398	3	is	be	AUX
ejpam-6073	398	4	a	a	DET
ejpam-6073	398	5	contraction	contraction	NOUN
ejpam-6073	398	6	.	.	PUNCT
ejpam-6073	399	1	the	the	DET
ejpam-6073	399	2	banach	banach	ADV
ejpam-6073	399	3	fixed	fix	VERB
ejpam-6073	399	4	theorem	theorem	NOUN
ejpam-6073	399	5	implies	imply	VERB
ejpam-6073	399	6	the	the	DET
ejpam-6073	399	7	existence	existence	NOUN
ejpam-6073	399	8	of	of	ADP
ejpam-6073	399	9	a	a	DET
ejpam-6073	399	10	unique	unique	ADJ
ejpam-6073	399	11	(	(	PUNCT
ejpam-6073	399	12	z	z	NOUN
ejpam-6073	399	13	,	,	PUNCT
ejpam-6073	399	14	u	u	NOUN
ejpam-6073	399	15	)	)	PUNCT
ejpam-6073	399	16	∈	∈	PROPN
ejpam-6073	399	17	d(0,m	d(0,m	NOUN
ejpam-6073	399	18	)	)	PUNCT
ejpam-6073	399	19	,	,	PUNCT
ejpam-6073	399	20	such	such	ADJ
ejpam-6073	399	21	that	that	SCONJ
ejpam-6073	399	22	k(z	k(z	PROPN
ejpam-6073	399	23	,	,	PUNCT
ejpam-6073	399	24	u	u	NOUN
ejpam-6073	399	25	)	)	PUNCT
ejpam-6073	399	26	=	=	SYM
ejpam-6073	400	1	(	(	PUNCT
ejpam-6073	400	2	z	z	NOUN
ejpam-6073	400	3	,	,	PUNCT
ejpam-6073	400	4	u	u	NOUN
ejpam-6073	400	5	)	)	PUNCT
ejpam-6073	400	6	.	.	PUNCT
ejpam-6073	401	1	hence	hence	ADV
ejpam-6073	401	2	,	,	PUNCT
ejpam-6073	401	3	,	,	PUNCT
ejpam-6073	401	4	(	(	PUNCT
ejpam-6073	401	5	z	z	X
ejpam-6073	401	6	,	,	PUNCT
ejpam-6073	401	7	u	u	NOUN
ejpam-6073	401	8	)	)	PUNCT
ejpam-6073	401	9	is	be	AUX
ejpam-6073	401	10	a	a	DET
ejpam-6073	401	11	weak	weak	ADJ
ejpam-6073	401	12	solution	solution	NOUN
ejpam-6073	401	13	of	of	ADP
ejpam-6073	401	14	system	system	NOUN
ejpam-6073	401	15	(	(	PUNCT
ejpam-6073	401	16	6	6	NUM
ejpam-6073	401	17	)	)	PUNCT
ejpam-6073	401	18	.	.	PUNCT
ejpam-6073	402	1	the	the	DET
ejpam-6073	402	2	uniqueness	uniqueness	NOUN
ejpam-6073	402	3	of	of	ADP
ejpam-6073	402	4	this	this	DET
ejpam-6073	402	5	solution	solution	NOUN
ejpam-6073	402	6	can	can	AUX
ejpam-6073	402	7	be	be	AUX
ejpam-6073	402	8	obtained	obtain	VERB
ejpam-6073	402	9	by	by	ADP
ejpam-6073	402	10	applying	apply	VERB
ejpam-6073	402	11	the	the	DET
ejpam-6073	402	12	energy	energy	NOUN
ejpam-6073	402	13	method	method	NOUN
ejpam-6073	402	14	.	.	PUNCT
ejpam-6073	403	1	5	5	X
ejpam-6073	403	2	.	.	X
ejpam-6073	403	3	global	global	ADJ
ejpam-6073	403	4	existence	existence	NOUN
ejpam-6073	403	5	in	in	ADP
ejpam-6073	403	6	this	this	DET
ejpam-6073	403	7	section	section	NOUN
ejpam-6073	403	8	,	,	PUNCT
ejpam-6073	403	9	we	we	PRON
ejpam-6073	403	10	prove	prove	VERB
ejpam-6073	403	11	that	that	DET
ejpam-6073	403	12	system	system	NOUN
ejpam-6073	403	13	(	(	PUNCT
ejpam-6073	403	14	6	6	NUM
ejpam-6073	403	15	)	)	PUNCT
ejpam-6073	403	16	has	have	VERB
ejpam-6073	403	17	a	a	DET
ejpam-6073	403	18	global	global	ADJ
ejpam-6073	403	19	solution	solution	NOUN
ejpam-6073	403	20	if	if	SCONJ
ejpam-6073	403	21	p	p	NOUN
ejpam-6073	403	22	≤	≤	X
ejpam-6073	403	23	m	m	PROPN
ejpam-6073	403	24	and	and	CCONJ
ejpam-6073	403	25	q	q	PROPN
ejpam-6073	403	26	≤	≤	NOUN
ejpam-6073	403	27	ℓ.	ℓ.	NOUN
ejpam-6073	403	28	proposition	proposition	NOUN
ejpam-6073	403	29	1	1	NUM
ejpam-6073	403	30	.	.	PUNCT
ejpam-6073	403	31	assume	assume	VERB
ejpam-6073	403	32	that	that	SCONJ
ejpam-6073	403	33	p	p	PROPN
ejpam-6073	403	34	≤	≤	X
ejpam-6073	403	35	m	m	PROPN
ejpam-6073	403	36	and	and	CCONJ
ejpam-6073	403	37	q	q	PROPN
ejpam-6073	403	38	≤	≤	PROPN
ejpam-6073	403	39	ℓ.	ℓ.	NOUN
ejpam-6073	403	40	then	then	ADV
ejpam-6073	403	41	,	,	PUNCT
ejpam-6073	403	42	system	system	NOUN
ejpam-6073	403	43	6	6	NUM
ejpam-6073	403	44	admits	admit	VERB
ejpam-6073	403	45	a	a	DET
ejpam-6073	403	46	unique	unique	ADJ
ejpam-6073	403	47	global	global	ADJ
ejpam-6073	403	48	solution	solution	NOUN
ejpam-6073	403	49	.	.	PUNCT
ejpam-6073	404	1	proof	proof	NOUN
ejpam-6073	404	2	.	.	PUNCT
ejpam-6073	405	1	similar	similar	ADJ
ejpam-6073	405	2	to	to	ADP
ejpam-6073	405	3	[	[	X
ejpam-6073	405	4	25	25	NUM
ejpam-6073	405	5	]	]	PUNCT
ejpam-6073	405	6	,	,	PUNCT
ejpam-6073	405	7	we	we	PRON
ejpam-6073	405	8	define	define	VERB
ejpam-6073	405	9	the	the	DET
ejpam-6073	405	10	following	follow	VERB
ejpam-6073	405	11	e(t	e(t	NOUN
ejpam-6073	405	12	)	)	PUNCT
ejpam-6073	405	13	:	:	PUNCT
ejpam-6073	406	1	=	=	SYM
ejpam-6073	406	2	e(t	e(t	NOUN
ejpam-6073	406	3	)	)	PUNCT
ejpam-6073	407	1	+	+	NUM
ejpam-6073	407	2	2c	2c	NUM
ejpam-6073	407	3	∫	∫	PROPN
ejpam-6073	407	4	ω	ω	PROPN
ejpam-6073	407	5	|z|m(x	|z|m(x	PROPN
ejpam-6073	407	6	)	)	PUNCT
ejpam-6073	407	7	m(x	m(x	PROPN
ejpam-6073	407	8	)	)	PUNCT
ejpam-6073	407	9	dx+	dx+	NOUN
ejpam-6073	407	10	2d	2d	PROPN
ejpam-6073	407	11	∫	∫	PROPN
ejpam-6073	407	12	ω	ω	NUM
ejpam-6073	407	13	|u|ℓ(x	|u|ℓ(x	NUM
ejpam-6073	407	14	)	)	PUNCT
ejpam-6073	408	1	ℓ(x	ℓ(x	PROPN
ejpam-6073	408	2	)	)	PUNCT
ejpam-6073	408	3	dx	dx	PROPN
ejpam-6073	409	1	=	=	NOUN
ejpam-6073	409	2	1	1	NUM
ejpam-6073	409	3	2	2	NUM
ejpam-6073	409	4	∫	∫	NOUN
ejpam-6073	409	5	ω	ω	NOUN
ejpam-6073	409	6	[	[	PUNCT
ejpam-6073	409	7	ρzz	ρzz	NOUN
ejpam-6073	409	8	2	2	NUM
ejpam-6073	409	9	t	t	NOUN
ejpam-6073	409	10	+	+	CCONJ
ejpam-6073	409	11	ρuu	ρuu	PROPN
ejpam-6073	409	12	2	2	NUM
ejpam-6073	409	13	t	t	NOUN
ejpam-6073	409	14	+	+	CCONJ
ejpam-6073	409	15	a3u	a3u	ADP
ejpam-6073	409	16	2	2	NUM
ejpam-6073	409	17	x	x	SYM
ejpam-6073	409	18	+	+	CCONJ
ejpam-6073	409	19	a1z	a1z	PROPN
ejpam-6073	409	20	2	2	NUM
ejpam-6073	409	21	x	x	SYM
ejpam-6073	409	22	+	+	X
ejpam-6073	409	23	2a2zxux	2a2zxux	NUM
ejpam-6073	409	24	]	]	PUNCT
ejpam-6073	409	25	dx	dx	PROPN
ejpam-6073	410	1	+	+	PROPN
ejpam-6073	410	2	c	c	PROPN
ejpam-6073	410	3	∫	∫	PROPN
ejpam-6073	410	4	ω	ω	PROPN
ejpam-6073	410	5	|z|m(x	|z|m(x	PROPN
ejpam-6073	410	6	)	)	PUNCT
ejpam-6073	410	7	m(x	m(x	PROPN
ejpam-6073	410	8	)	)	PUNCT
ejpam-6073	410	9	dx+	dx+	NOUN
ejpam-6073	411	1	d	d	X
ejpam-6073	411	2	∫	∫	PROPN
ejpam-6073	411	3	ω	ω	NUM
ejpam-6073	411	4	|u|ℓ(x	|u|ℓ(x	NUM
ejpam-6073	411	5	)	)	PUNCT
ejpam-6073	411	6	ℓ(x	ℓ(x	PROPN
ejpam-6073	411	7	)	)	PUNCT
ejpam-6073	411	8	dx	dx	PROPN
ejpam-6073	411	9	.	.	PUNCT
ejpam-6073	412	1	(	(	PUNCT
ejpam-6073	412	2	42	42	NUM
ejpam-6073	412	3	)	)	PUNCT
ejpam-6073	412	4	therefore	therefore	ADV
ejpam-6073	412	5	,	,	PUNCT
ejpam-6073	412	6	e	e	NOUN
ejpam-6073	412	7	′(t	′(t	PROPN
ejpam-6073	412	8	)	)	PUNCT
ejpam-6073	412	9	=	=	PUNCT
ejpam-6073	413	1	−γ	−γ	ADJ
ejpam-6073	413	2	∫	∫	PROPN
ejpam-6073	413	3	ω	ω	NUM
ejpam-6073	413	4	|zt|p(·)dx−	|zt|p(·)dx−	PROPN
ejpam-6073	413	5	β	β	PROPN
ejpam-6073	413	6	∫	∫	PROPN
ejpam-6073	413	7	ω	ω	X
ejpam-6073	413	8	|ut|q(·)dx+	|ut|q(·)dx+	NUM
ejpam-6073	413	9	2c	2c	NUM
ejpam-6073	413	10	∫	∫	NOUN
ejpam-6073	413	11	ω	ω	PROPN
ejpam-6073	414	1	|z|m(·)−2ztdx+	|z|m(·)−2ztdx+	PROPN
ejpam-6073	414	2	2d	2d	NUM
ejpam-6073	414	3	∫	∫	PROPN
ejpam-6073	414	4	ω	ω	NUM
ejpam-6073	414	5	|u|ℓ(·)−2utdx	|u|ℓ(·)−2utdx	PROPN
ejpam-6073	414	6	.	.	PUNCT
ejpam-6073	415	1	by	by	ADP
ejpam-6073	415	2	using	use	VERB
ejpam-6073	415	3	young	young	PROPN
ejpam-6073	415	4	’s	’s	PART
ejpam-6073	415	5	inequality	inequality	NOUN
ejpam-6073	415	6	,	,	PUNCT
ejpam-6073	415	7	we	we	PRON
ejpam-6073	415	8	obtain	obtain	VERB
ejpam-6073	415	9	for	for	ADP
ejpam-6073	415	10	any	any	DET
ejpam-6073	415	11	ε	ε	PROPN
ejpam-6073	415	12	,	,	PUNCT
ejpam-6073	415	13	δ	δ	PROPN
ejpam-6073	415	14	>	>	X
ejpam-6073	415	15	0	0	PROPN
ejpam-6073	415	16	,	,	PUNCT
ejpam-6073	415	17	e	e	NOUN
ejpam-6073	415	18	′(t	′(t	PROPN
ejpam-6073	415	19	)	)	PUNCT
ejpam-6073	415	20	≤	≤	NOUN
ejpam-6073	416	1	−γ	−γ	NOUN
ejpam-6073	416	2	∫	∫	PROPN
ejpam-6073	416	3	ω	ω	X
ejpam-6073	416	4	|zt|p(·)dx−	|zt|p(·)dx−	PROPN
ejpam-6073	417	1	β	β	PROPN
ejpam-6073	417	2	∫	∫	PROPN
ejpam-6073	417	3	ω	ω	NUM
ejpam-6073	417	4	|ut|q(·)dx	|ut|q(·)dx	X
ejpam-6073	417	5	(	(	PUNCT
ejpam-6073	417	6	43	43	NUM
ejpam-6073	417	7	)	)	PUNCT
ejpam-6073	418	1	+	+	NOUN
ejpam-6073	418	2	ε	ε	PROPN
ejpam-6073	418	3	∫	∫	PROPN
ejpam-6073	418	4	ω	ω	PROPN
ejpam-6073	418	5	|zt|m(.)dx+	|zt|m(.)dx+	NOUN
ejpam-6073	418	6	δ	δ	PROPN
ejpam-6073	418	7	∫	∫	PROPN
ejpam-6073	418	8	ω	ω	PROPN
ejpam-6073	418	9	|ut|ℓ(·)dx	|ut|ℓ(·)dx	X
ejpam-6073	418	10	(	(	PUNCT
ejpam-6073	418	11	44	44	NUM
ejpam-6073	418	12	)	)	PUNCT
ejpam-6073	418	13	+	+	CCONJ
ejpam-6073	418	14	∫	∫	PROPN
ejpam-6073	418	15	ω	ω	PROPN
ejpam-6073	418	16	cε(x)|z|m(.)dx+	cε(x)|z|m(.)dx+	NUM
ejpam-6073	418	17	∫	∫	PROPN
ejpam-6073	418	18	ω	ω	NUM
ejpam-6073	418	19	cδ(x)|u|ℓ(·)dx	cδ(x)|u|ℓ(·)dx	PROPN
ejpam-6073	418	20	.	.	PUNCT
ejpam-6073	419	1	(	(	PUNCT
ejpam-6073	419	2	45	45	NUM
ejpam-6073	419	3	)	)	PUNCT
ejpam-6073	419	4	by	by	ADP
ejpam-6073	419	5	noting	note	VERB
ejpam-6073	419	6	that	that	SCONJ
ejpam-6073	419	7	p	p	PROPN
ejpam-6073	419	8	≤	≤	X
ejpam-6073	419	9	m	m	PROPN
ejpam-6073	419	10	and	and	CCONJ
ejpam-6073	419	11	q	q	PROPN
ejpam-6073	419	12	≤	≤	NUM
ejpam-6073	419	13	ℓ	ℓ	PUNCT
ejpam-6073	419	14	,	,	PUNCT
ejpam-6073	419	15	we	we	PRON
ejpam-6073	419	16	have	have	VERB
ejpam-6073	419	17	e	e	NOUN
ejpam-6073	419	18	′(t	′(t	PROPN
ejpam-6073	419	19	)	)	PUNCT
ejpam-6073	419	20	≤	≤	NOUN
ejpam-6073	419	21	−γ	−γ	NOUN
ejpam-6073	419	22	∫	∫	PROPN
ejpam-6073	419	23	ω	ω	X
ejpam-6073	419	24	|zt|p(·)dx−	|zt|p(·)dx−	PROPN
ejpam-6073	419	25	β	β	PROPN
ejpam-6073	419	26	∫	∫	PROPN
ejpam-6073	419	27	ω	ω	X
ejpam-6073	419	28	|ut|q(·)dx+	|ut|q(·)dx+	PUNCT
ejpam-6073	419	29	cε	cε	PROPN
ejpam-6073	419	30	∫	∫	PROPN
ejpam-6073	419	31	ω	ω	SYM
ejpam-6073	419	32	|zt|p(·)dx+	|zt|p(·)dx+	PROPN
ejpam-6073	419	33	cδ	cδ	NOUN
ejpam-6073	419	34	∫	∫	PROPN
ejpam-6073	419	35	ω	ω	NUM
ejpam-6073	419	36	|ut|q(·)dx	|ut|q(·)dx	X
ejpam-6073	419	37	(	(	PUNCT
ejpam-6073	419	38	46	46	NUM
ejpam-6073	419	39	)	)	PUNCT
ejpam-6073	419	40	a.	a.	NOUN
ejpam-6073	419	41	m.	m.	PROPN
ejpam-6073	419	42	al	al	PROPN
ejpam-6073	419	43	-	-	PROPN
ejpam-6073	419	44	mahdi	mahdi	PROPN
ejpam-6073	419	45	et	et	PROPN
ejpam-6073	419	46	al	al	PROPN
ejpam-6073	419	47	.	.	PUNCT
ejpam-6073	419	48	/	/	SYM
ejpam-6073	419	49	eur	eur	PROPN
ejpam-6073	419	50	.	.	PUNCT
ejpam-6073	420	1	j.	j.	PROPN
ejpam-6073	420	2	pure	pure	PROPN
ejpam-6073	420	3	appl	appl	PROPN
ejpam-6073	420	4	.	.	PROPN
ejpam-6073	420	5	math	math	PROPN
ejpam-6073	420	6	,	,	PUNCT
ejpam-6073	420	7	18	18	NUM
ejpam-6073	420	8	(	(	PUNCT
ejpam-6073	420	9	3	3	NUM
ejpam-6073	420	10	)	)	PUNCT
ejpam-6073	420	11	(	(	PUNCT
ejpam-6073	420	12	2025	2025	NUM
ejpam-6073	420	13	)	)	PUNCT
ejpam-6073	420	14	,	,	PUNCT
ejpam-6073	420	15	6073	6073	NUM
ejpam-6073	420	16	19	19	NUM
ejpam-6073	420	17	of	of	ADP
ejpam-6073	420	18	29	29	NUM
ejpam-6073	420	19	+	+	NUM
ejpam-6073	420	20	∫	∫	PROPN
ejpam-6073	420	21	ω	ω	NUM
ejpam-6073	420	22	cε(x)|z|m(·)dx+	cε(x)|z|m(·)dx+	PROPN
ejpam-6073	420	23	∫	∫	PROPN
ejpam-6073	420	24	ω	ω	NUM
ejpam-6073	420	25	cδ(x)|u|ℓ(·)dx	cδ(x)|u|ℓ(·)dx	PROPN
ejpam-6073	420	26	.	.	PUNCT
ejpam-6073	421	1	(	(	PUNCT
ejpam-6073	421	2	47	47	NUM
ejpam-6073	421	3	)	)	PUNCT
ejpam-6073	421	4	choosing	choose	VERB
ejpam-6073	421	5	ε	ε	PROPN
ejpam-6073	421	6	and	and	CCONJ
ejpam-6073	421	7	δ	δ	PROPN
ejpam-6073	421	8	such	such	ADJ
ejpam-6073	421	9	that	that	SCONJ
ejpam-6073	421	10	γ	γ	PROPN
ejpam-6073	421	11	−	−	PROPN
ejpam-6073	421	12	cε	cε	NOUN
ejpam-6073	421	13	>	>	X
ejpam-6073	421	14	0	0	PUNCT
ejpam-6073	421	15	and	and	CCONJ
ejpam-6073	421	16	β	β	X
ejpam-6073	421	17	−	−	NOUN
ejpam-6073	421	18	cδ	cδ	INTJ
ejpam-6073	421	19	>	>	X
ejpam-6073	421	20	0	0	NUM
ejpam-6073	421	21	,	,	PUNCT
ejpam-6073	421	22	we	we	PRON
ejpam-6073	421	23	obtain	obtain	VERB
ejpam-6073	421	24	e	e	NOUN
ejpam-6073	421	25	′(t	′(t	NOUN
ejpam-6073	421	26	)	)	PUNCT
ejpam-6073	422	1	≤	≤	NUM
ejpam-6073	422	2	c	c	X
ejpam-6073	422	3	(	(	PUNCT
ejpam-6073	422	4	m2	m2	PROPN
ejpam-6073	422	5	∫	∫	PROPN
ejpam-6073	422	6	ω	ω	PROPN
ejpam-6073	422	7	|z|m(x	|z|m(x	PROPN
ejpam-6073	422	8	)	)	PUNCT
ejpam-6073	422	9	m(x	m(x	PROPN
ejpam-6073	422	10	)	)	PUNCT
ejpam-6073	422	11	dx+	dx+	NOUN
ejpam-6073	422	12	ℓ2	ℓ2	PROPN
ejpam-6073	422	13	∫	∫	PROPN
ejpam-6073	422	14	ω	ω	PROPN
ejpam-6073	422	15	|u|ℓ	|u|ℓ	PROPN
ejpam-6073	422	16	(	(	PUNCT
ejpam-6073	422	17	·	·	PUNCT
ejpam-6073	422	18	)	)	PUNCT
ejpam-6073	422	19	ℓ(x	ℓ(x	PROPN
ejpam-6073	422	20	)	)	PUNCT
ejpam-6073	422	21	dx	dx	PROPN
ejpam-6073	422	22	)	)	PUNCT
ejpam-6073	422	23	≤	≤	NOUN
ejpam-6073	422	24	ce(t	ce(t	PRON
ejpam-6073	422	25	)	)	PUNCT
ejpam-6073	422	26	.	.	PUNCT
ejpam-6073	423	1	(	(	PUNCT
ejpam-6073	423	2	48	48	NUM
ejpam-6073	423	3	)	)	PUNCT
ejpam-6073	423	4	a	a	DET
ejpam-6073	423	5	simple	simple	ADJ
ejpam-6073	423	6	integration	integration	NOUN
ejpam-6073	423	7	gives	give	VERB
ejpam-6073	423	8	e(t	e(t	NOUN
ejpam-6073	423	9	)	)	PUNCT
ejpam-6073	423	10	≤	≤	NOUN
ejpam-6073	423	11	e(0)ect	e(0)ect	NOUN
ejpam-6073	423	12	.	.	PUNCT
ejpam-6073	424	1	(	(	PUNCT
ejpam-6073	424	2	49	49	NUM
ejpam-6073	424	3	)	)	PUNCT
ejpam-6073	424	4	the	the	DET
ejpam-6073	424	5	last	last	ADJ
ejpam-6073	424	6	estimate	estimate	NOUN
ejpam-6073	424	7	together	together	ADV
ejpam-6073	424	8	with	with	ADP
ejpam-6073	424	9	the	the	DET
ejpam-6073	424	10	continuation	continuation	NOUN
ejpam-6073	424	11	principle	principle	NOUN
ejpam-6073	424	12	completes	complete	VERB
ejpam-6073	424	13	our	our	PRON
ejpam-6073	424	14	proof	proof	NOUN
ejpam-6073	424	15	.	.	PUNCT
ejpam-6073	425	1	6	6	X
ejpam-6073	425	2	.	.	X
ejpam-6073	425	3	blow	blow	NOUN
ejpam-6073	425	4	-	-	PUNCT
ejpam-6073	425	5	up	up	NOUN
ejpam-6073	425	6	in	in	ADP
ejpam-6073	425	7	this	this	DET
ejpam-6073	425	8	section	section	NOUN
ejpam-6073	425	9	,	,	PUNCT
ejpam-6073	425	10	we	we	PRON
ejpam-6073	425	11	show	show	VERB
ejpam-6073	425	12	that	that	SCONJ
ejpam-6073	425	13	the	the	DET
ejpam-6073	425	14	solution	solution	NOUN
ejpam-6073	425	15	of	of	ADP
ejpam-6073	425	16	system	system	NOUN
ejpam-6073	425	17	(	(	PUNCT
ejpam-6073	425	18	6	6	NUM
ejpam-6073	425	19	)	)	PUNCT
ejpam-6073	425	20	blows	blow	VERB
ejpam-6073	425	21	up	up	ADP
ejpam-6073	425	22	in	in	ADP
ejpam-6073	425	23	a	a	DET
ejpam-6073	425	24	finite	finite	ADJ
ejpam-6073	425	25	time	time	NOUN
ejpam-6073	425	26	.	.	PUNCT
ejpam-6073	426	1	our	our	PRON
ejpam-6073	426	2	blow	blow	VERB
ejpam-6073	426	3	-	-	PUNCT
ejpam-6073	426	4	up	up	ADP
ejpam-6073	426	5	result	result	NOUN
ejpam-6073	426	6	reads	read	NOUN
ejpam-6073	426	7	as	as	SCONJ
ejpam-6073	426	8	follows	follow	VERB
ejpam-6073	426	9	:	:	PUNCT
ejpam-6073	426	10	theorem	theorem	NOUN
ejpam-6073	426	11	3	3	X
ejpam-6073	426	12	.	.	PUNCT
ejpam-6073	426	13	assume	assume	VERB
ejpam-6073	426	14	that	that	SCONJ
ejpam-6073	426	15	(	(	PUNCT
ejpam-6073	426	16	a1	a1	NOUN
ejpam-6073	426	17	)	)	PUNCT
ejpam-6073	426	18	and	and	CCONJ
ejpam-6073	426	19	(	(	PUNCT
ejpam-6073	426	20	a2	a2	NOUN
ejpam-6073	426	21	)	)	PUNCT
ejpam-6073	426	22	hold	hold	NOUN
ejpam-6073	426	23	and	and	CCONJ
ejpam-6073	426	24	e(0	e(0	NOUN
ejpam-6073	426	25	)	)	PUNCT
ejpam-6073	426	26	<	<	X
ejpam-6073	427	1	0	0	X
ejpam-6073	427	2	.	.	PUNCT
ejpam-6073	428	1	then	then	ADV
ejpam-6073	428	2	the	the	DET
ejpam-6073	428	3	solution	solution	NOUN
ejpam-6073	428	4	of	of	ADP
ejpam-6073	428	5	system	system	NOUN
ejpam-6073	428	6	6	6	NUM
ejpam-6073	428	7	blows	blow	NOUN
ejpam-6073	428	8	-	-	PUNCT
ejpam-6073	428	9	up	up	NOUN
ejpam-6073	428	10	in	in	ADP
ejpam-6073	428	11	a	a	DET
ejpam-6073	428	12	finite	finite	ADJ
ejpam-6073	428	13	time	time	NOUN
ejpam-6073	428	14	.	.	PUNCT
ejpam-6073	429	1	proof	proof	NOUN
ejpam-6073	429	2	.	.	PUNCT
ejpam-6073	430	1	we	we	PRON
ejpam-6073	430	2	set	set	VERB
ejpam-6073	430	3	h(t	h(t	PROPN
ejpam-6073	430	4	)	)	PUNCT
ejpam-6073	430	5	:	:	PUNCT
ejpam-6073	431	1	=	=	NUM
ejpam-6073	431	2	−e(t	−e(t	NOUN
ejpam-6073	431	3	)	)	PUNCT
ejpam-6073	431	4	then	then	ADV
ejpam-6073	431	5	h	h	PROPN
ejpam-6073	431	6	′(t	′(t	PROPN
ejpam-6073	431	7	)	)	PUNCT
ejpam-6073	431	8	=	=	SYM
ejpam-6073	431	9	−e′(t	−e′(t	PROPN
ejpam-6073	431	10	)	)	PUNCT
ejpam-6073	431	11	≥	≥	NOUN
ejpam-6073	431	12	0	0	NUM
ejpam-6073	431	13	and	and	CCONJ
ejpam-6073	431	14	then	then	ADV
ejpam-6073	431	15	for	for	ADP
ejpam-6073	431	16	every	every	DET
ejpam-6073	431	17	t	t	NOUN
ejpam-6073	431	18	∈	∈	PROPN
ejpam-6073	432	1	[	[	X
ejpam-6073	432	2	0	0	NUM
ejpam-6073	432	3	,	,	PUNCT
ejpam-6073	432	4	t	t	NOUN
ejpam-6073	432	5	)	)	PUNCT
ejpam-6073	432	6	,	,	PUNCT
ejpam-6073	432	7	we	we	PRON
ejpam-6073	432	8	have	have	VERB
ejpam-6073	432	9	0	0	NUM
ejpam-6073	432	10	<	<	X
ejpam-6073	432	11	h(0	h(0	PROPN
ejpam-6073	432	12	)	)	PUNCT
ejpam-6073	432	13	≤	≤	ADV
ejpam-6073	432	14	h(t	h(t	PROPN
ejpam-6073	432	15	)	)	PUNCT
ejpam-6073	432	16	≤	≤	NOUN
ejpam-6073	432	17	c	c	PART
ejpam-6073	432	18	m1	m1	PROPN
ejpam-6073	432	19	∫	∫	PROPN
ejpam-6073	432	20	ω	ω	PROPN
ejpam-6073	432	21	|z|m(x)dx+	|z|m(x)dx+	PROPN
ejpam-6073	432	22	d	d	PROPN
ejpam-6073	432	23	ℓ1	ℓ1	VERB
ejpam-6073	432	24	∫	∫	PROPN
ejpam-6073	432	25	ω	ω	PROPN
ejpam-6073	432	26	|u|ℓ(x)dx	|u|ℓ(x)dx	PROPN
ejpam-6073	432	27	.	.	PUNCT
ejpam-6073	433	1	(	(	PUNCT
ejpam-6073	433	2	50	50	NUM
ejpam-6073	433	3	)	)	PUNCT
ejpam-6073	433	4	we	we	PRON
ejpam-6073	433	5	then	then	ADV
ejpam-6073	433	6	define	define	VERB
ejpam-6073	433	7	f	f	PROPN
ejpam-6073	433	8	(	(	PUNCT
ejpam-6073	433	9	t	t	PROPN
ejpam-6073	433	10	)	)	PUNCT
ejpam-6073	433	11	=	=	SYM
ejpam-6073	433	12	h1−α(t	h1−α(t	VERB
ejpam-6073	433	13	)	)	PUNCT
ejpam-6073	434	1	+	+	CCONJ
ejpam-6073	434	2	ε	ε	PROPN
ejpam-6073	434	3	∫	∫	PROPN
ejpam-6073	434	4	ω	ω	PROPN
ejpam-6073	434	5	(	(	PUNCT
ejpam-6073	434	6	ρzzzt	ρzzzt	NOUN
ejpam-6073	434	7	+	+	CCONJ
ejpam-6073	434	8	ρuuut)dx	ρuuut)dx	PROPN
ejpam-6073	434	9	,	,	PUNCT
ejpam-6073	434	10	(	(	PUNCT
ejpam-6073	434	11	51	51	NUM
ejpam-6073	434	12	)	)	PUNCT
ejpam-6073	434	13	for	for	ADP
ejpam-6073	434	14	0	0	NUM
ejpam-6073	434	15	<	<	X
ejpam-6073	434	16	α	α	X
ejpam-6073	434	17	<	<	X
ejpam-6073	434	18	1	1	NUM
ejpam-6073	434	19	and	and	CCONJ
ejpam-6073	434	20	a	a	DET
ejpam-6073	434	21	positive	positive	ADJ
ejpam-6073	434	22	number	number	NOUN
ejpam-6073	434	23	ε	ε	PROPN
ejpam-6073	434	24	to	to	PART
ejpam-6073	434	25	be	be	AUX
ejpam-6073	434	26	chosen	choose	VERB
ejpam-6073	434	27	later	later	ADV
ejpam-6073	434	28	.	.	PUNCT
ejpam-6073	435	1	by	by	ADP
ejpam-6073	435	2	taking	take	VERB
ejpam-6073	435	3	the	the	DET
ejpam-6073	435	4	derivative	derivative	NOUN
ejpam-6073	435	5	of	of	ADP
ejpam-6073	435	6	f	f	PROPN
ejpam-6073	435	7	and	and	CCONJ
ejpam-6073	435	8	using	use	VERB
ejpam-6073	435	9	eq	eq	X
ejpam-6073	435	10	.	.	PUNCT
ejpam-6073	436	1	(	(	PUNCT
ejpam-6073	436	2	6	6	NUM
ejpam-6073	436	3	)	)	PUNCT
ejpam-6073	436	4	,	,	PUNCT
ejpam-6073	436	5	we	we	PRON
ejpam-6073	436	6	obtain	obtain	VERB
ejpam-6073	436	7	f	f	PROPN
ejpam-6073	436	8	′(t	′(t	PROPN
ejpam-6073	436	9	)	)	PUNCT
ejpam-6073	436	10	=	=	PUNCT
ejpam-6073	437	1	(	(	PUNCT
ejpam-6073	437	2	1−	1−	NUM
ejpam-6073	437	3	α)h−α(t)h	α)h−α(t)h	NUM
ejpam-6073	437	4	′(t	′(t	NOUN
ejpam-6073	437	5	)	)	PUNCT
ejpam-6073	438	1	+	+	CCONJ
ejpam-6073	438	2	ε	ε	PROPN
ejpam-6073	438	3	∫	∫	PROPN
ejpam-6073	438	4	ω	ω	NUM
ejpam-6073	438	5	ρzz	ρzz	NOUN
ejpam-6073	438	6	2	2	NUM
ejpam-6073	438	7	t	t	NOUN
ejpam-6073	438	8	dx+	dx+	NOUN
ejpam-6073	438	9	ε	ε	PROPN
ejpam-6073	438	10	∫	∫	PROPN
ejpam-6073	438	11	ω	ω	PROPN
ejpam-6073	438	12	ρuu	ρuu	PROPN
ejpam-6073	438	13	2	2	NUM
ejpam-6073	438	14	tdx−	tdx−	PROPN
ejpam-6073	439	1	εa3	εa3	ADJ
ejpam-6073	439	2	∫	∫	PROPN
ejpam-6073	440	1	ω	ω	NUM
ejpam-6073	440	2	u2xdx−	u2xdx−	PROPN
ejpam-6073	440	3	εa1	εa1	PROPN
ejpam-6073	440	4	∫	∫	PROPN
ejpam-6073	440	5	ω	ω	PROPN
ejpam-6073	440	6	z2xdx	z2xdx	PROPN
ejpam-6073	440	7	−2εa2	−2εa2	PROPN
ejpam-6073	441	1	∫	∫	PROPN
ejpam-6073	441	2	ω	ω	PROPN
ejpam-6073	441	3	uxzxdx−	uxzxdx−	PROPN
ejpam-6073	442	1	εγ	εγ	PROPN
ejpam-6073	442	2	∫	∫	PROPN
ejpam-6073	442	3	ω	ω	PROPN
ejpam-6073	442	4	z|zt|p(·)−2ztdx−	z|zt|p(·)−2ztdx−	PROPN
ejpam-6073	442	5	εβ	εβ	PROPN
ejpam-6073	443	1	∫	∫	PROPN
ejpam-6073	443	2	ω	ω	NUM
ejpam-6073	444	1	u|ut|q(·)−2utdx	u|ut|q(·)−2utdx	PROPN
ejpam-6073	444	2	+	+	ADP
ejpam-6073	444	3	εc	εc	PROPN
ejpam-6073	444	4	∫	∫	PROPN
ejpam-6073	444	5	ω	ω	NUM
ejpam-6073	444	6	|z|m(·)dx+	|z|m(·)dx+	VERB
ejpam-6073	444	7	εc	εc	NOUN
ejpam-6073	444	8	∫	∫	PROPN
ejpam-6073	444	9	ω	ω	PROPN
ejpam-6073	444	10	|u|ℓ(·)dx	|u|ℓ(·)dx	VERB
ejpam-6073	444	11	.	.	PUNCT
ejpam-6073	445	1	(	(	PUNCT
ejpam-6073	445	2	52	52	NUM
ejpam-6073	445	3	)	)	PUNCT
ejpam-6073	445	4	adding	add	VERB
ejpam-6073	445	5	and	and	CCONJ
ejpam-6073	445	6	subtracting	subtract	VERB
ejpam-6073	445	7	ε(1	ε(1	PROPN
ejpam-6073	445	8	−	−	NOUN
ejpam-6073	445	9	θ)m1ℓ1h(t	θ)m1ℓ1h(t	NOUN
ejpam-6073	445	10	)	)	PUNCT
ejpam-6073	445	11	,	,	PUNCT
ejpam-6073	445	12	for	for	ADP
ejpam-6073	445	13	0	0	NUM
ejpam-6073	445	14	<	<	X
ejpam-6073	445	15	θ	θ	X
ejpam-6073	445	16	<	<	X
ejpam-6073	445	17	1	1	NUM
ejpam-6073	445	18	,	,	PUNCT
ejpam-6073	445	19	to	to	ADP
ejpam-6073	445	20	the	the	DET
ejpam-6073	445	21	right	right	ADJ
ejpam-6073	445	22	-	-	PUNCT
ejpam-6073	445	23	hand	hand	NOUN
ejpam-6073	445	24	side	side	NOUN
ejpam-6073	445	25	of	of	ADP
ejpam-6073	445	26	(	(	PUNCT
ejpam-6073	445	27	52	52	NUM
ejpam-6073	445	28	)	)	PUNCT
ejpam-6073	445	29	,	,	PUNCT
ejpam-6073	445	30	we	we	PRON
ejpam-6073	445	31	arrive	arrive	VERB
ejpam-6073	445	32	at	at	ADP
ejpam-6073	445	33	f	f	PROPN
ejpam-6073	445	34	′(t	′(t	PROPN
ejpam-6073	445	35	)	)	PUNCT
ejpam-6073	445	36	=	=	PUNCT
ejpam-6073	446	1	(	(	PUNCT
ejpam-6073	446	2	1−	1−	NUM
ejpam-6073	446	3	α)h−α(t)h	α)h−α(t)h	NUM
ejpam-6073	446	4	′(t	′(t	NOUN
ejpam-6073	446	5	)	)	PUNCT
ejpam-6073	447	1	+	+	NUM
ejpam-6073	447	2	ε(1−	ε(1−	PROPN
ejpam-6073	447	3	θ)m1ℓ1h(t	θ)m1ℓ1h(t	PROPN
ejpam-6073	447	4	)	)	PUNCT
ejpam-6073	447	5	a.	a.	NOUN
ejpam-6073	447	6	m.	m.	PROPN
ejpam-6073	447	7	al	al	PROPN
ejpam-6073	447	8	-	-	PROPN
ejpam-6073	447	9	mahdi	mahdi	PROPN
ejpam-6073	447	10	et	et	PROPN
ejpam-6073	447	11	al	al	PROPN
ejpam-6073	447	12	.	.	PUNCT
ejpam-6073	447	13	/	/	SYM
ejpam-6073	447	14	eur	eur	PROPN
ejpam-6073	447	15	.	.	PUNCT
ejpam-6073	448	1	j.	j.	PROPN
ejpam-6073	448	2	pure	pure	PROPN
ejpam-6073	448	3	appl	appl	PROPN
ejpam-6073	448	4	.	.	PROPN
ejpam-6073	448	5	math	math	PROPN
ejpam-6073	448	6	,	,	PUNCT
ejpam-6073	448	7	18	18	NUM
ejpam-6073	448	8	(	(	PUNCT
ejpam-6073	448	9	3	3	NUM
ejpam-6073	448	10	)	)	PUNCT
ejpam-6073	448	11	(	(	PUNCT
ejpam-6073	448	12	2025	2025	NUM
ejpam-6073	448	13	)	)	PUNCT
ejpam-6073	448	14	,	,	PUNCT
ejpam-6073	448	15	6073	6073	NUM
ejpam-6073	448	16	20	20	NUM
ejpam-6073	448	17	of	of	ADP
ejpam-6073	448	18	29	29	NUM
ejpam-6073	449	1	+	+	NUM
ejpam-6073	449	2	ερz	ερz	NOUN
ejpam-6073	449	3	(	(	PUNCT
ejpam-6073	449	4	1	1	NUM
ejpam-6073	449	5	+	+	CCONJ
ejpam-6073	449	6	(	(	PUNCT
ejpam-6073	449	7	1−	1−	NUM
ejpam-6073	449	8	θ)m1ℓ1	θ)m1ℓ1	NOUN
ejpam-6073	449	9	2	2	NUM
ejpam-6073	449	10	)	)	PUNCT
ejpam-6073	449	11	∫	∫	PROPN
ejpam-6073	449	12	ω	ω	PROPN
ejpam-6073	449	13	z2	z2	PROPN
ejpam-6073	449	14	t	t	PROPN
ejpam-6073	449	15	dx+	dx+	NOUN
ejpam-6073	449	16	ερu	ερu	NOUN
ejpam-6073	449	17	(	(	PUNCT
ejpam-6073	449	18	1	1	NUM
ejpam-6073	449	19	+	+	CCONJ
ejpam-6073	449	20	(	(	PUNCT
ejpam-6073	449	21	1−	1−	NUM
ejpam-6073	449	22	θ)m1ℓ1	θ)m1ℓ1	NOUN
ejpam-6073	449	23	2	2	NUM
ejpam-6073	449	24	)	)	PUNCT
ejpam-6073	449	25	∫	∫	PROPN
ejpam-6073	450	1	ω	ω	NUM
ejpam-6073	450	2	u2tdx	u2tdx	PROPN
ejpam-6073	450	3	−εa3	−εa3	PROPN
ejpam-6073	450	4	(	(	PUNCT
ejpam-6073	450	5	(	(	PUNCT
ejpam-6073	450	6	1−	1−	NUM
ejpam-6073	450	7	θ)m1ℓ1	θ)m1ℓ1	NOUN
ejpam-6073	450	8	2	2	NUM
ejpam-6073	450	9	−	−	NOUN
ejpam-6073	450	10	1	1	NUM
ejpam-6073	450	11	)	)	PUNCT
ejpam-6073	450	12	∫	∫	PROPN
ejpam-6073	451	1	ω	ω	NUM
ejpam-6073	451	2	u2xdx−	u2xdx−	PROPN
ejpam-6073	451	3	εa1	εa1	NOUN
ejpam-6073	451	4	(	(	PUNCT
ejpam-6073	451	5	(	(	PUNCT
ejpam-6073	451	6	1−	1−	NUM
ejpam-6073	451	7	θ)m1ℓ1	θ)m1ℓ1	NOUN
ejpam-6073	451	8	2	2	NUM
ejpam-6073	451	9	−	−	NOUN
ejpam-6073	451	10	1	1	NUM
ejpam-6073	451	11	)	)	PUNCT
ejpam-6073	451	12	∫	∫	PROPN
ejpam-6073	452	1	ω	ω	PROPN
ejpam-6073	452	2	z2xdx	z2xdx	PROPN
ejpam-6073	452	3	−2εa2	−2εa2	NOUN
ejpam-6073	452	4	(	(	PUNCT
ejpam-6073	452	5	(	(	PUNCT
ejpam-6073	452	6	1−	1−	NUM
ejpam-6073	452	7	θ)m1ℓ1	θ)m1ℓ1	NOUN
ejpam-6073	452	8	2	2	NUM
ejpam-6073	452	9	−	−	NOUN
ejpam-6073	452	10	1	1	NUM
ejpam-6073	452	11	)	)	PUNCT
ejpam-6073	452	12	∫	∫	PROPN
ejpam-6073	452	13	ω	ω	PROPN
ejpam-6073	453	1	uxzxdx+	uxzxdx+	X
ejpam-6073	453	2	εcℓ1	εcℓ1	PROPN
ejpam-6073	453	3	∫	∫	PROPN
ejpam-6073	453	4	ω	ω	NUM
ejpam-6073	453	5	|z|m(·)dx+	|z|m(·)dx+	PROPN
ejpam-6073	453	6	εcm1	εcm1	NOUN
ejpam-6073	453	7	∫	∫	PROPN
ejpam-6073	453	8	ω	ω	PROPN
ejpam-6073	453	9	|u|ℓ(·)dx	|u|ℓ(·)dx	VERB
ejpam-6073	453	10	−εγ	−εγ	PROPN
ejpam-6073	453	11	∫	∫	PROPN
ejpam-6073	454	1	ω	ω	PROPN
ejpam-6073	454	2	z|zt|p(·)−2ztdx−	z|zt|p(·)−2ztdx−	PROPN
ejpam-6073	454	3	εβ	εβ	PROPN
ejpam-6073	455	1	∫	∫	PROPN
ejpam-6073	455	2	ω	ω	PROPN
ejpam-6073	455	3	u|ut|q(·)−2utdx	u|ut|q(·)−2utdx	PROPN
ejpam-6073	455	4	.	.	PUNCT
ejpam-6073	456	1	(	(	PUNCT
ejpam-6073	456	2	53	53	NUM
ejpam-6073	456	3	)	)	PUNCT
ejpam-6073	456	4	for	for	ADP
ejpam-6073	456	5	θ	θ	PROPN
ejpam-6073	456	6	small	small	ADJ
ejpam-6073	456	7	enough	enough	ADV
ejpam-6073	456	8	,	,	PUNCT
ejpam-6073	456	9	we	we	PRON
ejpam-6073	456	10	have	have	VERB
ejpam-6073	456	11	for	for	ADP
ejpam-6073	456	12	some	some	DET
ejpam-6073	456	13	positive	positive	ADJ
ejpam-6073	456	14	constant	constant	ADJ
ejpam-6073	456	15	η	η	PROPN
ejpam-6073	456	16	f	f	PROPN
ejpam-6073	456	17	′(t	′(t	PROPN
ejpam-6073	456	18	)	)	PUNCT
ejpam-6073	456	19	≥	≥	NOUN
ejpam-6073	456	20	(	(	PUNCT
ejpam-6073	456	21	1−	1−	NUM
ejpam-6073	456	22	α)h−α(t)h	α)h−α(t)h	NUM
ejpam-6073	456	23	′(t	′(t	NOUN
ejpam-6073	456	24	)	)	PUNCT
ejpam-6073	457	1	+	+	NOUN
ejpam-6073	457	2	εη	εη	ADJ
ejpam-6073	457	3	[	[	PUNCT
ejpam-6073	457	4	h(t	h(t	PROPN
ejpam-6073	457	5	)	)	PUNCT
ejpam-6073	457	6	+	+	NUM
ejpam-6073	457	7	||ut||22	||ut||22	NOUN
ejpam-6073	457	8	+	+	CCONJ
ejpam-6073	457	9	||zt||22	||zt||22	NOUN
ejpam-6073	457	10	+	+	CCONJ
ejpam-6073	457	11	||ux||22	||ux||22	NOUN
ejpam-6073	457	12	+	+	CCONJ
ejpam-6073	457	13	||zx||22	||zx||22	NOUN
ejpam-6073	457	14	+	+	NUM
ejpam-6073	457	15	∫	∫	PROPN
ejpam-6073	457	16	ω	ω	NUM
ejpam-6073	457	17	|z|m(·)dx+	|z|m(·)dx+	PROPN
ejpam-6073	457	18	∫	∫	NOUN
ejpam-6073	457	19	ω	ω	NUM
ejpam-6073	457	20	1|u|ℓ(·)dx	1|u|ℓ(·)dx	NUM
ejpam-6073	457	21	]	]	PUNCT
ejpam-6073	458	1	−εγ	−εγ	PROPN
ejpam-6073	458	2	∫	∫	PROPN
ejpam-6073	459	1	ω	ω	PROPN
ejpam-6073	459	2	z|zt|p(·)−2ztdx−	z|zt|p(·)−2ztdx−	PROPN
ejpam-6073	459	3	εβ	εβ	PROPN
ejpam-6073	459	4	∫	∫	PROPN
ejpam-6073	459	5	ω	ω	PROPN
ejpam-6073	459	6	u|ut|q(·)−2utdx	u|ut|q(·)−2utdx	PROPN
ejpam-6073	459	7	,	,	PUNCT
ejpam-6073	459	8	(	(	PUNCT
ejpam-6073	459	9	54	54	NUM
ejpam-6073	459	10	)	)	PUNCT
ejpam-6073	459	11	now	now	ADV
ejpam-6073	459	12	,	,	PUNCT
ejpam-6073	459	13	by	by	ADP
ejpam-6073	459	14	using	use	VERB
ejpam-6073	459	15	young	young	PROPN
ejpam-6073	459	16	’s	’s	PART
ejpam-6073	459	17	inequality	inequality	NOUN
ejpam-6073	459	18	,	,	PUNCT
ejpam-6073	459	19	we	we	PRON
ejpam-6073	459	20	estimate	estimate	VERB
ejpam-6073	459	21	the	the	DET
ejpam-6073	459	22	last	last	ADJ
ejpam-6073	459	23	term	term	NOUN
ejpam-6073	459	24	in	in	ADP
ejpam-6073	459	25	(	(	PUNCT
ejpam-6073	459	26	54	54	NUM
ejpam-6073	459	27	)	)	PUNCT
ejpam-6073	459	28	as	as	SCONJ
ejpam-6073	459	29	follows	follow	VERB
ejpam-6073	459	30	:	:	PUNCT
ejpam-6073	459	31	for	for	ADP
ejpam-6073	459	32	any	any	DET
ejpam-6073	459	33	σ1	σ1	NOUN
ejpam-6073	459	34	,	,	PUNCT
ejpam-6073	459	35	σ2	σ2	PROPN
ejpam-6073	459	36	>	>	X
ejpam-6073	459	37	0	0	PROPN
ejpam-6073	459	38	,	,	PUNCT
ejpam-6073	459	39	we	we	PRON
ejpam-6073	459	40	have	have	VERB
ejpam-6073	459	41	∫	∫	PROPN
ejpam-6073	459	42	ω	ω	PROPN
ejpam-6073	460	1	|z||zt|p(·)−1dx	|z||zt|p(·)−1dx	ADP
ejpam-6073	460	2	≤	≤	ADJ
ejpam-6073	460	3	1	1	NUM
ejpam-6073	460	4	p1	p1	PROPN
ejpam-6073	460	5	∫	∫	PROPN
ejpam-6073	460	6	ω	ω	PROPN
ejpam-6073	460	7	σ	σ	PROPN
ejpam-6073	460	8	p(x	p(x	PROPN
ejpam-6073	460	9	)	)	PUNCT
ejpam-6073	460	10	1	1	NUM
ejpam-6073	460	11	|z|p(x)dx+	|z|p(x)dx+	NOUN
ejpam-6073	460	12	(	(	PUNCT
ejpam-6073	460	13	p2	p2	PROPN
ejpam-6073	460	14	−	−	PROPN
ejpam-6073	460	15	1	1	NUM
ejpam-6073	460	16	)	)	PUNCT
ejpam-6073	460	17	p2	p2	PROPN
ejpam-6073	461	1	∫	∫	PROPN
ejpam-6073	461	2	ω	ω	PROPN
ejpam-6073	461	3	σ	σ	PROPN
ejpam-6073	461	4	−p(x	−p(x	PROPN
ejpam-6073	461	5	)	)	PUNCT
ejpam-6073	461	6	p(x)−1	p(x)−1	NOUN
ejpam-6073	461	7	1	1	NUM
ejpam-6073	461	8	|zt|p(x)dx,∫	|zt|p(x)dx,∫	NOUN
ejpam-6073	461	9	ω	ω	NUM
ejpam-6073	461	10	|u||ut|q(·)−1dx	|u||ut|q(·)−1dx	PROPN
ejpam-6073	461	11	≤	≤	ADV
ejpam-6073	461	12	1	1	NUM
ejpam-6073	461	13	q1	q1	PROPN
ejpam-6073	461	14	∫	∫	PROPN
ejpam-6073	461	15	ω	ω	PROPN
ejpam-6073	461	16	σ	σ	PROPN
ejpam-6073	461	17	q(x	q(x	PROPN
ejpam-6073	461	18	)	)	PUNCT
ejpam-6073	461	19	2	2	NUM
ejpam-6073	461	20	|u|q(x)dx+	|u|q(x)dx+	NOUN
ejpam-6073	461	21	(	(	PUNCT
ejpam-6073	461	22	q2	q2	NOUN
ejpam-6073	461	23	−	−	NOUN
ejpam-6073	461	24	1	1	X
ejpam-6073	461	25	)	)	PUNCT
ejpam-6073	461	26	q2	q2	NOUN
ejpam-6073	461	27	∫	∫	PROPN
ejpam-6073	461	28	ω	ω	PROPN
ejpam-6073	461	29	σ	σ	PROPN
ejpam-6073	461	30	−q(x	−q(x	PROPN
ejpam-6073	461	31	)	)	PUNCT
ejpam-6073	461	32	q(x)−1	q(x)−1	NOUN
ejpam-6073	461	33	2	2	NUM
ejpam-6073	461	34	|ut|q(x)dx	|ut|q(x)dx	NOUN
ejpam-6073	461	35	.	.	PUNCT
ejpam-6073	462	1	(	(	PUNCT
ejpam-6073	462	2	55	55	NUM
ejpam-6073	462	3	)	)	PUNCT
ejpam-6073	462	4	therefore	therefore	ADV
ejpam-6073	462	5	,	,	PUNCT
ejpam-6073	462	6	by	by	ADP
ejpam-6073	462	7	choosing	choose	VERB
ejpam-6073	462	8	σ1	σ1	PROPN
ejpam-6073	462	9	and	and	CCONJ
ejpam-6073	462	10	σ2	σ2	NOUN
ejpam-6073	462	11	such	such	ADJ
ejpam-6073	462	12	that	that	SCONJ
ejpam-6073	462	13	σ	σ	PROPN
ejpam-6073	462	14	−p(x	−p(x	PROPN
ejpam-6073	462	15	)	)	PUNCT
ejpam-6073	462	16	p(x)−1	p(x)−1	NOUN
ejpam-6073	462	17	1	1	NUM
ejpam-6073	462	18	=	=	NOUN
ejpam-6073	462	19	ξ1h	ξ1h	VERB
ejpam-6073	462	20	−α(t	−α(t	NOUN
ejpam-6073	462	21	)	)	PUNCT
ejpam-6073	462	22	,	,	PUNCT
ejpam-6073	462	23	σ	σ	PROPN
ejpam-6073	462	24	−p(x	−p(x	PROPN
ejpam-6073	462	25	)	)	PUNCT
ejpam-6073	462	26	p(x)−1	p(x)−1	NOUN
ejpam-6073	462	27	2	2	NUM
ejpam-6073	462	28	=	=	SYM
ejpam-6073	462	29	ξ2h	ξ2h	NUM
ejpam-6073	462	30	−α(t	−α(t	NOUN
ejpam-6073	462	31	)	)	PUNCT
ejpam-6073	462	32	(	(	PUNCT
ejpam-6073	462	33	56	56	NUM
ejpam-6073	462	34	)	)	PUNCT
ejpam-6073	462	35	for	for	ADP
ejpam-6073	462	36	sufficiently	sufficiently	ADV
ejpam-6073	462	37	large	large	ADJ
ejpam-6073	462	38	constants	constant	NOUN
ejpam-6073	462	39	ξi	ξi	VERB
ejpam-6073	462	40	,	,	PUNCT
ejpam-6073	462	41	i	i	NOUN
ejpam-6073	462	42	=	=	NOUN
ejpam-6073	462	43	1	1	NUM
ejpam-6073	462	44	,	,	PUNCT
ejpam-6073	462	45	2	2	NUM
ejpam-6073	462	46	,	,	PUNCT
ejpam-6073	462	47	to	to	PART
ejpam-6073	462	48	be	be	AUX
ejpam-6073	462	49	specified	specify	VERB
ejpam-6073	462	50	later	later	ADV
ejpam-6073	462	51	,	,	PUNCT
ejpam-6073	462	52	and	and	CCONJ
ejpam-6073	462	53	substituting	substitute	VERB
ejpam-6073	462	54	these	these	PRON
ejpam-6073	462	55	into	into	ADP
ejpam-6073	462	56	(	(	PUNCT
ejpam-6073	462	57	55	55	NUM
ejpam-6073	462	58	)	)	PUNCT
ejpam-6073	462	59	,	,	PUNCT
ejpam-6073	462	60	we	we	PRON
ejpam-6073	462	61	obtain	obtain	VERB
ejpam-6073	462	62	:	:	PUNCT
ejpam-6073	463	1	∫	∫	PROPN
ejpam-6073	463	2	ω	ω	PROPN
ejpam-6073	463	3	|z||zt|p(·)−1dx+	|z||zt|p(·)−1dx+	PROPN
ejpam-6073	463	4	∫	∫	PROPN
ejpam-6073	463	5	ω	ω	PROPN
ejpam-6073	463	6	|u||ut|q(·)−1dx	|u||ut|q(·)−1dx	PROPN
ejpam-6073	463	7	≤	≤	ADV
ejpam-6073	463	8	1	1	NUM
ejpam-6073	463	9	p1	p1	PROPN
ejpam-6073	463	10	∫	∫	PROPN
ejpam-6073	463	11	ω	ω	PROPN
ejpam-6073	464	1	ξ	ξ	PROPN
ejpam-6073	464	2	1−p(x	1−p(x	NUM
ejpam-6073	464	3	)	)	PUNCT
ejpam-6073	464	4	1	1	NUM
ejpam-6073	464	5	|z|p(x)hα(p(x)−1)dx+	|z|p(x)hα(p(x)−1)dx+	NOUN
ejpam-6073	464	6	(	(	PUNCT
ejpam-6073	464	7	p2	p2	PROPN
ejpam-6073	464	8	−	−	PROPN
ejpam-6073	464	9	1	1	X
ejpam-6073	464	10	)	)	PUNCT
ejpam-6073	464	11	cp2	cp2	NOUN
ejpam-6073	464	12	ξ1h	ξ1h	VERB
ejpam-6073	464	13	−α(t)h	−α(t)h	ADJ
ejpam-6073	464	14	′(t	′(t	NOUN
ejpam-6073	464	15	)	)	PUNCT
ejpam-6073	465	1	+	+	CCONJ
ejpam-6073	465	2	1	1	NUM
ejpam-6073	465	3	q1	q1	PROPN
ejpam-6073	465	4	∫	∫	PROPN
ejpam-6073	465	5	ω	ω	PROPN
ejpam-6073	466	1	ξ	ξ	PROPN
ejpam-6073	466	2	1−q(x	1−q(x	NUM
ejpam-6073	466	3	)	)	PUNCT
ejpam-6073	466	4	2	2	NUM
ejpam-6073	466	5	|u|q(x)hα(q(x)−1)dx+	|u|q(x)hα(q(x)−1)dx+	ADJ
ejpam-6073	466	6	(	(	PUNCT
ejpam-6073	466	7	q2	q2	NOUN
ejpam-6073	466	8	−	−	NOUN
ejpam-6073	466	9	1	1	X
ejpam-6073	466	10	)	)	PUNCT
ejpam-6073	466	11	dq2	dq2	NOUN
ejpam-6073	466	12	ξ2h	ξ2h	PUNCT
ejpam-6073	466	13	−α(t)h	−α(t)h	ADJ
ejpam-6073	466	14	′(t	′(t	NOUN
ejpam-6073	466	15	)	)	PUNCT
ejpam-6073	466	16	.	.	PUNCT
ejpam-6073	467	1	(	(	PUNCT
ejpam-6073	467	2	57	57	X
ejpam-6073	467	3	)	)	PUNCT
ejpam-6073	467	4	combining	combine	VERB
ejpam-6073	467	5	(	(	PUNCT
ejpam-6073	467	6	54	54	NUM
ejpam-6073	467	7	)	)	PUNCT
ejpam-6073	467	8	and	and	CCONJ
ejpam-6073	467	9	(	(	PUNCT
ejpam-6073	467	10	57	57	NUM
ejpam-6073	467	11	)	)	PUNCT
ejpam-6073	467	12	,	,	PUNCT
ejpam-6073	467	13	we	we	PRON
ejpam-6073	467	14	obtain	obtain	VERB
ejpam-6073	467	15	f	f	PROPN
ejpam-6073	467	16	′(t	′(t	PROPN
ejpam-6073	467	17	)	)	PUNCT
ejpam-6073	467	18	≥	≥	NOUN
ejpam-6073	467	19	[	[	PUNCT
ejpam-6073	467	20	(	(	PUNCT
ejpam-6073	467	21	1−	1−	NUM
ejpam-6073	467	22	α)−	α)−	PROPN
ejpam-6073	467	23	ε	ε	PROPN
ejpam-6073	467	24	(	(	PUNCT
ejpam-6073	467	25	(	(	PUNCT
ejpam-6073	467	26	p2	p2	PROPN
ejpam-6073	467	27	−	−	NOUN
ejpam-6073	467	28	1	1	NUM
ejpam-6073	467	29	)	)	PUNCT
ejpam-6073	467	30	p2	p2	PROPN
ejpam-6073	467	31	ξ1	ξ1	NOUN
ejpam-6073	467	32	)	)	PUNCT
ejpam-6073	467	33	−	−	PROPN
ejpam-6073	468	1	ε	ε	PROPN
ejpam-6073	468	2	(	(	PUNCT
ejpam-6073	468	3	(	(	PUNCT
ejpam-6073	468	4	q2	q2	NOUN
ejpam-6073	468	5	−	−	NOUN
ejpam-6073	468	6	1	1	X
ejpam-6073	468	7	)	)	PUNCT
ejpam-6073	468	8	q2	q2	NOUN
ejpam-6073	468	9	ξ2	ξ2	NOUN
ejpam-6073	468	10	)	)	PUNCT
ejpam-6073	468	11	]	]	PUNCT
ejpam-6073	468	12	h−α(t)h	h−α(t)h	PROPN
ejpam-6073	468	13	′(t	′(t	PROPN
ejpam-6073	468	14	)	)	PUNCT
ejpam-6073	468	15	a.	a.	NOUN
ejpam-6073	468	16	m.	m.	PROPN
ejpam-6073	468	17	al	al	PROPN
ejpam-6073	468	18	-	-	PROPN
ejpam-6073	468	19	mahdi	mahdi	PROPN
ejpam-6073	468	20	et	et	PROPN
ejpam-6073	468	21	al	al	PROPN
ejpam-6073	468	22	.	.	PUNCT
ejpam-6073	468	23	/	/	SYM
ejpam-6073	468	24	eur	eur	PROPN
ejpam-6073	468	25	.	.	PUNCT
ejpam-6073	469	1	j.	j.	PROPN
ejpam-6073	469	2	pure	pure	PROPN
ejpam-6073	469	3	appl	appl	PROPN
ejpam-6073	469	4	.	.	PROPN
ejpam-6073	469	5	math	math	PROPN
ejpam-6073	469	6	,	,	PUNCT
ejpam-6073	469	7	18	18	NUM
ejpam-6073	469	8	(	(	PUNCT
ejpam-6073	469	9	3	3	NUM
ejpam-6073	469	10	)	)	PUNCT
ejpam-6073	469	11	(	(	PUNCT
ejpam-6073	469	12	2025	2025	NUM
ejpam-6073	469	13	)	)	PUNCT
ejpam-6073	469	14	,	,	PUNCT
ejpam-6073	469	15	6073	6073	NUM
ejpam-6073	469	16	21	21	NUM
ejpam-6073	469	17	of	of	ADP
ejpam-6073	469	18	29	29	NUM
ejpam-6073	470	1	+	+	NOUN
ejpam-6073	470	2	εη	εη	ADJ
ejpam-6073	470	3	[	[	PUNCT
ejpam-6073	470	4	h(t	h(t	PROPN
ejpam-6073	470	5	)	)	PUNCT
ejpam-6073	471	1	+	+	NUM
ejpam-6073	471	2	||ut||22	||ut||22	NOUN
ejpam-6073	471	3	+	+	CCONJ
ejpam-6073	471	4	||zt||22	||zt||22	NOUN
ejpam-6073	471	5	+	+	CCONJ
ejpam-6073	471	6	||ux||22	||ux||22	NOUN
ejpam-6073	471	7	+	+	CCONJ
ejpam-6073	471	8	||zx||22	||zx||22	NOUN
ejpam-6073	471	9	+	+	NUM
ejpam-6073	471	10	∫	∫	PROPN
ejpam-6073	471	11	ω	ω	NUM
ejpam-6073	471	12	|z|m(·)dx+	|z|m(·)dx+	PROPN
ejpam-6073	471	13	∫	∫	PROPN
ejpam-6073	471	14	ω	ω	NOUN
ejpam-6073	471	15	|u|ℓ(·)dx	|u|ℓ(·)dx	VERB
ejpam-6073	471	16	]	]	PUNCT
ejpam-6073	471	17	−cεξ	−cεξ	X
ejpam-6073	471	18	1−p1	1−p1	NUM
ejpam-6073	471	19	1	1	NUM
ejpam-6073	471	20	p1	p1	NOUN
ejpam-6073	471	21	hα(p2(x)−1)(t	hα(p2(x)−1)(t	PUNCT
ejpam-6073	471	22	)	)	PUNCT
ejpam-6073	471	23	∫	∫	PROPN
ejpam-6073	472	1	ω	ω	INTJ
ejpam-6073	472	2	|z|p(x)dx−	|z|p(x)dx−	PROPN
ejpam-6073	472	3	dε	dε	PROPN
ejpam-6073	472	4	ξ1−q1	ξ1−q1	NUM
ejpam-6073	472	5	2	2	NUM
ejpam-6073	472	6	q1	q1	PROPN
ejpam-6073	472	7	hα(q2(x)−1)(t	hα(q2(x)−1)(t	NOUN
ejpam-6073	472	8	)	)	PUNCT
ejpam-6073	472	9	∫	∫	PROPN
ejpam-6073	473	1	ω	ω	NUM
ejpam-6073	473	2	|u|q(x)dx.(58	|u|q(x)dx.(58	NOUN
ejpam-6073	473	3	)	)	PUNCT
ejpam-6073	473	4	recalling	recall	VERB
ejpam-6073	473	5	(	(	PUNCT
ejpam-6073	473	6	16	16	NUM
ejpam-6073	473	7	)	)	PUNCT
ejpam-6073	473	8	and	and	CCONJ
ejpam-6073	473	9	(	(	PUNCT
ejpam-6073	473	10	17	17	NUM
ejpam-6073	473	11	)	)	PUNCT
ejpam-6073	473	12	,	,	PUNCT
ejpam-6073	473	13	then	then	ADV
ejpam-6073	473	14	eq	eq	ADP
ejpam-6073	473	15	.	.	PUNCT
ejpam-6073	474	1	(	(	PUNCT
ejpam-6073	474	2	18	18	NUM
ejpam-6073	474	3	)	)	PUNCT
ejpam-6073	474	4	becomes	become	VERB
ejpam-6073	474	5	hα(p2(x)−1)(t	hα(p2(x)−1)(t	NOUN
ejpam-6073	474	6	)	)	PUNCT
ejpam-6073	474	7	∫	∫	PROPN
ejpam-6073	474	8	ω	ω	NUM
ejpam-6073	474	9	|z|p(x)dx+hα(q2(x)−1)(t	|z|p(x)dx+hα(q2(x)−1)(t	PROPN
ejpam-6073	474	10	)	)	PUNCT
ejpam-6073	474	11	∫	∫	PROPN
ejpam-6073	474	12	ω	ω	NUM
ejpam-6073	474	13	|u|q(x)dx	|u|q(x)dx	NOUN
ejpam-6073	474	14	≤	≤	NOUN
ejpam-6073	474	15	hα(p∗(x)−1)(t	hα(p∗(x)−1)(t	ADJ
ejpam-6073	474	16	)	)	PUNCT
ejpam-6073	475	1	[	[	X
ejpam-6073	475	2	∫	∫	X
ejpam-6073	475	3	ω	ω	NUM
ejpam-6073	475	4	|z|p(x)dx+	|z|p(x)dx+	ADJ
ejpam-6073	475	5	∫	∫	PROPN
ejpam-6073	475	6	ω	ω	NUM
ejpam-6073	475	7	|u|q(x)dx	|u|q(x)dx	NOUN
ejpam-6073	475	8	]	]	PUNCT
ejpam-6073	475	9	≤	≤	NUM
ejpam-6073	475	10	c	c	NOUN
ejpam-6073	475	11	(	(	PUNCT
ejpam-6073	475	12	ϱ(z	ϱ(z	PROPN
ejpam-6073	475	13	)	)	PUNCT
ejpam-6073	475	14	p1	p1	NOUN
ejpam-6073	475	15	m1	m1	PROPN
ejpam-6073	475	16	+	+	NOUN
ejpam-6073	475	17	α(p∗(x)−1	α(p∗(x)−1	NOUN
ejpam-6073	475	18	)	)	PUNCT
ejpam-6073	475	19	+	+	NUM
ejpam-6073	475	20	ϱ(z	ϱ(z	NOUN
ejpam-6073	475	21	)	)	PUNCT
ejpam-6073	475	22	p2	p2	PROPN
ejpam-6073	475	23	m1	m1	PROPN
ejpam-6073	475	24	+	+	NOUN
ejpam-6073	475	25	α(p∗(x)−1	α(p∗(x)−1	NOUN
ejpam-6073	475	26	)	)	PUNCT
ejpam-6073	475	27	+	+	X
ejpam-6073	475	28	ϱ(u	ϱ(u	ADP
ejpam-6073	475	29	)	)	PUNCT
ejpam-6073	475	30	q1	q1	NOUN
ejpam-6073	475	31	ℓ1	ℓ1	NOUN
ejpam-6073	475	32	+	+	NOUN
ejpam-6073	475	33	α(p∗(x)−1	α(p∗(x)−1	NOUN
ejpam-6073	475	34	)	)	PUNCT
ejpam-6073	475	35	+	+	X
ejpam-6073	475	36	ϱ(u	ϱ(u	ADP
ejpam-6073	475	37	)	)	PUNCT
ejpam-6073	475	38	q2	q2	NOUN
ejpam-6073	475	39	ℓ1	ℓ1	NOUN
ejpam-6073	475	40	+	+	NOUN
ejpam-6073	475	41	α(p∗(x)−1	α(p∗(x)−1	NOUN
ejpam-6073	475	42	)	)	PUNCT
ejpam-6073	475	43	)	)	PUNCT
ejpam-6073	476	1	≤	≤	NUM
ejpam-6073	476	2	c	c	NOUN
ejpam-6073	476	3	(	(	PUNCT
ejpam-6073	476	4	||zx||22	||zx||22	NOUN
ejpam-6073	476	5	+	+	X
ejpam-6073	476	6	ϱ(z	ϱ(z	NOUN
ejpam-6073	476	7	)	)	PUNCT
ejpam-6073	476	8	+	+	NUM
ejpam-6073	476	9	||ux||22	||ux||22	NOUN
ejpam-6073	476	10	+	+	CCONJ
ejpam-6073	476	11	ϱ(u	ϱ(u	NOUN
ejpam-6073	476	12	)	)	PUNCT
ejpam-6073	476	13	)	)	PUNCT
ejpam-6073	476	14	,	,	PUNCT
ejpam-6073	476	15	where	where	SCONJ
ejpam-6073	476	16	p∗(x	p∗(x	NOUN
ejpam-6073	476	17	)	)	PUNCT
ejpam-6073	476	18	=	=	SYM
ejpam-6073	476	19	max{p2(x	max{p2(x	PROPN
ejpam-6073	476	20	)	)	PUNCT
ejpam-6073	476	21	,	,	PUNCT
ejpam-6073	476	22	q2(x	q2(x	X
ejpam-6073	476	23	)	)	PUNCT
ejpam-6073	476	24	}	}	PUNCT
ejpam-6073	476	25	.	.	PUNCT
ejpam-6073	477	1	using	use	VERB
ejpam-6073	477	2	(	(	PUNCT
ejpam-6073	477	3	58	58	NUM
ejpam-6073	477	4	)	)	PUNCT
ejpam-6073	477	5	,	,	PUNCT
ejpam-6073	477	6	we	we	PRON
ejpam-6073	477	7	arrive	arrive	VERB
ejpam-6073	477	8	at	at	ADP
ejpam-6073	477	9	f	f	PROPN
ejpam-6073	477	10	′(t	′(t	PROPN
ejpam-6073	477	11	)	)	PUNCT
ejpam-6073	477	12	≥	≥	NOUN
ejpam-6073	477	13	[	[	PUNCT
ejpam-6073	477	14	(	(	PUNCT
ejpam-6073	477	15	1−	1−	NUM
ejpam-6073	477	16	α)−	α)−	PROPN
ejpam-6073	477	17	ε	ε	PROPN
ejpam-6073	477	18	(	(	PUNCT
ejpam-6073	477	19	(	(	PUNCT
ejpam-6073	477	20	p2	p2	PROPN
ejpam-6073	477	21	−	−	NOUN
ejpam-6073	477	22	1	1	NUM
ejpam-6073	477	23	)	)	PUNCT
ejpam-6073	477	24	p2	p2	PROPN
ejpam-6073	477	25	ξ1	ξ1	NOUN
ejpam-6073	477	26	)	)	PUNCT
ejpam-6073	477	27	−	−	PROPN
ejpam-6073	478	1	ε	ε	PROPN
ejpam-6073	478	2	(	(	PUNCT
ejpam-6073	478	3	(	(	PUNCT
ejpam-6073	478	4	q2	q2	NOUN
ejpam-6073	478	5	−	−	NOUN
ejpam-6073	478	6	1	1	X
ejpam-6073	478	7	)	)	PUNCT
ejpam-6073	478	8	q2	q2	NOUN
ejpam-6073	478	9	ξ2	ξ2	NOUN
ejpam-6073	478	10	)	)	PUNCT
ejpam-6073	478	11	]	]	PUNCT
ejpam-6073	478	12	h−α(t)h	h−α(t)h	PROPN
ejpam-6073	478	13	′(t	′(t	PROPN
ejpam-6073	478	14	)	)	PUNCT
ejpam-6073	479	1	+	+	NOUN
ejpam-6073	479	2	ε(η	ε(η	ADJ
ejpam-6073	479	3	−	−	PROPN
ejpam-6073	479	4	λ	λ	NOUN
ejpam-6073	479	5	)	)	PUNCT
ejpam-6073	479	6	[	[	PUNCT
ejpam-6073	479	7	h(t	h(t	PROPN
ejpam-6073	479	8	)	)	PUNCT
ejpam-6073	479	9	+	+	NUM
ejpam-6073	479	10	||ut||22	||ut||22	NOUN
ejpam-6073	479	11	+	+	CCONJ
ejpam-6073	479	12	||zt||22	||zt||22	NOUN
ejpam-6073	479	13	+	+	CCONJ
ejpam-6073	479	14	||ux||22	||ux||22	NOUN
ejpam-6073	479	15	+	+	CCONJ
ejpam-6073	479	16	||zx||22	||zx||22	NOUN
ejpam-6073	479	17	+	+	X
ejpam-6073	479	18	ϱ(z	ϱ(z	NOUN
ejpam-6073	479	19	)	)	PUNCT
ejpam-6073	479	20	+	+	CCONJ
ejpam-6073	479	21	ϱ(u	ϱ(u	NOUN
ejpam-6073	479	22	)	)	PUNCT
ejpam-6073	479	23	]	]	PUNCT
ejpam-6073	479	24	,	,	PUNCT
ejpam-6073	479	25	(	(	PUNCT
ejpam-6073	479	26	59	59	NUM
ejpam-6073	479	27	)	)	PUNCT
ejpam-6073	479	28	λ	λ	NOUN
ejpam-6073	479	29	:	:	PUNCT
ejpam-6073	479	30	=	=	PUNCT
ejpam-6073	479	31	c	c	X
ejpam-6073	479	32	ξ	ξ	DET
ejpam-6073	479	33	1−p1	1−p1	NUM
ejpam-6073	479	34	p1	p1	NOUN
ejpam-6073	479	35	+	+	CCONJ
ejpam-6073	479	36	d	d	PROPN
ejpam-6073	479	37	ξ1−q1	ξ1−q1	PROPN
ejpam-6073	479	38	q1	q1	PROPN
ejpam-6073	479	39	>	>	X
ejpam-6073	479	40	0	0	PUNCT
ejpam-6073	479	41	and	and	CCONJ
ejpam-6073	479	42	ξ	ξ	X
ejpam-6073	479	43	=	=	SYM
ejpam-6073	479	44	max{ξ1	max{ξ1	PROPN
ejpam-6073	479	45	,	,	PUNCT
ejpam-6073	479	46	ξ2	ξ2	NOUN
ejpam-6073	479	47	}	}	PUNCT
ejpam-6073	479	48	.	.	PUNCT
ejpam-6073	480	1	now	now	ADV
ejpam-6073	480	2	,	,	PUNCT
ejpam-6073	480	3	we	we	PRON
ejpam-6073	480	4	choose	choose	VERB
ejpam-6073	480	5	ξ	ξ	PROPN
ejpam-6073	480	6	large	large	ADJ
ejpam-6073	480	7	enough	enough	ADV
ejpam-6073	480	8	such	such	ADJ
ejpam-6073	480	9	that	that	DET
ejpam-6073	480	10	µ	µ	X
ejpam-6073	480	11	:	:	PUNCT
ejpam-6073	480	12	=	=	SYM
ejpam-6073	480	13	η	η	PROPN
ejpam-6073	480	14	−	−	PROPN
ejpam-6073	480	15	λ	λ	PROPN
ejpam-6073	480	16	>	>	X
ejpam-6073	480	17	0	0	NUM
ejpam-6073	480	18	.	.	PUNCT
ejpam-6073	481	1	then	then	ADV
ejpam-6073	481	2	,	,	PUNCT
ejpam-6073	481	3	we	we	PRON
ejpam-6073	481	4	pick	pick	VERB
ejpam-6073	481	5	ε	ε	PROPN
ejpam-6073	481	6	small	small	ADJ
ejpam-6073	481	7	enough	enough	ADV
ejpam-6073	481	8	so	so	SCONJ
ejpam-6073	481	9	that	that	SCONJ
ejpam-6073	481	10	(	(	PUNCT
ejpam-6073	481	11	1−	1−	NUM
ejpam-6073	481	12	α)−	α)−	PROPN
ejpam-6073	481	13	ε	ε	PROPN
ejpam-6073	482	1	[	[	X
ejpam-6073	482	2	(	(	PUNCT
ejpam-6073	482	3	(	(	PUNCT
ejpam-6073	482	4	p2	p2	PROPN
ejpam-6073	482	5	−	−	NOUN
ejpam-6073	482	6	1	1	NUM
ejpam-6073	482	7	)	)	PUNCT
ejpam-6073	482	8	p2	p2	PROPN
ejpam-6073	482	9	ξ1	ξ1	NOUN
ejpam-6073	482	10	)	)	PUNCT
ejpam-6073	483	1	+	+	CCONJ
ejpam-6073	483	2	(	(	PUNCT
ejpam-6073	483	3	(	(	PUNCT
ejpam-6073	483	4	q2	q2	NOUN
ejpam-6073	483	5	−	−	NOUN
ejpam-6073	483	6	1	1	X
ejpam-6073	483	7	)	)	PUNCT
ejpam-6073	483	8	q2	q2	NOUN
ejpam-6073	483	9	ξ2	ξ2	NOUN
ejpam-6073	483	10	)	)	PUNCT
ejpam-6073	483	11	]	]	PUNCT
ejpam-6073	483	12	≥	≥	NOUN
ejpam-6073	483	13	0	0	NUM
ejpam-6073	483	14	,	,	PUNCT
ejpam-6073	483	15	and	and	CCONJ
ejpam-6073	483	16	f	f	PROPN
ejpam-6073	483	17	(	(	PUNCT
ejpam-6073	483	18	0	0	NUM
ejpam-6073	483	19	)	)	PUNCT
ejpam-6073	483	20	=	=	SYM
ejpam-6073	483	21	h1−α(0	h1−α(0	NOUN
ejpam-6073	483	22	)	)	PUNCT
ejpam-6073	484	1	+	+	CCONJ
ejpam-6073	484	2	ε	ε	PROPN
ejpam-6073	484	3	∫	∫	PROPN
ejpam-6073	484	4	ω	ω	PROPN
ejpam-6073	484	5	(	(	PUNCT
ejpam-6073	484	6	ρzz0z1	ρzz0z1	NOUN
ejpam-6073	484	7	+	+	CCONJ
ejpam-6073	484	8	ρuu0u1)dx	ρuu0u1)dx	NUM
ejpam-6073	484	9	>	>	X
ejpam-6073	484	10	0	0	NUM
ejpam-6073	484	11	.	.	PUNCT
ejpam-6073	484	12	using	use	VERB
ejpam-6073	484	13	the	the	DET
ejpam-6073	484	14	last	last	ADJ
ejpam-6073	484	15	results	result	NOUN
ejpam-6073	484	16	,	,	PUNCT
ejpam-6073	484	17	recalling	recall	VERB
ejpam-6073	484	18	(	(	PUNCT
ejpam-6073	484	19	17	17	NUM
ejpam-6073	484	20	)	)	PUNCT
ejpam-6073	484	21	and	and	CCONJ
ejpam-6073	484	22	(	(	PUNCT
ejpam-6073	484	23	16	16	NUM
ejpam-6073	484	24	)	)	PUNCT
ejpam-6073	484	25	,	,	PUNCT
ejpam-6073	484	26	eq	eq	NOUN
ejpam-6073	484	27	.	.	PUNCT
ejpam-6073	485	1	(	(	PUNCT
ejpam-6073	485	2	60	60	NUM
ejpam-6073	485	3	)	)	PUNCT
ejpam-6073	485	4	becomes	become	VERB
ejpam-6073	485	5	f	f	PROPN
ejpam-6073	485	6	′(t	′(t	PROPN
ejpam-6073	485	7	)	)	PUNCT
ejpam-6073	485	8	≥	≥	NOUN
ejpam-6073	485	9	µε	µε	ADP
ejpam-6073	485	10	[	[	PUNCT
ejpam-6073	485	11	h(t	h(t	PROPN
ejpam-6073	485	12	)	)	PUNCT
ejpam-6073	485	13	+	+	NUM
ejpam-6073	485	14	||ut||22	||ut||22	NOUN
ejpam-6073	485	15	+	+	CCONJ
ejpam-6073	485	16	||zt||22	||zt||22	NOUN
ejpam-6073	485	17	+	+	CCONJ
ejpam-6073	485	18	||ux||22	||ux||22	NOUN
ejpam-6073	485	19	+	+	CCONJ
ejpam-6073	485	20	||zx||22	||zx||22	NOUN
ejpam-6073	485	21	+	+	X
ejpam-6073	485	22	ϱ(z	ϱ(z	NOUN
ejpam-6073	485	23	)	)	PUNCT
ejpam-6073	486	1	+	+	CCONJ
ejpam-6073	486	2	ϱ(u	ϱ(u	ADP
ejpam-6073	486	3	)	)	PUNCT
ejpam-6073	486	4	]	]	PUNCT
ejpam-6073	487	1	≥	≥	X
ejpam-6073	487	2	µε	µε	ADP
ejpam-6073	487	3	[	[	PUNCT
ejpam-6073	487	4	h(t	h(t	PROPN
ejpam-6073	487	5	)	)	PUNCT
ejpam-6073	487	6	+	+	NUM
ejpam-6073	487	7	||ut||22	||ut||22	NOUN
ejpam-6073	487	8	+	+	CCONJ
ejpam-6073	487	9	||zt||22	||zt||22	NOUN
ejpam-6073	487	10	+	+	CCONJ
ejpam-6073	487	11	||ux||22	||ux||22	NOUN
ejpam-6073	488	1	+	+	CCONJ
ejpam-6073	488	2	||zx||22	||zx||22	NOUN
ejpam-6073	488	3	+	+	CCONJ
ejpam-6073	488	4	||z||m1	||z||m1	NOUN
ejpam-6073	488	5	m1	m1	NOUN
ejpam-6073	488	6	+	+	CCONJ
ejpam-6073	488	7	||u||ℓ1ℓ1	||u||ℓ1ℓ1	PROPN
ejpam-6073	488	8	]	]	PUNCT
ejpam-6073	488	9	>	>	X
ejpam-6073	488	10	0	0	X
ejpam-6073	488	11	.	.	PUNCT
ejpam-6073	489	1	(	(	PUNCT
ejpam-6073	489	2	60	60	NUM
ejpam-6073	489	3	)	)	PUNCT
ejpam-6073	489	4	hence	hence	ADV
ejpam-6073	489	5	,	,	PUNCT
ejpam-6073	489	6	f	f	PROPN
ejpam-6073	489	7	is	be	AUX
ejpam-6073	489	8	non	non	ADJ
ejpam-6073	489	9	-	-	ADJ
ejpam-6073	489	10	decreasing	decrease	VERB
ejpam-6073	489	11	;	;	PUNCT
ejpam-6073	489	12	that	that	PRON
ejpam-6073	489	13	is	is	ADV
ejpam-6073	489	14	,	,	PUNCT
ejpam-6073	489	15	we	we	PRON
ejpam-6073	489	16	have	have	VERB
ejpam-6073	489	17	f	f	PROPN
ejpam-6073	489	18	(	(	PUNCT
ejpam-6073	489	19	t	t	PROPN
ejpam-6073	489	20	)	)	PUNCT
ejpam-6073	489	21	≥	≥	NOUN
ejpam-6073	489	22	f	f	X
ejpam-6073	489	23	(	(	PUNCT
ejpam-6073	489	24	0	0	NUM
ejpam-6073	489	25	)	)	PUNCT
ejpam-6073	489	26	,	,	PUNCT
ejpam-6073	489	27	∀	∀	X
ejpam-6073	489	28	t	t	NOUN
ejpam-6073	489	29	≥	≥	NOUN
ejpam-6073	489	30	0	0	NUM
ejpam-6073	489	31	.	.	PUNCT
ejpam-6073	490	1	(	(	PUNCT
ejpam-6073	490	2	61	61	NUM
ejpam-6073	490	3	)	)	PUNCT
ejpam-6073	490	4	a.	a.	NOUN
ejpam-6073	490	5	m.	m.	PROPN
ejpam-6073	490	6	al	al	PROPN
ejpam-6073	490	7	-	-	PROPN
ejpam-6073	490	8	mahdi	mahdi	PROPN
ejpam-6073	490	9	et	et	PROPN
ejpam-6073	490	10	al	al	PROPN
ejpam-6073	490	11	.	.	PUNCT
ejpam-6073	490	12	/	/	SYM
ejpam-6073	490	13	eur	eur	PROPN
ejpam-6073	490	14	.	.	PUNCT
ejpam-6073	491	1	j.	j.	PROPN
ejpam-6073	491	2	pure	pure	PROPN
ejpam-6073	491	3	appl	appl	PROPN
ejpam-6073	491	4	.	.	PROPN
ejpam-6073	491	5	math	math	PROPN
ejpam-6073	491	6	,	,	PUNCT
ejpam-6073	491	7	18	18	NUM
ejpam-6073	491	8	(	(	PUNCT
ejpam-6073	491	9	3	3	NUM
ejpam-6073	491	10	)	)	PUNCT
ejpam-6073	491	11	(	(	PUNCT
ejpam-6073	491	12	2025	2025	NUM
ejpam-6073	491	13	)	)	PUNCT
ejpam-6073	491	14	,	,	PUNCT
ejpam-6073	491	15	6073	6073	NUM
ejpam-6073	491	16	22	22	NUM
ejpam-6073	491	17	of	of	ADP
ejpam-6073	491	18	29	29	NUM
ejpam-6073	491	19	using	use	VERB
ejpam-6073	491	20	(	(	PUNCT
ejpam-6073	491	21	51	51	NUM
ejpam-6073	491	22	)	)	PUNCT
ejpam-6073	491	23	and	and	CCONJ
ejpam-6073	491	24	(	(	PUNCT
ejpam-6073	491	25	60	60	NUM
ejpam-6073	491	26	)	)	PUNCT
ejpam-6073	491	27	,	,	PUNCT
ejpam-6073	491	28	we	we	PRON
ejpam-6073	491	29	have	have	AUX
ejpam-6073	491	30	f	f	PROPN
ejpam-6073	491	31	′(t	′(t	PROPN
ejpam-6073	491	32	)	)	PUNCT
ejpam-6073	491	33	≥	≥	NOUN
ejpam-6073	491	34	νf	νf	VERB
ejpam-6073	491	35	1	1	NUM
ejpam-6073	491	36	1−α	1−α	NUM
ejpam-6073	491	37	,	,	PUNCT
ejpam-6073	491	38	∀	∀	X
ejpam-6073	491	39	t	t	NOUN
ejpam-6073	491	40	≥	≥	NOUN
ejpam-6073	491	41	0	0	NUM
ejpam-6073	491	42	.	.	PUNCT
ejpam-6073	492	1	(	(	PUNCT
ejpam-6073	492	2	62	62	NUM
ejpam-6073	492	3	)	)	PUNCT
ejpam-6073	492	4	a	a	DET
ejpam-6073	492	5	simple	simple	ADJ
ejpam-6073	492	6	integration	integration	NOUN
ejpam-6073	492	7	of	of	ADP
ejpam-6073	492	8	(	(	PUNCT
ejpam-6073	492	9	62	62	NUM
ejpam-6073	492	10	)	)	PUNCT
ejpam-6073	492	11	,	,	PUNCT
ejpam-6073	492	12	we	we	PRON
ejpam-6073	492	13	obtain	obtain	VERB
ejpam-6073	492	14	f	f	PROPN
ejpam-6073	492	15	α	α	PRON
ejpam-6073	492	16	1−α	1−α	NUM
ejpam-6073	492	17	(	(	PUNCT
ejpam-6073	492	18	t	t	PROPN
ejpam-6073	492	19	)	)	PUNCT
ejpam-6073	492	20	≥	≥	NOUN
ejpam-6073	492	21	1	1	NUM
ejpam-6073	492	22	f	f	PROPN
ejpam-6073	492	23	−α	−α	NOUN
ejpam-6073	492	24	1−α	1−α	NUM
ejpam-6073	493	1	(	(	PUNCT
ejpam-6073	493	2	0)−	0)−	NUM
ejpam-6073	493	3	νtα	νtα	NOUN
ejpam-6073	493	4	1−α	1−α	NUM
ejpam-6073	493	5	,	,	PUNCT
ejpam-6073	493	6	(	(	PUNCT
ejpam-6073	493	7	63	63	NUM
ejpam-6073	493	8	)	)	PUNCT
ejpam-6073	493	9	where	where	SCONJ
ejpam-6073	493	10	0	0	NUM
ejpam-6073	493	11	<	<	X
ejpam-6073	493	12	α	α	X
ejpam-6073	493	13	<	<	X
ejpam-6073	493	14	1	1	NUM
ejpam-6073	493	15	and	and	CCONJ
ejpam-6073	493	16	ν	ν	X
ejpam-6073	493	17	>	>	X
ejpam-6073	493	18	0	0	NUM
ejpam-6073	493	19	.	.	PUNCT
ejpam-6073	494	1	therefore	therefore	ADV
ejpam-6073	494	2	,	,	PUNCT
ejpam-6073	494	3	(	(	PUNCT
ejpam-6073	494	4	63	63	NUM
ejpam-6073	494	5	)	)	PUNCT
ejpam-6073	494	6	shows	show	VERB
ejpam-6073	494	7	that	that	SCONJ
ejpam-6073	494	8	f	f	PROPN
ejpam-6073	494	9	blows	blow	VERB
ejpam-6073	494	10	-	-	PUNCT
ejpam-6073	494	11	up	up	NOUN
ejpam-6073	494	12	in	in	ADP
ejpam-6073	494	13	the	the	DET
ejpam-6073	494	14	finite	finite	ADJ
ejpam-6073	494	15	time	time	NOUN
ejpam-6073	494	16	t∗	t∗	PROPN
ejpam-6073	494	17	≤	≤	NOUN
ejpam-6073	494	18	1−	1−	NUM
ejpam-6073	494	19	α	α	NOUN
ejpam-6073	494	20	να	να	VERB
ejpam-6073	495	1	[	[	X
ejpam-6073	495	2	f	f	X
ejpam-6073	495	3	(	(	PUNCT
ejpam-6073	495	4	0	0	NUM
ejpam-6073	495	5	)	)	PUNCT
ejpam-6073	495	6	]	]	PUNCT
ejpam-6073	495	7	α	α	PRON
ejpam-6073	495	8	1−α	1−α	NUM
ejpam-6073	495	9	.	.	PUNCT
ejpam-6073	496	1	(	(	PUNCT
ejpam-6073	496	2	64	64	NUM
ejpam-6073	496	3	)	)	PUNCT
ejpam-6073	496	4	this	this	PRON
ejpam-6073	496	5	completes	complete	VERB
ejpam-6073	496	6	the	the	DET
ejpam-6073	496	7	proof	proof	NOUN
ejpam-6073	496	8	.	.	PUNCT
ejpam-6073	497	1	remark	remark	NOUN
ejpam-6073	497	2	2	2	NUM
ejpam-6073	497	3	.	.	PUNCT
ejpam-6073	498	1	in	in	ADP
ejpam-6073	498	2	the	the	DET
ejpam-6073	498	3	context	context	NOUN
ejpam-6073	498	4	of	of	ADP
ejpam-6073	498	5	swelling	swell	VERB
ejpam-6073	498	6	porous	porous	ADJ
ejpam-6073	498	7	-	-	PUNCT
ejpam-6073	498	8	elastic	elastic	ADJ
ejpam-6073	498	9	systems	system	NOUN
ejpam-6073	498	10	,	,	PUNCT
ejpam-6073	498	11	blow	blow	NOUN
ejpam-6073	498	12	-	-	PUNCT
ejpam-6073	498	13	up	up	NOUN
ejpam-6073	498	14	represents	represent	VERB
ejpam-6073	498	15	the	the	DET
ejpam-6073	498	16	onset	onset	NOUN
ejpam-6073	498	17	of	of	ADP
ejpam-6073	498	18	mechanical	mechanical	ADJ
ejpam-6073	498	19	failure	failure	NOUN
ejpam-6073	498	20	,	,	PUNCT
ejpam-6073	498	21	which	which	PRON
ejpam-6073	498	22	can	can	AUX
ejpam-6073	498	23	manifest	manifest	VERB
ejpam-6073	498	24	physically	physically	ADV
ejpam-6073	498	25	as	as	ADP
ejpam-6073	498	26	excessive	excessive	ADJ
ejpam-6073	498	27	deformation	deformation	NOUN
ejpam-6073	498	28	,	,	PUNCT
ejpam-6073	498	29	material	material	NOUN
ejpam-6073	498	30	rupture	rupture	NOUN
ejpam-6073	498	31	,	,	PUNCT
ejpam-6073	498	32	or	or	CCONJ
ejpam-6073	498	33	cracking	cracking	NOUN
ejpam-6073	498	34	,	,	PUNCT
ejpam-6073	498	35	depending	depend	VERB
ejpam-6073	498	36	on	on	ADP
ejpam-6073	498	37	the	the	DET
ejpam-6073	498	38	specific	specific	ADJ
ejpam-6073	498	39	application	application	NOUN
ejpam-6073	498	40	.	.	PUNCT
ejpam-6073	499	1	when	when	SCONJ
ejpam-6073	499	2	a	a	DET
ejpam-6073	499	3	solution	solution	NOUN
ejpam-6073	499	4	blows	blow	VERB
ejpam-6073	499	5	up	up	ADP
ejpam-6073	499	6	in	in	ADP
ejpam-6073	499	7	finite	finite	ADJ
ejpam-6073	499	8	time	time	NOUN
ejpam-6073	499	9	,	,	PUNCT
ejpam-6073	499	10	it	it	PRON
ejpam-6073	499	11	signifies	signify	VERB
ejpam-6073	499	12	that	that	SCONJ
ejpam-6073	499	13	certain	certain	ADJ
ejpam-6073	499	14	physical	physical	ADJ
ejpam-6073	499	15	quantities	quantity	NOUN
ejpam-6073	499	16	,	,	PUNCT
ejpam-6073	499	17	such	such	ADJ
ejpam-6073	499	18	as	as	ADP
ejpam-6073	499	19	stress	stress	NOUN
ejpam-6073	499	20	,	,	PUNCT
ejpam-6073	499	21	strain	strain	NOUN
ejpam-6073	499	22	,	,	PUNCT
ejpam-6073	499	23	or	or	CCONJ
ejpam-6073	499	24	displacement	displacement	NOUN
ejpam-6073	499	25	,	,	PUNCT
ejpam-6073	499	26	become	become	VERB
ejpam-6073	499	27	unbounded	unbounded	ADJ
ejpam-6073	499	28	,	,	PUNCT
ejpam-6073	499	29	indicating	indicate	VERB
ejpam-6073	499	30	an	an	DET
ejpam-6073	499	31	irreversible	irreversible	ADJ
ejpam-6073	499	32	breakdown	breakdown	NOUN
ejpam-6073	499	33	of	of	ADP
ejpam-6073	499	34	the	the	DET
ejpam-6073	499	35	material	material	NOUN
ejpam-6073	499	36	structure	structure	NOUN
ejpam-6073	499	37	.	.	PUNCT
ejpam-6073	500	1	thus	thus	ADV
ejpam-6073	500	2	,	,	PUNCT
ejpam-6073	500	3	blow	blow	NOUN
ejpam-6073	500	4	-	-	PUNCT
ejpam-6073	500	5	up	up	NOUN
ejpam-6073	500	6	in	in	ADP
ejpam-6073	500	7	our	our	PRON
ejpam-6073	500	8	model	model	NOUN
ejpam-6073	500	9	provides	provide	VERB
ejpam-6073	500	10	a	a	DET
ejpam-6073	500	11	mathematical	mathematical	ADJ
ejpam-6073	500	12	framework	framework	NOUN
ejpam-6073	500	13	for	for	ADP
ejpam-6073	500	14	predicting	predict	VERB
ejpam-6073	500	15	critical	critical	ADJ
ejpam-6073	500	16	thresholds	threshold	NOUN
ejpam-6073	500	17	beyond	beyond	ADP
ejpam-6073	500	18	which	which	PRON
ejpam-6073	500	19	the	the	DET
ejpam-6073	500	20	material	material	NOUN
ejpam-6073	500	21	loses	lose	VERB
ejpam-6073	500	22	stability	stability	NOUN
ejpam-6073	500	23	,	,	PUNCT
ejpam-6073	500	24	aiding	aid	VERB
ejpam-6073	500	25	in	in	ADP
ejpam-6073	500	26	failure	failure	NOUN
ejpam-6073	500	27	analysis	analysis	NOUN
ejpam-6073	500	28	and	and	CCONJ
ejpam-6073	500	29	design	design	NOUN
ejpam-6073	500	30	optimization	optimization	NOUN
ejpam-6073	500	31	of	of	ADP
ejpam-6073	500	32	porous	porous	ADJ
ejpam-6073	500	33	-	-	PUNCT
ejpam-6073	500	34	elastic	elastic	ADJ
ejpam-6073	500	35	structures	structure	NOUN
ejpam-6073	500	36	.	.	PUNCT
ejpam-6073	501	1	7	7	X
ejpam-6073	501	2	.	.	X
ejpam-6073	501	3	numerical	numerical	ADJ
ejpam-6073	501	4	tests	test	NOUN
ejpam-6073	501	5	in	in	ADP
ejpam-6073	501	6	the	the	DET
ejpam-6073	501	7	following	follow	VERB
ejpam-6073	501	8	section	section	NOUN
ejpam-6073	501	9	,	,	PUNCT
ejpam-6073	501	10	we	we	PRON
ejpam-6073	501	11	illustrate	illustrate	VERB
ejpam-6073	501	12	the	the	DET
ejpam-6073	501	13	blow	blow	NOUN
ejpam-6073	501	14	up	up	ADP
ejpam-6073	501	15	results	result	NOUN
ejpam-6073	501	16	proved	prove	VERB
ejpam-6073	501	17	in	in	ADP
ejpam-6073	501	18	theorems	theorem	NOUN
ejpam-6073	501	19	6.1	6.1	NUM
ejpam-6073	501	20	.	.	PUNCT
ejpam-6073	502	1	we	we	PRON
ejpam-6073	502	2	perform	perform	VERB
ejpam-6073	502	3	four	four	NUM
ejpam-6073	502	4	numerical	numerical	ADJ
ejpam-6073	502	5	tests	test	NOUN
ejpam-6073	502	6	for	for	ADP
ejpam-6073	502	7	the	the	DET
ejpam-6073	502	8	blow	blow	NOUN
ejpam-6073	502	9	up	up	ADP
ejpam-6073	502	10	behavior	behavior	NOUN
ejpam-6073	502	11	of	of	ADP
ejpam-6073	502	12	a	a	DET
ejpam-6073	502	13	one	one	NUM
ejpam-6073	502	14	-	-	PUNCT
ejpam-6073	502	15	dimensional	dimensional	ADJ
ejpam-6073	502	16	real	real	ADV
ejpam-6073	502	17	-	-	PUNCT
ejpam-6073	502	18	valued	value	VERB
ejpam-6073	502	19	function	function	NOUN
ejpam-6073	502	20	.	.	PUNCT
ejpam-6073	503	1	we	we	PRON
ejpam-6073	503	2	discretize	discretize	VERB
ejpam-6073	503	3	the	the	DET
ejpam-6073	503	4	system	system	NOUN
ejpam-6073	503	5	1.6	1.6	NUM
ejpam-6073	503	6	using	use	VERB
ejpam-6073	503	7	a	a	DET
ejpam-6073	503	8	second	second	ADJ
ejpam-6073	503	9	order	order	NOUN
ejpam-6073	503	10	finite	finite	ADJ
ejpam-6073	503	11	difference	difference	NOUN
ejpam-6073	503	12	method	method	NOUN
ejpam-6073	503	13	explicit	explicit	ADJ
ejpam-6073	503	14	in	in	ADP
ejpam-6073	503	15	time	time	NOUN
ejpam-6073	503	16	and	and	CCONJ
ejpam-6073	503	17	in	in	ADP
ejpam-6073	503	18	space	space	NOUN
ejpam-6073	503	19	.	.	PUNCT
ejpam-6073	504	1	for	for	ADP
ejpam-6073	504	2	more	more	ADJ
ejpam-6073	504	3	stability	stability	NOUN
ejpam-6073	504	4	,	,	PUNCT
ejpam-6073	504	5	we	we	PRON
ejpam-6073	504	6	combine	combine	VERB
ejpam-6073	504	7	the	the	DET
ejpam-6073	504	8	finite	finite	ADJ
ejpam-6073	504	9	difference	difference	NOUN
ejpam-6073	504	10	method	method	NOUN
ejpam-6073	504	11	with	with	ADP
ejpam-6073	504	12	the	the	DET
ejpam-6073	504	13	conservative	conservative	ADJ
ejpam-6073	504	14	scheme	scheme	NOUN
ejpam-6073	504	15	of	of	ADP
ejpam-6073	504	16	lax	lax	NOUN
ejpam-6073	504	17	-	-	PUNCT
ejpam-6073	504	18	wendroff	wendroff	NOUN
ejpam-6073	504	19	.	.	PUNCT
ejpam-6073	505	1	for	for	ADP
ejpam-6073	505	2	more	more	ADJ
ejpam-6073	505	3	details	detail	NOUN
ejpam-6073	505	4	,	,	PUNCT
ejpam-6073	505	5	we	we	PRON
ejpam-6073	505	6	refer	refer	VERB
ejpam-6073	505	7	to	to	ADP
ejpam-6073	505	8	our	our	PRON
ejpam-6073	505	9	previous	previous	ADJ
ejpam-6073	505	10	works	work	NOUN
ejpam-6073	505	11	[	[	X
ejpam-6073	505	12	12	12	NUM
ejpam-6073	505	13	,	,	PUNCT
ejpam-6073	505	14	35	35	NUM
ejpam-6073	505	15	]	]	PUNCT
ejpam-6073	505	16	.	.	PUNCT
ejpam-6073	506	1	we	we	PRON
ejpam-6073	506	2	examine	examine	VERB
ejpam-6073	506	3	the	the	DET
ejpam-6073	506	4	following	follow	VERB
ejpam-6073	506	5	four	four	NUM
ejpam-6073	506	6	tests	test	NOUN
ejpam-6073	506	7	.	.	PUNCT
ejpam-6073	507	1	for	for	ADP
ejpam-6073	507	2	these	these	DET
ejpam-6073	507	3	test	test	NOUN
ejpam-6073	507	4	,	,	PUNCT
ejpam-6073	507	5	we	we	PRON
ejpam-6073	507	6	define	define	VERB
ejpam-6073	507	7	the	the	DET
ejpam-6073	507	8	parameters	parameter	NOUN
ejpam-6073	507	9	a1	a1	NOUN
ejpam-6073	507	10	=	=	NOUN
ejpam-6073	507	11	a3	a3	NOUN
ejpam-6073	507	12	=	=	SYM
ejpam-6073	507	13	1	1	NUM
ejpam-6073	507	14	and	and	CCONJ
ejpam-6073	507	15	a2	a2	PROPN
ejpam-6073	507	16	=	=	NOUN
ejpam-6073	507	17	0.95	0.95	NUM
ejpam-6073	507	18	satisfying	satisfy	VERB
ejpam-6073	507	19	the	the	DET
ejpam-6073	507	20	conditions	condition	NOUN
ejpam-6073	507	21	(	(	PUNCT
ejpam-6073	507	22	a2	a2	PROPN
ejpam-6073	507	23	)	)	PUNCT
ejpam-6073	507	24	.	.	PUNCT
ejpam-6073	508	1	the	the	DET
ejpam-6073	508	2	used	use	VERB
ejpam-6073	508	3	spatial	spatial	ADJ
ejpam-6073	508	4	-	-	PUNCT
ejpam-6073	508	5	temporal	temporal	ADJ
ejpam-6073	508	6	domain	domain	NOUN
ejpam-6073	508	7	is	be	AUX
ejpam-6073	508	8	[	[	X
ejpam-6073	508	9	0	0	NUM
ejpam-6073	508	10	,	,	PUNCT
ejpam-6073	508	11	1]2	1]2	NUM
ejpam-6073	508	12	×	×	NOUN
ejpam-6073	509	1	[	[	X
ejpam-6073	509	2	0	0	NUM
ejpam-6073	509	3	,	,	PUNCT
ejpam-6073	509	4	1	1	NUM
ejpam-6073	509	5	]	]	NUM
ejpam-6073	509	6	:	:	PUNCT
ejpam-6073	509	7	•	•	NUM
ejpam-6073	509	8	test	test	NOUN
ejpam-6073	509	9	1	1	NUM
ejpam-6073	509	10	:	:	PUNCT
ejpam-6073	509	11	in	in	ADP
ejpam-6073	509	12	the	the	DET
ejpam-6073	509	13	first	first	ADJ
ejpam-6073	509	14	test	test	NOUN
ejpam-6073	509	15	,	,	PUNCT
ejpam-6073	509	16	we	we	PRON
ejpam-6073	509	17	examine	examine	VERB
ejpam-6073	509	18	the	the	DET
ejpam-6073	509	19	blow	blow	NOUN
ejpam-6073	509	20	up	up	ADP
ejpam-6073	509	21	of	of	ADP
ejpam-6073	509	22	the	the	DET
ejpam-6073	509	23	energy	energy	NOUN
ejpam-6073	509	24	function	function	NOUN
ejpam-6073	509	25	using	use	VERB
ejpam-6073	509	26	the	the	DET
ejpam-6073	509	27	nonlinear	nonlinear	ADJ
ejpam-6073	509	28	exponent	exponent	NOUN
ejpam-6073	509	29	function	function	NOUN
ejpam-6073	509	30	p(x	p(x	PROPN
ejpam-6073	509	31	)	)	PUNCT
ejpam-6073	509	32	=	=	SYM
ejpam-6073	509	33	q(x	q(x	PROPN
ejpam-6073	509	34	)	)	PUNCT
ejpam-6073	509	35	=	=	PUNCT
ejpam-6073	510	1	1	1	NUM
ejpam-6073	510	2	+	+	NUM
ejpam-6073	510	3	1	1	NUM
ejpam-6073	510	4	(	(	PUNCT
ejpam-6073	510	5	1	1	NUM
ejpam-6073	510	6	+	+	NUM
ejpam-6073	510	7	x2	x2	NOUN
ejpam-6073	510	8	)	)	PUNCT
ejpam-6073	510	9	<	<	X
ejpam-6073	510	10	m(x	m(x	PROPN
ejpam-6073	510	11	)	)	PUNCT
ejpam-6073	510	12	=	=	SYM
ejpam-6073	510	13	ℓ(x	ℓ(x	PROPN
ejpam-6073	510	14	)	)	PUNCT
ejpam-6073	510	15	=	=	SYM
ejpam-6073	510	16	2	2	NUM
ejpam-6073	510	17	+	+	NUM
ejpam-6073	510	18	2	2	NUM
ejpam-6073	510	19	(	(	PUNCT
ejpam-6073	510	20	1	1	NUM
ejpam-6073	510	21	+	+	NUM
ejpam-6073	510	22	x2	x2	NOUN
ejpam-6073	510	23	)	)	PUNCT
ejpam-6073	510	24	,	,	PUNCT
ejpam-6073	510	25	which	which	PRON
ejpam-6073	510	26	satisfies	satisfy	VERB
ejpam-6073	510	27	the	the	DET
ejpam-6073	510	28	condition	condition	NOUN
ejpam-6073	510	29	(	(	PUNCT
ejpam-6073	510	30	a1	a1	NOUN
ejpam-6073	510	31	)	)	PUNCT
ejpam-6073	510	32	.	.	PUNCT
ejpam-6073	511	1	a.	a.	PROPN
ejpam-6073	511	2	m.	m.	PROPN
ejpam-6073	511	3	al	al	PROPN
ejpam-6073	511	4	-	-	PROPN
ejpam-6073	511	5	mahdi	mahdi	PROPN
ejpam-6073	511	6	et	et	PROPN
ejpam-6073	511	7	al	al	PROPN
ejpam-6073	511	8	.	.	PUNCT
ejpam-6073	511	9	/	/	SYM
ejpam-6073	511	10	eur	eur	PROPN
ejpam-6073	511	11	.	.	PUNCT
ejpam-6073	512	1	j.	j.	PROPN
ejpam-6073	512	2	pure	pure	PROPN
ejpam-6073	512	3	appl	appl	PROPN
ejpam-6073	512	4	.	.	PROPN
ejpam-6073	512	5	math	math	PROPN
ejpam-6073	512	6	,	,	PUNCT
ejpam-6073	512	7	18	18	NUM
ejpam-6073	512	8	(	(	PUNCT
ejpam-6073	512	9	3	3	NUM
ejpam-6073	512	10	)	)	PUNCT
ejpam-6073	512	11	(	(	PUNCT
ejpam-6073	512	12	2025	2025	NUM
ejpam-6073	512	13	)	)	PUNCT
ejpam-6073	512	14	,	,	PUNCT
ejpam-6073	512	15	6073	6073	NUM
ejpam-6073	512	16	23	23	NUM
ejpam-6073	512	17	of	of	ADP
ejpam-6073	512	18	29	29	NUM
ejpam-6073	512	19	•	•	NUM
ejpam-6073	512	20	test	test	NOUN
ejpam-6073	512	21	2	2	NUM
ejpam-6073	512	22	:	:	PUNCT
ejpam-6073	512	23	in	in	ADP
ejpam-6073	512	24	the	the	DET
ejpam-6073	512	25	second	second	ADJ
ejpam-6073	512	26	numerical	numerical	ADJ
ejpam-6073	512	27	test	test	NOUN
ejpam-6073	512	28	,	,	PUNCT
ejpam-6073	512	29	we	we	PRON
ejpam-6073	512	30	modify	modify	VERB
ejpam-6073	512	31	the	the	DET
ejpam-6073	512	32	inequality	inequality	NOUN
ejpam-6073	512	33	in	in	ADP
ejpam-6073	512	34	the	the	DET
ejpam-6073	512	35	first	first	ADJ
ejpam-6073	512	36	test	test	NOUN
ejpam-6073	512	37	p(x	p(x	NOUN
ejpam-6073	512	38	)	)	PUNCT
ejpam-6073	512	39	=	=	SYM
ejpam-6073	512	40	q(x	q(x	PROPN
ejpam-6073	512	41	)	)	PUNCT
ejpam-6073	512	42	=	=	SYM
ejpam-6073	512	43	m(x	m(x	PROPN
ejpam-6073	512	44	)	)	PUNCT
ejpam-6073	512	45	=	=	SYM
ejpam-6073	513	1	1	1	NUM
ejpam-6073	513	2	+	+	NUM
ejpam-6073	513	3	1	1	NUM
ejpam-6073	513	4	(	(	PUNCT
ejpam-6073	513	5	1	1	NUM
ejpam-6073	513	6	+	+	NUM
ejpam-6073	513	7	x2	x2	NOUN
ejpam-6073	513	8	)	)	PUNCT
ejpam-6073	513	9	<	<	X
ejpam-6073	513	10	ℓ(x	ℓ(x	PROPN
ejpam-6073	513	11	)	)	PUNCT
ejpam-6073	513	12	=	=	SYM
ejpam-6073	513	13	2	2	NUM
ejpam-6073	513	14	+	+	NUM
ejpam-6073	513	15	2	2	NUM
ejpam-6073	513	16	(	(	PUNCT
ejpam-6073	513	17	1	1	NUM
ejpam-6073	513	18	+	+	NUM
ejpam-6073	513	19	x2	x2	NOUN
ejpam-6073	513	20	)	)	PUNCT
ejpam-6073	513	21	,	,	PUNCT
ejpam-6073	513	22	which	which	PRON
ejpam-6073	513	23	satisfies	satisfy	VERB
ejpam-6073	513	24	the	the	DET
ejpam-6073	513	25	condition	condition	NOUN
ejpam-6073	513	26	(	(	PUNCT
ejpam-6073	513	27	a1	a1	NOUN
ejpam-6073	513	28	)	)	PUNCT
ejpam-6073	513	29	.	.	PUNCT
ejpam-6073	514	1	•	•	NUM
ejpam-6073	514	2	test	test	NOUN
ejpam-6073	514	3	3	3	NUM
ejpam-6073	514	4	:	:	PUNCT
ejpam-6073	514	5	similarly	similarly	ADV
ejpam-6073	514	6	,	,	PUNCT
ejpam-6073	514	7	in	in	ADP
ejpam-6073	514	8	the	the	DET
ejpam-6073	514	9	third	third	ADJ
ejpam-6073	514	10	numerical	numerical	PROPN
ejpam-6073	514	11	test	test	NOUN
ejpam-6073	514	12	,	,	PUNCT
ejpam-6073	514	13	we	we	PRON
ejpam-6073	514	14	use	use	VERB
ejpam-6073	514	15	p(x	p(x	NOUN
ejpam-6073	514	16	)	)	PUNCT
ejpam-6073	514	17	=	=	SYM
ejpam-6073	514	18	q(x	q(x	PROPN
ejpam-6073	514	19	)	)	PUNCT
ejpam-6073	514	20	=	=	SYM
ejpam-6073	514	21	ℓ(x	ℓ(x	PROPN
ejpam-6073	514	22	)	)	PUNCT
ejpam-6073	514	23	=	=	SYM
ejpam-6073	515	1	1	1	NUM
ejpam-6073	515	2	+	+	NUM
ejpam-6073	515	3	1	1	NUM
ejpam-6073	515	4	(	(	PUNCT
ejpam-6073	515	5	1	1	NUM
ejpam-6073	515	6	+	+	NUM
ejpam-6073	515	7	x2	x2	NOUN
ejpam-6073	515	8	)	)	PUNCT
ejpam-6073	515	9	<	<	X
ejpam-6073	515	10	m(x	m(x	PROPN
ejpam-6073	515	11	)	)	PUNCT
ejpam-6073	515	12	=	=	SYM
ejpam-6073	515	13	2	2	NUM
ejpam-6073	515	14	+	+	NUM
ejpam-6073	515	15	2	2	NUM
ejpam-6073	515	16	(	(	PUNCT
ejpam-6073	515	17	1	1	NUM
ejpam-6073	515	18	+	+	NUM
ejpam-6073	515	19	x2	x2	NOUN
ejpam-6073	515	20	)	)	PUNCT
ejpam-6073	515	21	,	,	PUNCT
ejpam-6073	515	22	which	which	PRON
ejpam-6073	515	23	satisfies	satisfy	VERB
ejpam-6073	515	24	the	the	DET
ejpam-6073	515	25	condition	condition	NOUN
ejpam-6073	515	26	(	(	PUNCT
ejpam-6073	515	27	a1	a1	NOUN
ejpam-6073	515	28	)	)	PUNCT
ejpam-6073	515	29	.	.	PUNCT
ejpam-6073	516	1	•	•	NUM
ejpam-6073	516	2	test	test	NOUN
ejpam-6073	516	3	4	4	NUM
ejpam-6073	516	4	:	:	PUNCT
ejpam-6073	516	5	in	in	ADP
ejpam-6073	516	6	the	the	DET
ejpam-6073	516	7	fourth	fourth	PROPN
ejpam-6073	516	8	numerical	numerical	PROPN
ejpam-6073	516	9	test	test	NOUN
ejpam-6073	516	10	,	,	PUNCT
ejpam-6073	516	11	we	we	PRON
ejpam-6073	516	12	set	set	VERB
ejpam-6073	516	13	the	the	DET
ejpam-6073	516	14	following	follow	VERB
ejpam-6073	516	15	equality	equality	NOUN
ejpam-6073	516	16	of	of	ADP
ejpam-6073	516	17	the	the	DET
ejpam-6073	516	18	non	non	ADJ
ejpam-6073	516	19	-	-	ADJ
ejpam-6073	516	20	linear	linear	ADJ
ejpam-6073	516	21	exponent	exponent	NOUN
ejpam-6073	516	22	functions	function	NOUN
ejpam-6073	516	23	p(x	p(x	PROPN
ejpam-6073	516	24	)	)	PUNCT
ejpam-6073	516	25	=	=	SYM
ejpam-6073	516	26	q(x	q(x	PROPN
ejpam-6073	516	27	)	)	PUNCT
ejpam-6073	516	28	=	=	SYM
ejpam-6073	516	29	m(x	m(x	PROPN
ejpam-6073	516	30	)	)	PUNCT
ejpam-6073	516	31	=	=	SYM
ejpam-6073	516	32	ℓ(x	ℓ(x	PROPN
ejpam-6073	516	33	)	)	PUNCT
ejpam-6073	516	34	=	=	SYM
ejpam-6073	517	1	1	1	NUM
ejpam-6073	517	2	+	+	NUM
ejpam-6073	517	3	1	1	NUM
ejpam-6073	517	4	(	(	PUNCT
ejpam-6073	517	5	1	1	NUM
ejpam-6073	517	6	+	+	NUM
ejpam-6073	517	7	x2	x2	NOUN
ejpam-6073	517	8	)	)	PUNCT
ejpam-6073	517	9	,	,	PUNCT
ejpam-6073	517	10	which	which	PRON
ejpam-6073	517	11	satisfies	satisfy	VERB
ejpam-6073	517	12	the	the	DET
ejpam-6073	517	13	condition	condition	NOUN
ejpam-6073	517	14	(	(	PUNCT
ejpam-6073	517	15	a1	a1	NOUN
ejpam-6073	517	16	)	)	PUNCT
ejpam-6073	517	17	.	.	PUNCT
ejpam-6073	518	1	we	we	PRON
ejpam-6073	518	2	run	run	VERB
ejpam-6073	518	3	our	our	PRON
ejpam-6073	518	4	code	code	NOUN
ejpam-6073	518	5	using	use	VERB
ejpam-6073	518	6	the	the	DET
ejpam-6073	518	7	following	follow	VERB
ejpam-6073	518	8	initial	initial	ADJ
ejpam-6073	518	9	solution	solution	NOUN
ejpam-6073	518	10	:	:	PUNCT
ejpam-6073	518	11	u(x	u(x	NOUN
ejpam-6073	518	12	,	,	PUNCT
ejpam-6073	518	13	0	0	NUM
ejpam-6073	518	14	)	)	PUNCT
ejpam-6073	518	15	=	=	SYM
ejpam-6073	518	16	sin(πx	sin(πx	NOUN
ejpam-6073	518	17	)	)	PUNCT
ejpam-6073	518	18	,	,	PUNCT
ejpam-6073	518	19	(	(	PUNCT
ejpam-6073	518	20	65	65	NUM
ejpam-6073	518	21	)	)	PUNCT
ejpam-6073	518	22	z(x	z(x	NUM
ejpam-6073	518	23	,	,	PUNCT
ejpam-6073	518	24	0	0	NUM
ejpam-6073	518	25	)	)	PUNCT
ejpam-6073	518	26	=	=	NOUN
ejpam-6073	519	1	2x(x−	2x(x−	NUM
ejpam-6073	519	2	1	1	NUM
ejpam-6073	519	3	)	)	PUNCT
ejpam-6073	519	4	(	(	PUNCT
ejpam-6073	519	5	66	66	NUM
ejpam-6073	519	6	)	)	PUNCT
ejpam-6073	519	7	as	as	SCONJ
ejpam-6073	519	8	mentioned	mention	VERB
ejpam-6073	519	9	in	in	ADP
ejpam-6073	519	10	the	the	DET
ejpam-6073	519	11	system	system	NOUN
ejpam-6073	519	12	(	(	PUNCT
ejpam-6073	519	13	1.6	1.6	NUM
ejpam-6073	519	14	)	)	PUNCT
ejpam-6073	519	15	,	,	PUNCT
ejpam-6073	519	16	we	we	PRON
ejpam-6073	519	17	set	set	VERB
ejpam-6073	519	18	u1(x	u1(x	ADV
ejpam-6073	519	19	,	,	PUNCT
ejpam-6073	519	20	0	0	NUM
ejpam-6073	519	21	)	)	PUNCT
ejpam-6073	519	22	=	=	SYM
ejpam-6073	519	23	u(x	u(x	NOUN
ejpam-6073	519	24	,	,	PUNCT
ejpam-6073	519	25	,	,	PUNCT
ejpam-6073	519	26	0	0	NUM
ejpam-6073	519	27	)	)	PUNCT
ejpam-6073	519	28	.	.	PUNCT
ejpam-6073	520	1	we	we	PRON
ejpam-6073	520	2	also	also	ADV
ejpam-6073	520	3	have	have	VERB
ejpam-6073	520	4	to	to	PART
ejpam-6073	520	5	mention	mention	VERB
ejpam-6073	520	6	that	that	PRON
ejpam-6073	520	7	to	to	PART
ejpam-6073	520	8	visualize	visualize	VERB
ejpam-6073	520	9	the	the	DET
ejpam-6073	520	10	blow	blow	NOUN
ejpam-6073	520	11	up	up	ADP
ejpam-6073	520	12	behavior	behavior	NOUN
ejpam-6073	520	13	of	of	ADP
ejpam-6073	520	14	the	the	DET
ejpam-6073	520	15	initial	initial	ADJ
ejpam-6073	520	16	solution	solution	NOUN
ejpam-6073	520	17	(	(	PUNCT
ejpam-6073	520	18	65	65	NUM
ejpam-6073	520	19	)	)	PUNCT
ejpam-6073	520	20	,	,	PUNCT
ejpam-6073	520	21	we	we	PRON
ejpam-6073	520	22	use	use	VERB
ejpam-6073	520	23	a	a	DET
ejpam-6073	520	24	very	very	ADV
ejpam-6073	520	25	small	small	ADJ
ejpam-6073	520	26	and	and	CCONJ
ejpam-6073	520	27	constant	constant	ADJ
ejpam-6073	520	28	temporal	temporal	ADJ
ejpam-6073	520	29	step	step	NOUN
ejpam-6073	520	30	∆t	∆t	PROPN
ejpam-6073	521	1	=	=	SYM
ejpam-6073	521	2	10−5	10−5	NUM
ejpam-6073	521	3	and	and	CCONJ
ejpam-6073	521	4	the	the	DET
ejpam-6073	521	5	equidistant	equidistant	ADJ
ejpam-6073	521	6	spatial	spatial	ADJ
ejpam-6073	521	7	step	step	NOUN
ejpam-6073	521	8	∆x	∆x	PROPN
ejpam-6073	521	9	=	=	SYM
ejpam-6073	521	10	∆y	∆y	PROPN
ejpam-6073	521	11	=	=	SYM
ejpam-6073	521	12	10−2	10−2	NUM
ejpam-6073	521	13	.	.	PUNCT
ejpam-6073	522	1	in	in	ADP
ejpam-6073	522	2	the	the	DET
ejpam-6073	522	3	left	left	ADJ
ejpam-6073	522	4	two	two	NUM
ejpam-6073	522	5	column	column	NOUN
ejpam-6073	522	6	of	of	ADP
ejpam-6073	522	7	the	the	DET
ejpam-6073	522	8	figures	figure	NOUN
ejpam-6073	522	9	3	3	NUM
ejpam-6073	522	10	-	-	SYM
ejpam-6073	522	11	6	6	NUM
ejpam-6073	522	12	,	,	PUNCT
ejpam-6073	522	13	we	we	PRON
ejpam-6073	522	14	plot	plot	VERB
ejpam-6073	522	15	the	the	DET
ejpam-6073	522	16	cross	cross	NOUN
ejpam-6073	522	17	section	section	NOUN
ejpam-6073	522	18	of	of	ADP
ejpam-6073	522	19	the	the	DET
ejpam-6073	522	20	evolution	evolution	NOUN
ejpam-6073	522	21	of	of	ADP
ejpam-6073	522	22	the	the	DET
ejpam-6073	522	23	solution	solution	NOUN
ejpam-6073	522	24	at	at	ADP
ejpam-6073	522	25	different	different	ADJ
ejpam-6073	522	26	time	time	NOUN
ejpam-6073	522	27	steps	step	NOUN
ejpam-6073	522	28	t	t	PROPN
ejpam-6073	522	29	=	=	SYM
ejpam-6073	522	30	0	0	NUM
ejpam-6073	522	31	,	,	PUNCT
ejpam-6073	522	32	t	t	NOUN
ejpam-6073	522	33	=	=	NUM
ejpam-6073	522	34	0.25	0.25	NUM
ejpam-6073	522	35	and	and	CCONJ
ejpam-6073	522	36	t	t	NOUN
ejpam-6073	522	37	=	=	NUM
ejpam-6073	522	38	0.75	0.75	NUM
ejpam-6073	522	39	.	.	PUNCT
ejpam-6073	523	1	in	in	ADP
ejpam-6073	523	2	the	the	DET
ejpam-6073	523	3	right	right	ADJ
ejpam-6073	523	4	column	column	NOUN
ejpam-6073	523	5	of	of	ADP
ejpam-6073	523	6	the	the	DET
ejpam-6073	523	7	figures	figure	NOUN
ejpam-6073	523	8	3	3	NUM
ejpam-6073	523	9	-	-	SYM
ejpam-6073	523	10	6	6	NUM
ejpam-6073	523	11	,	,	PUNCT
ejpam-6073	523	12	we	we	PRON
ejpam-6073	523	13	plot	plot	VERB
ejpam-6073	523	14	the	the	DET
ejpam-6073	523	15	blow	blow	NOUN
ejpam-6073	523	16	up	up	ADP
ejpam-6073	523	17	of	of	ADP
ejpam-6073	523	18	the	the	DET
ejpam-6073	523	19	energies	energy	NOUN
ejpam-6073	523	20	for	for	ADP
ejpam-6073	523	21	the	the	DET
ejpam-6073	523	22	four	four	NUM
ejpam-6073	523	23	tests	test	NOUN
ejpam-6073	523	24	.	.	PUNCT
ejpam-6073	524	1	a.	a.	PROPN
ejpam-6073	524	2	m.	m.	PROPN
ejpam-6073	524	3	al	al	PROPN
ejpam-6073	524	4	-	-	PROPN
ejpam-6073	524	5	mahdi	mahdi	PROPN
ejpam-6073	524	6	et	et	PROPN
ejpam-6073	524	7	al	al	PROPN
ejpam-6073	524	8	.	.	PUNCT
ejpam-6073	524	9	/	/	SYM
ejpam-6073	524	10	eur	eur	PROPN
ejpam-6073	524	11	.	.	PUNCT
ejpam-6073	525	1	j.	j.	PROPN
ejpam-6073	525	2	pure	pure	PROPN
ejpam-6073	525	3	appl	appl	PROPN
ejpam-6073	525	4	.	.	PROPN
ejpam-6073	525	5	math	math	PROPN
ejpam-6073	525	6	,	,	PUNCT
ejpam-6073	525	7	18	18	NUM
ejpam-6073	525	8	(	(	PUNCT
ejpam-6073	525	9	3	3	NUM
ejpam-6073	525	10	)	)	PUNCT
ejpam-6073	525	11	(	(	PUNCT
ejpam-6073	525	12	2025	2025	NUM
ejpam-6073	525	13	)	)	PUNCT
ejpam-6073	525	14	,	,	PUNCT
ejpam-6073	525	15	6073	6073	NUM
ejpam-6073	525	16	24	24	NUM
ejpam-6073	525	17	of	of	ADP
ejpam-6073	525	18	29	29	NUM
ejpam-6073	525	19	0	0	NUM
ejpam-6073	525	20	0.002	0.002	NUM
ejpam-6073	525	21	0.004	0.004	NUM
ejpam-6073	525	22	0.006	0.006	NUM
ejpam-6073	525	23	0.008	0.008	NUM
ejpam-6073	525	24	0.01	0.01	NUM
ejpam-6073	525	25	0.012	0.012	NUM
ejpam-6073	525	26	-50	-50	PUNCT
ejpam-6073	525	27	0	0	NUM
ejpam-6073	525	28	50	50	NUM
ejpam-6073	525	29	u	u	NOUN
ejpam-6073	525	30	(	(	PUNCT
ejpam-6073	525	31	t	t	PROPN
ejpam-6073	525	32	,	,	PUNCT
ejpam-6073	525	33	0	0	NUM
ejpam-6073	525	34	.	.	NOUN
ejpam-6073	525	35	2	2	NUM
ejpam-6073	525	36	5	5	NUM
ejpam-6073	525	37	)	)	PUNCT
ejpam-6073	525	38	0	0	NUM
ejpam-6073	525	39	0.002	0.002	NUM
ejpam-6073	525	40	0.004	0.004	NUM
ejpam-6073	525	41	0.006	0.006	NUM
ejpam-6073	525	42	0.008	0.008	NUM
ejpam-6073	525	43	0.01	0.01	NUM
ejpam-6073	525	44	0.012	0.012	NUM
ejpam-6073	525	45	-20	-20	NUM
ejpam-6073	525	46	0	0	NUM
ejpam-6073	525	47	20	20	NUM
ejpam-6073	525	48	u	u	NOUN
ejpam-6073	525	49	(	(	PUNCT
ejpam-6073	525	50	t	t	PROPN
ejpam-6073	525	51	,	,	PUNCT
ejpam-6073	525	52	0	0	NUM
ejpam-6073	525	53	.5	.5	NUM
ejpam-6073	525	54	0	0	NUM
ejpam-6073	525	55	)	)	PUNCT
ejpam-6073	525	56	0	0	NUM
ejpam-6073	525	57	0.002	0.002	NUM
ejpam-6073	525	58	0.004	0.004	NUM
ejpam-6073	525	59	0.006	0.006	NUM
ejpam-6073	525	60	0.008	0.008	NUM
ejpam-6073	525	61	0.01	0.01	NUM
ejpam-6073	525	62	0.012	0.012	NUM
ejpam-6073	525	63	time	time	NOUN
ejpam-6073	525	64	-5	-5	PUNCT
ejpam-6073	525	65	0	0	NUM
ejpam-6073	525	66	5	5	NUM
ejpam-6073	525	67	u	u	NOUN
ejpam-6073	525	68	(	(	PUNCT
ejpam-6073	525	69	t	t	PROPN
ejpam-6073	525	70	,	,	PUNCT
ejpam-6073	525	71	0	0	NUM
ejpam-6073	525	72	.	.	NOUN
ejpam-6073	525	73	75	75	NUM
ejpam-6073	525	74	)	)	PUNCT
ejpam-6073	525	75	0	0	NUM
ejpam-6073	526	1	0.002	0.002	NUM
ejpam-6073	526	2	0.004	0.004	NUM
ejpam-6073	526	3	0.006	0.006	NUM
ejpam-6073	526	4	0.008	0.008	NUM
ejpam-6073	526	5	0.01	0.01	NUM
ejpam-6073	526	6	0.012	0.012	NUM
ejpam-6073	526	7	-5	-5	NOUN
ejpam-6073	526	8	0	0	NUM
ejpam-6073	526	9	5	5	NUM
ejpam-6073	526	10	z	z	NOUN
ejpam-6073	526	11	(	(	PUNCT
ejpam-6073	526	12	t	t	PROPN
ejpam-6073	526	13	,	,	PUNCT
ejpam-6073	526	14	0	0	NUM
ejpam-6073	526	15	.	.	NOUN
ejpam-6073	526	16	25	25	NUM
ejpam-6073	526	17	)	)	PUNCT
ejpam-6073	526	18	0	0	NUM
ejpam-6073	526	19	0.002	0.002	NUM
ejpam-6073	526	20	0.004	0.004	NUM
ejpam-6073	526	21	0.006	0.006	NUM
ejpam-6073	526	22	0.008	0.008	NUM
ejpam-6073	526	23	0.01	0.01	NUM
ejpam-6073	526	24	0.012	0.012	NUM
ejpam-6073	526	25	-5	-5	NOUN
ejpam-6073	526	26	0	0	NUM
ejpam-6073	526	27	5	5	NUM
ejpam-6073	526	28	z	z	NOUN
ejpam-6073	526	29	(	(	PUNCT
ejpam-6073	526	30	t	t	PROPN
ejpam-6073	526	31	,	,	PUNCT
ejpam-6073	526	32	0	0	NUM
ejpam-6073	526	33	.	.	NOUN
ejpam-6073	526	34	50	50	NUM
ejpam-6073	526	35	)	)	PUNCT
ejpam-6073	526	36	0	0	NUM
ejpam-6073	526	37	0.002	0.002	NUM
ejpam-6073	526	38	0.004	0.004	NUM
ejpam-6073	526	39	0.006	0.006	NUM
ejpam-6073	526	40	0.008	0.008	NUM
ejpam-6073	526	41	0.01	0.01	NUM
ejpam-6073	526	42	0.012	0.012	NUM
ejpam-6073	526	43	time	time	NOUN
ejpam-6073	526	44	-1	-1	NOUN
ejpam-6073	526	45	0	0	NUM
ejpam-6073	526	46	1	1	NUM
ejpam-6073	526	47	z	z	NOUN
ejpam-6073	526	48	(	(	PUNCT
ejpam-6073	526	49	t	t	PROPN
ejpam-6073	526	50	,	,	PUNCT
ejpam-6073	526	51	0	0	NUM
ejpam-6073	526	52	.	.	NOUN
ejpam-6073	526	53	75	75	NUM
ejpam-6073	526	54	)	)	PUNCT
ejpam-6073	526	55	0	0	NUM
ejpam-6073	526	56	0.002	0.002	NUM
ejpam-6073	526	57	0.004	0.004	NUM
ejpam-6073	526	58	0.006	0.006	NUM
ejpam-6073	526	59	0.008	0.008	NUM
ejpam-6073	526	60	0.01	0.01	NUM
ejpam-6073	526	61	0.012	0.012	NUM
ejpam-6073	526	62	time	time	NOUN
ejpam-6073	526	63	0	0	NUM
ejpam-6073	526	64	500	500	NUM
ejpam-6073	526	65	1000	1000	NUM
ejpam-6073	526	66	1500	1500	NUM
ejpam-6073	526	67	2000	2000	NUM
ejpam-6073	526	68	2500	2500	NUM
ejpam-6073	526	69	3000	3000	NUM
ejpam-6073	526	70	e	e	X
ejpam-6073	526	71	(	(	PUNCT
ejpam-6073	526	72	t	t	NOUN
ejpam-6073	526	73	)	)	PUNCT
ejpam-6073	526	74	figure	figure	NOUN
ejpam-6073	526	75	3	3	NUM
ejpam-6073	526	76	:	:	PUNCT
ejpam-6073	526	77	test	test	NOUN
ejpam-6073	526	78	1	1	NUM
ejpam-6073	526	79	:	:	PUNCT
ejpam-6073	526	80	blow	blow	VERB
ejpam-6073	526	81	up	up	ADP
ejpam-6073	526	82	under	under	ADP
ejpam-6073	526	83	p(x	p(x	NOUN
ejpam-6073	526	84	)	)	PUNCT
ejpam-6073	526	85	<	<	X
ejpam-6073	526	86	m(x	m(x	PROPN
ejpam-6073	526	87	)	)	PUNCT
ejpam-6073	526	88	and	and	CCONJ
ejpam-6073	526	89	ℓ(x	ℓ(x	PROPN
ejpam-6073	526	90	)	)	PUNCT
ejpam-6073	526	91	<	<	X
ejpam-6073	526	92	m(x	m(x	PROPN
ejpam-6073	526	93	)	)	PUNCT
ejpam-6073	526	94	.	.	PUNCT
ejpam-6073	527	1	0	0	NUM
ejpam-6073	528	1	0.002	0.002	NUM
ejpam-6073	528	2	0.004	0.004	NUM
ejpam-6073	528	3	0.006	0.006	NUM
ejpam-6073	528	4	0.008	0.008	NUM
ejpam-6073	528	5	0.01	0.01	NUM
ejpam-6073	528	6	0.012	0.012	NUM
ejpam-6073	528	7	-50	-50	PUNCT
ejpam-6073	528	8	0	0	NUM
ejpam-6073	528	9	50	50	NUM
ejpam-6073	528	10	u	u	NOUN
ejpam-6073	528	11	(	(	PUNCT
ejpam-6073	528	12	t	t	PROPN
ejpam-6073	528	13	,	,	PUNCT
ejpam-6073	528	14	0	0	NUM
ejpam-6073	528	15	.	.	NOUN
ejpam-6073	528	16	2	2	NUM
ejpam-6073	528	17	5	5	NUM
ejpam-6073	528	18	)	)	PUNCT
ejpam-6073	528	19	0	0	NUM
ejpam-6073	528	20	0.002	0.002	NUM
ejpam-6073	528	21	0.004	0.004	NUM
ejpam-6073	528	22	0.006	0.006	NUM
ejpam-6073	528	23	0.008	0.008	NUM
ejpam-6073	528	24	0.01	0.01	NUM
ejpam-6073	528	25	0.012	0.012	NUM
ejpam-6073	528	26	-20	-20	NUM
ejpam-6073	528	27	0	0	NUM
ejpam-6073	528	28	20	20	NUM
ejpam-6073	528	29	u	u	NOUN
ejpam-6073	528	30	(	(	PUNCT
ejpam-6073	528	31	t	t	PROPN
ejpam-6073	528	32	,	,	PUNCT
ejpam-6073	528	33	0	0	NUM
ejpam-6073	528	34	.	.	NOUN
ejpam-6073	528	35	50	50	NUM
ejpam-6073	528	36	)	)	PUNCT
ejpam-6073	528	37	0	0	NUM
ejpam-6073	529	1	0.002	0.002	NUM
ejpam-6073	529	2	0.004	0.004	NUM
ejpam-6073	529	3	0.006	0.006	NUM
ejpam-6073	529	4	0.008	0.008	NUM
ejpam-6073	529	5	0.01	0.01	NUM
ejpam-6073	529	6	0.012	0.012	NUM
ejpam-6073	529	7	time	time	NOUN
ejpam-6073	529	8	-5	-5	PUNCT
ejpam-6073	529	9	0	0	NUM
ejpam-6073	529	10	5	5	NUM
ejpam-6073	529	11	u	u	NOUN
ejpam-6073	529	12	(	(	PUNCT
ejpam-6073	529	13	t	t	PROPN
ejpam-6073	529	14	,	,	PUNCT
ejpam-6073	529	15	0	0	NUM
ejpam-6073	529	16	.	.	NOUN
ejpam-6073	529	17	75	75	NUM
ejpam-6073	529	18	)	)	PUNCT
ejpam-6073	529	19	0	0	NUM
ejpam-6073	529	20	0.002	0.002	NUM
ejpam-6073	529	21	0.004	0.004	NUM
ejpam-6073	529	22	0.006	0.006	NUM
ejpam-6073	529	23	0.008	0.008	NUM
ejpam-6073	529	24	0.01	0.01	NUM
ejpam-6073	529	25	0.012	0.012	NUM
ejpam-6073	529	26	-5	-5	NOUN
ejpam-6073	529	27	0	0	NUM
ejpam-6073	529	28	5	5	NUM
ejpam-6073	529	29	z	z	NOUN
ejpam-6073	529	30	(	(	PUNCT
ejpam-6073	529	31	t	t	PROPN
ejpam-6073	529	32	,	,	PUNCT
ejpam-6073	529	33	0	0	NUM
ejpam-6073	529	34	.	.	NOUN
ejpam-6073	529	35	25	25	NUM
ejpam-6073	529	36	)	)	PUNCT
ejpam-6073	529	37	0	0	NUM
ejpam-6073	529	38	0.002	0.002	NUM
ejpam-6073	529	39	0.004	0.004	NUM
ejpam-6073	529	40	0.006	0.006	NUM
ejpam-6073	529	41	0.008	0.008	NUM
ejpam-6073	529	42	0.01	0.01	NUM
ejpam-6073	529	43	0.012	0.012	NUM
ejpam-6073	529	44	-5	-5	NOUN
ejpam-6073	529	45	0	0	NUM
ejpam-6073	529	46	5	5	NUM
ejpam-6073	529	47	z	z	NOUN
ejpam-6073	529	48	(	(	PUNCT
ejpam-6073	529	49	t	t	PROPN
ejpam-6073	529	50	,	,	PUNCT
ejpam-6073	529	51	0	0	NUM
ejpam-6073	529	52	.	.	NOUN
ejpam-6073	529	53	50	50	NUM
ejpam-6073	529	54	)	)	PUNCT
ejpam-6073	529	55	0	0	NUM
ejpam-6073	529	56	0.002	0.002	NUM
ejpam-6073	529	57	0.004	0.004	NUM
ejpam-6073	529	58	0.006	0.006	NUM
ejpam-6073	529	59	0.008	0.008	NUM
ejpam-6073	529	60	0.01	0.01	NUM
ejpam-6073	529	61	0.012	0.012	NUM
ejpam-6073	529	62	time	time	NOUN
ejpam-6073	529	63	-1	-1	NOUN
ejpam-6073	529	64	0	0	NUM
ejpam-6073	529	65	1	1	NUM
ejpam-6073	529	66	z	z	NOUN
ejpam-6073	529	67	(	(	PUNCT
ejpam-6073	529	68	t	t	PROPN
ejpam-6073	529	69	,	,	PUNCT
ejpam-6073	529	70	0	0	NUM
ejpam-6073	529	71	.	.	NOUN
ejpam-6073	529	72	75	75	NUM
ejpam-6073	529	73	)	)	PUNCT
ejpam-6073	529	74	0	0	NUM
ejpam-6073	529	75	0.002	0.002	NUM
ejpam-6073	529	76	0.004	0.004	NUM
ejpam-6073	529	77	0.006	0.006	NUM
ejpam-6073	529	78	0.008	0.008	NUM
ejpam-6073	529	79	0.01	0.01	NUM
ejpam-6073	529	80	0.012	0.012	NUM
ejpam-6073	529	81	time	time	NOUN
ejpam-6073	529	82	0	0	NUM
ejpam-6073	529	83	500	500	NUM
ejpam-6073	529	84	1000	1000	NUM
ejpam-6073	529	85	1500	1500	NUM
ejpam-6073	529	86	2000	2000	NUM
ejpam-6073	529	87	2500	2500	NUM
ejpam-6073	529	88	3000	3000	NUM
ejpam-6073	529	89	e	e	X
ejpam-6073	529	90	(	(	PUNCT
ejpam-6073	529	91	t	t	NOUN
ejpam-6073	529	92	)	)	PUNCT
ejpam-6073	529	93	figure	figure	NOUN
ejpam-6073	529	94	4	4	NUM
ejpam-6073	529	95	:	:	PUNCT
ejpam-6073	529	96	test	test	NOUN
ejpam-6073	529	97	2	2	NUM
ejpam-6073	529	98	:	:	PUNCT
ejpam-6073	529	99	blow	blow	VERB
ejpam-6073	529	100	up	up	ADP
ejpam-6073	529	101	under	under	ADP
ejpam-6073	529	102	p(x	p(x	NOUN
ejpam-6073	529	103	)	)	PUNCT
ejpam-6073	529	104	=	=	SYM
ejpam-6073	529	105	m(x	m(x	PROPN
ejpam-6073	529	106	)	)	PUNCT
ejpam-6073	529	107	and	and	CCONJ
ejpam-6073	529	108	ℓ(x	ℓ(x	PROPN
ejpam-6073	529	109	)	)	PUNCT
ejpam-6073	529	110	<	<	X
ejpam-6073	529	111	m(x	m(x	PROPN
ejpam-6073	529	112	)	)	PUNCT
ejpam-6073	529	113	.	.	PUNCT
ejpam-6073	530	1	a.	a.	PROPN
ejpam-6073	530	2	m.	m.	PROPN
ejpam-6073	530	3	al	al	PROPN
ejpam-6073	530	4	-	-	PROPN
ejpam-6073	530	5	mahdi	mahdi	PROPN
ejpam-6073	530	6	et	et	PROPN
ejpam-6073	530	7	al	al	PROPN
ejpam-6073	530	8	.	.	PUNCT
ejpam-6073	530	9	/	/	SYM
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ejpam-6073	530	11	.	.	PUNCT
ejpam-6073	531	1	j.	j.	PROPN
ejpam-6073	531	2	pure	pure	PROPN
ejpam-6073	531	3	appl	appl	PROPN
ejpam-6073	531	4	.	.	PROPN
ejpam-6073	531	5	math	math	PROPN
ejpam-6073	531	6	,	,	PUNCT
ejpam-6073	531	7	18	18	NUM
ejpam-6073	531	8	(	(	PUNCT
ejpam-6073	531	9	3	3	NUM
ejpam-6073	531	10	)	)	PUNCT
ejpam-6073	531	11	(	(	PUNCT
ejpam-6073	531	12	2025	2025	NUM
ejpam-6073	531	13	)	)	PUNCT
ejpam-6073	531	14	,	,	PUNCT
ejpam-6073	531	15	6073	6073	NUM
ejpam-6073	531	16	25	25	NUM
ejpam-6073	531	17	of	of	ADP
ejpam-6073	531	18	29	29	NUM
ejpam-6073	531	19	0	0	NUM
ejpam-6073	531	20	0.002	0.002	NUM
ejpam-6073	531	21	0.004	0.004	NUM
ejpam-6073	531	22	0.006	0.006	NUM
ejpam-6073	531	23	0.008	0.008	NUM
ejpam-6073	531	24	0.01	0.01	NUM
ejpam-6073	531	25	0.012	0.012	NUM
ejpam-6073	531	26	-50	-50	PUNCT
ejpam-6073	531	27	0	0	NUM
ejpam-6073	531	28	50	50	NUM
ejpam-6073	531	29	u	u	NOUN
ejpam-6073	531	30	(	(	PUNCT
ejpam-6073	531	31	t	t	PROPN
ejpam-6073	531	32	,	,	PUNCT
ejpam-6073	531	33	0	0	NUM
ejpam-6073	531	34	.	.	NOUN
ejpam-6073	531	35	2	2	NUM
ejpam-6073	531	36	5	5	NUM
ejpam-6073	531	37	)	)	PUNCT
ejpam-6073	531	38	0	0	NUM
ejpam-6073	531	39	0.002	0.002	NUM
ejpam-6073	531	40	0.004	0.004	NUM
ejpam-6073	531	41	0.006	0.006	NUM
ejpam-6073	531	42	0.008	0.008	NUM
ejpam-6073	531	43	0.01	0.01	NUM
ejpam-6073	531	44	0.012	0.012	NUM
ejpam-6073	531	45	-20	-20	NUM
ejpam-6073	531	46	0	0	NUM
ejpam-6073	531	47	20	20	NUM
ejpam-6073	531	48	u	u	NOUN
ejpam-6073	531	49	(	(	PUNCT
ejpam-6073	531	50	t	t	PROPN
ejpam-6073	531	51	,	,	PUNCT
ejpam-6073	531	52	0	0	NUM
ejpam-6073	531	53	.5	.5	NUM
ejpam-6073	531	54	0	0	NUM
ejpam-6073	531	55	)	)	PUNCT
ejpam-6073	531	56	0	0	NUM
ejpam-6073	531	57	0.002	0.002	NUM
ejpam-6073	531	58	0.004	0.004	NUM
ejpam-6073	531	59	0.006	0.006	NUM
ejpam-6073	531	60	0.008	0.008	NUM
ejpam-6073	531	61	0.01	0.01	NUM
ejpam-6073	531	62	0.012	0.012	NUM
ejpam-6073	531	63	time	time	NOUN
ejpam-6073	531	64	-5	-5	PUNCT
ejpam-6073	531	65	0	0	NUM
ejpam-6073	531	66	5	5	NUM
ejpam-6073	531	67	u	u	NOUN
ejpam-6073	531	68	(	(	PUNCT
ejpam-6073	531	69	t	t	PROPN
ejpam-6073	531	70	,	,	PUNCT
ejpam-6073	531	71	0	0	NUM
ejpam-6073	531	72	.	.	NOUN
ejpam-6073	531	73	75	75	NUM
ejpam-6073	531	74	)	)	PUNCT
ejpam-6073	531	75	0	0	NUM
ejpam-6073	532	1	0.002	0.002	NUM
ejpam-6073	532	2	0.004	0.004	NUM
ejpam-6073	532	3	0.006	0.006	NUM
ejpam-6073	532	4	0.008	0.008	NUM
ejpam-6073	532	5	0.01	0.01	NUM
ejpam-6073	532	6	0.012	0.012	NUM
ejpam-6073	532	7	-5	-5	NOUN
ejpam-6073	532	8	0	0	NUM
ejpam-6073	532	9	5	5	NUM
ejpam-6073	532	10	z	z	NOUN
ejpam-6073	532	11	(	(	PUNCT
ejpam-6073	532	12	t	t	PROPN
ejpam-6073	532	13	,	,	PUNCT
ejpam-6073	532	14	0	0	NUM
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ejpam-6073	532	17	)	)	PUNCT
ejpam-6073	532	18	0	0	NUM
ejpam-6073	532	19	0.002	0.002	NUM
ejpam-6073	532	20	0.004	0.004	NUM
ejpam-6073	532	21	0.006	0.006	NUM
ejpam-6073	532	22	0.008	0.008	NUM
ejpam-6073	532	23	0.01	0.01	NUM
ejpam-6073	532	24	0.012	0.012	NUM
ejpam-6073	532	25	-5	-5	NOUN
ejpam-6073	532	26	0	0	NUM
ejpam-6073	532	27	5	5	NUM
ejpam-6073	532	28	z	z	NOUN
ejpam-6073	532	29	(	(	PUNCT
ejpam-6073	532	30	t	t	PROPN
ejpam-6073	532	31	,	,	PUNCT
ejpam-6073	532	32	0	0	NUM
ejpam-6073	532	33	.	.	NOUN
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ejpam-6073	532	35	)	)	PUNCT
ejpam-6073	532	36	0	0	NUM
ejpam-6073	532	37	0.002	0.002	NUM
ejpam-6073	532	38	0.004	0.004	NUM
ejpam-6073	532	39	0.006	0.006	NUM
ejpam-6073	532	40	0.008	0.008	NUM
ejpam-6073	532	41	0.01	0.01	NUM
ejpam-6073	532	42	0.012	0.012	NUM
ejpam-6073	532	43	time	time	NOUN
ejpam-6073	532	44	-1	-1	NOUN
ejpam-6073	532	45	0	0	NUM
ejpam-6073	532	46	1	1	NUM
ejpam-6073	532	47	z	z	NOUN
ejpam-6073	532	48	(	(	PUNCT
ejpam-6073	532	49	t	t	PROPN
ejpam-6073	532	50	,	,	PUNCT
ejpam-6073	532	51	0	0	NUM
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ejpam-6073	532	54	)	)	PUNCT
ejpam-6073	532	55	0	0	NUM
ejpam-6073	532	56	0.002	0.002	NUM
ejpam-6073	532	57	0.004	0.004	NUM
ejpam-6073	532	58	0.006	0.006	NUM
ejpam-6073	532	59	0.008	0.008	NUM
ejpam-6073	532	60	0.01	0.01	NUM
ejpam-6073	532	61	0.012	0.012	NUM
ejpam-6073	532	62	time	time	NOUN
ejpam-6073	532	63	0	0	NUM
ejpam-6073	532	64	500	500	NUM
ejpam-6073	532	65	1000	1000	NUM
ejpam-6073	532	66	1500	1500	NUM
ejpam-6073	532	67	2000	2000	NUM
ejpam-6073	532	68	2500	2500	NUM
ejpam-6073	532	69	3000	3000	NUM
ejpam-6073	532	70	e	e	X
ejpam-6073	532	71	(	(	PUNCT
ejpam-6073	532	72	t	t	NOUN
ejpam-6073	532	73	)	)	PUNCT
ejpam-6073	532	74	figure	figure	NOUN
ejpam-6073	532	75	5	5	NUM
ejpam-6073	532	76	:	:	PUNCT
ejpam-6073	532	77	test	test	NOUN
ejpam-6073	532	78	3	3	NUM
ejpam-6073	532	79	:	:	PUNCT
ejpam-6073	532	80	blow	blow	VERB
ejpam-6073	532	81	up	up	ADP
ejpam-6073	532	82	under	under	ADP
ejpam-6073	532	83	p(x	p(x	NOUN
ejpam-6073	532	84	)	)	PUNCT
ejpam-6073	532	85	<	<	X
ejpam-6073	532	86	m(x	m(x	PROPN
ejpam-6073	532	87	)	)	PUNCT
ejpam-6073	532	88	and	and	CCONJ
ejpam-6073	532	89	ℓ(x	ℓ(x	PROPN
ejpam-6073	532	90	)	)	PUNCT
ejpam-6073	532	91	=	=	SYM
ejpam-6073	532	92	m(x	m(x	PROPN
ejpam-6073	532	93	)	)	PUNCT
ejpam-6073	532	94	.	.	PUNCT
ejpam-6073	533	1	0	0	NUM
ejpam-6073	534	1	0.002	0.002	NUM
ejpam-6073	534	2	0.004	0.004	NUM
ejpam-6073	534	3	0.006	0.006	NUM
ejpam-6073	534	4	0.008	0.008	NUM
ejpam-6073	534	5	0.01	0.01	NUM
ejpam-6073	534	6	0.012	0.012	NUM
ejpam-6073	534	7	-50	-50	PUNCT
ejpam-6073	534	8	0	0	NUM
ejpam-6073	534	9	50	50	NUM
ejpam-6073	534	10	u	u	NOUN
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ejpam-6073	534	12	t	t	PROPN
ejpam-6073	534	13	,	,	PUNCT
ejpam-6073	534	14	0	0	NUM
ejpam-6073	534	15	.	.	NOUN
ejpam-6073	534	16	2	2	NUM
ejpam-6073	534	17	5	5	NUM
ejpam-6073	534	18	)	)	PUNCT
ejpam-6073	534	19	0	0	NUM
ejpam-6073	534	20	0.002	0.002	NUM
ejpam-6073	534	21	0.004	0.004	NUM
ejpam-6073	534	22	0.006	0.006	NUM
ejpam-6073	534	23	0.008	0.008	NUM
ejpam-6073	534	24	0.01	0.01	NUM
ejpam-6073	534	25	0.012	0.012	NUM
ejpam-6073	534	26	-20	-20	NUM
ejpam-6073	534	27	0	0	NUM
ejpam-6073	534	28	20	20	NUM
ejpam-6073	534	29	u	u	NOUN
ejpam-6073	534	30	(	(	PUNCT
ejpam-6073	534	31	t	t	PROPN
ejpam-6073	534	32	,	,	PUNCT
ejpam-6073	534	33	0	0	NUM
ejpam-6073	534	34	.	.	NOUN
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ejpam-6073	534	36	)	)	PUNCT
ejpam-6073	534	37	0	0	NUM
ejpam-6073	535	1	0.002	0.002	NUM
ejpam-6073	535	2	0.004	0.004	NUM
ejpam-6073	535	3	0.006	0.006	NUM
ejpam-6073	535	4	0.008	0.008	NUM
ejpam-6073	535	5	0.01	0.01	NUM
ejpam-6073	535	6	0.012	0.012	NUM
ejpam-6073	535	7	time	time	NOUN
ejpam-6073	535	8	-5	-5	PUNCT
ejpam-6073	535	9	0	0	NUM
ejpam-6073	535	10	5	5	NUM
ejpam-6073	535	11	u	u	NOUN
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ejpam-6073	535	13	t	t	PROPN
ejpam-6073	535	14	,	,	PUNCT
ejpam-6073	535	15	0	0	NUM
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ejpam-6073	535	18	)	)	PUNCT
ejpam-6073	535	19	0	0	NUM
ejpam-6073	535	20	0.002	0.002	NUM
ejpam-6073	535	21	0.004	0.004	NUM
ejpam-6073	535	22	0.006	0.006	NUM
ejpam-6073	535	23	0.008	0.008	NUM
ejpam-6073	535	24	0.01	0.01	NUM
ejpam-6073	535	25	0.012	0.012	NUM
ejpam-6073	535	26	-5	-5	NOUN
ejpam-6073	535	27	0	0	NUM
ejpam-6073	535	28	5	5	NUM
ejpam-6073	535	29	z	z	NOUN
ejpam-6073	535	30	(	(	PUNCT
ejpam-6073	535	31	t	t	PROPN
ejpam-6073	535	32	,	,	PUNCT
ejpam-6073	535	33	0	0	NUM
ejpam-6073	535	34	.	.	NOUN
ejpam-6073	535	35	25	25	NUM
ejpam-6073	535	36	)	)	PUNCT
ejpam-6073	535	37	0	0	NUM
ejpam-6073	535	38	0.002	0.002	NUM
ejpam-6073	535	39	0.004	0.004	NUM
ejpam-6073	535	40	0.006	0.006	NUM
ejpam-6073	535	41	0.008	0.008	NUM
ejpam-6073	535	42	0.01	0.01	NUM
ejpam-6073	535	43	0.012	0.012	NUM
ejpam-6073	535	44	-5	-5	NOUN
ejpam-6073	535	45	0	0	NUM
ejpam-6073	535	46	5	5	NUM
ejpam-6073	535	47	z	z	NOUN
ejpam-6073	535	48	(	(	PUNCT
ejpam-6073	535	49	t	t	PROPN
ejpam-6073	535	50	,	,	PUNCT
ejpam-6073	535	51	0	0	NUM
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ejpam-6073	535	53	50	50	NUM
ejpam-6073	535	54	)	)	PUNCT
ejpam-6073	535	55	0	0	NUM
ejpam-6073	535	56	0.002	0.002	NUM
ejpam-6073	535	57	0.004	0.004	NUM
ejpam-6073	535	58	0.006	0.006	NUM
ejpam-6073	535	59	0.008	0.008	NUM
ejpam-6073	535	60	0.01	0.01	NUM
ejpam-6073	535	61	0.012	0.012	NUM
ejpam-6073	535	62	time	time	NOUN
ejpam-6073	535	63	-1	-1	NOUN
ejpam-6073	535	64	0	0	NUM
ejpam-6073	535	65	1	1	NUM
ejpam-6073	535	66	z	z	NOUN
ejpam-6073	535	67	(	(	PUNCT
ejpam-6073	535	68	t	t	PROPN
ejpam-6073	535	69	,	,	PUNCT
ejpam-6073	535	70	0	0	NUM
ejpam-6073	535	71	.	.	NOUN
ejpam-6073	535	72	75	75	NUM
ejpam-6073	535	73	)	)	PUNCT
ejpam-6073	535	74	0	0	NUM
ejpam-6073	535	75	0.002	0.002	NUM
ejpam-6073	535	76	0.004	0.004	NUM
ejpam-6073	535	77	0.006	0.006	NUM
ejpam-6073	535	78	0.008	0.008	NUM
ejpam-6073	535	79	0.01	0.01	NUM
ejpam-6073	535	80	0.012	0.012	NUM
ejpam-6073	535	81	time	time	NOUN
ejpam-6073	535	82	0	0	NUM
ejpam-6073	535	83	500	500	NUM
ejpam-6073	535	84	1000	1000	NUM
ejpam-6073	535	85	1500	1500	NUM
ejpam-6073	535	86	2000	2000	NUM
ejpam-6073	535	87	2500	2500	NUM
ejpam-6073	535	88	3000	3000	NUM
ejpam-6073	535	89	e	e	X
ejpam-6073	535	90	(	(	PUNCT
ejpam-6073	535	91	t	t	NOUN
ejpam-6073	535	92	)	)	PUNCT
ejpam-6073	535	93	figure	figure	NOUN
ejpam-6073	535	94	6	6	NUM
ejpam-6073	535	95	:	:	PUNCT
ejpam-6073	535	96	test	test	NOUN
ejpam-6073	535	97	4	4	NUM
ejpam-6073	535	98	:	:	PUNCT
ejpam-6073	535	99	blow	blow	VERB
ejpam-6073	535	100	up	up	ADP
ejpam-6073	535	101	under	under	ADP
ejpam-6073	535	102	p(x	p(x	NOUN
ejpam-6073	535	103	)	)	PUNCT
ejpam-6073	535	104	=	=	SYM
ejpam-6073	535	105	m(x	m(x	PROPN
ejpam-6073	535	106	)	)	PUNCT
ejpam-6073	535	107	and	and	CCONJ
ejpam-6073	535	108	ℓ(x	ℓ(x	PROPN
ejpam-6073	535	109	)	)	PUNCT
ejpam-6073	535	110	=	=	SYM
ejpam-6073	535	111	m(x	m(x	PROPN
ejpam-6073	535	112	)	)	PUNCT
ejpam-6073	535	113	.	.	PUNCT
ejpam-6073	536	1	finally	finally	ADV
ejpam-6073	536	2	,	,	PUNCT
ejpam-6073	536	3	we	we	PRON
ejpam-6073	536	4	remarked	remark	VERB
ejpam-6073	536	5	that	that	SCONJ
ejpam-6073	536	6	even	even	ADV
ejpam-6073	536	7	for	for	ADP
ejpam-6073	536	8	a	a	DET
ejpam-6073	536	9	fine	fine	ADJ
ejpam-6073	536	10	spatial	spatial	ADJ
ejpam-6073	536	11	and	and	CCONJ
ejpam-6073	536	12	temporal	temporal	ADJ
ejpam-6073	536	13	discretization	discretization	NOUN
ejpam-6073	536	14	,	,	PUNCT
ejpam-6073	536	15	the	the	DET
ejpam-6073	536	16	blow	blow	NOUN
ejpam-6073	536	17	up	up	ADP
ejpam-6073	536	18	occurs	occur	VERB
ejpam-6073	536	19	after	after	ADP
ejpam-6073	536	20	a	a	DET
ejpam-6073	536	21	finite	finite	ADJ
ejpam-6073	536	22	number	number	NOUN
ejpam-6073	536	23	of	of	ADP
ejpam-6073	536	24	steps	step	NOUN
ejpam-6073	536	25	for	for	ADP
ejpam-6073	536	26	all	all	DET
ejpam-6073	536	27	the	the	DET
ejpam-6073	536	28	tests	test	NOUN
ejpam-6073	536	29	.	.	PUNCT
ejpam-6073	537	1	conclusion	conclusion	NOUN
ejpam-6073	537	2	in	in	ADP
ejpam-6073	537	3	this	this	DET
ejpam-6073	537	4	work	work	NOUN
ejpam-6073	537	5	,	,	PUNCT
ejpam-6073	537	6	we	we	PRON
ejpam-6073	537	7	investigated	investigate	VERB
ejpam-6073	537	8	a	a	DET
ejpam-6073	537	9	swelling	swell	VERB
ejpam-6073	537	10	soil	soil	NOUN
ejpam-6073	537	11	system	system	NOUN
ejpam-6073	537	12	incorporating	incorporate	VERB
ejpam-6073	537	13	two	two	NUM
ejpam-6073	537	14	nonlinear	nonlinear	ADJ
ejpam-6073	537	15	damping	damp	VERB
ejpam-6073	537	16	and	and	CCONJ
ejpam-6073	537	17	source	source	NOUN
ejpam-6073	537	18	terms	term	NOUN
ejpam-6073	537	19	of	of	ADP
ejpam-6073	537	20	variable	variable	ADJ
ejpam-6073	537	21	exponent	exponent	NOUN
ejpam-6073	537	22	-	-	PUNCT
ejpam-6073	537	23	type	type	NOUN
ejpam-6073	537	24	.	.	PUNCT
ejpam-6073	538	1	by	by	ADP
ejpam-6073	538	2	employing	employ	VERB
ejpam-6073	538	3	the	the	DET
ejpam-6073	538	4	faedo	faedo	ADJ
ejpam-6073	538	5	-	-	PUNCT
ejpam-6073	538	6	galerkin	galerkin	ADJ
ejpam-6073	538	7	method	method	NOUN
ejpam-6073	538	8	and	and	CCONJ
ejpam-6073	538	9	the	the	DET
ejpam-6073	538	10	banach	banach	NOUN
ejpam-6073	538	11	contraction	contraction	NOUN
ejpam-6073	538	12	theorem	theorem	VERB
ejpam-6073	538	13	,	,	PUNCT
ejpam-6073	538	14	we	we	PRON
ejpam-6073	538	15	established	establish	VERB
ejpam-6073	538	16	the	the	DET
ejpam-6073	538	17	local	local	ADJ
ejpam-6073	538	18	existence	existence	NOUN
ejpam-6073	538	19	and	and	CCONJ
ejpam-6073	538	20	uniqueness	uniqueness	NOUN
ejpam-6073	538	21	a.	a.	NOUN
ejpam-6073	538	22	m.	m.	PROPN
ejpam-6073	538	23	al	al	PROPN
ejpam-6073	538	24	-	-	PROPN
ejpam-6073	538	25	mahdi	mahdi	PROPN
ejpam-6073	538	26	et	et	PROPN
ejpam-6073	538	27	al	al	PROPN
ejpam-6073	538	28	.	.	PUNCT
ejpam-6073	538	29	/	/	SYM
ejpam-6073	538	30	eur	eur	PROPN
ejpam-6073	538	31	.	.	PUNCT
ejpam-6073	539	1	j.	j.	PROPN
ejpam-6073	539	2	pure	pure	PROPN
ejpam-6073	539	3	appl	appl	PROPN
ejpam-6073	539	4	.	.	PROPN
ejpam-6073	539	5	math	math	PROPN
ejpam-6073	539	6	,	,	PUNCT
ejpam-6073	539	7	18	18	NUM
ejpam-6073	539	8	(	(	PUNCT
ejpam-6073	539	9	3	3	NUM
ejpam-6073	539	10	)	)	PUNCT
ejpam-6073	539	11	(	(	PUNCT
ejpam-6073	539	12	2025	2025	NUM
ejpam-6073	539	13	)	)	PUNCT
ejpam-6073	539	14	,	,	PUNCT
ejpam-6073	539	15	6073	6073	NUM
ejpam-6073	539	16	26	26	NUM
ejpam-6073	539	17	of	of	ADP
ejpam-6073	539	18	29	29	NUM
ejpam-6073	539	19	of	of	ADP
ejpam-6073	539	20	weak	weak	ADJ
ejpam-6073	539	21	solutions	solution	NOUN
ejpam-6073	539	22	under	under	ADP
ejpam-6073	539	23	suitable	suitable	ADJ
ejpam-6073	539	24	conditions	condition	NOUN
ejpam-6073	539	25	on	on	ADP
ejpam-6073	539	26	the	the	DET
ejpam-6073	539	27	variable	variable	ADJ
ejpam-6073	539	28	exponent	exponent	NOUN
ejpam-6073	539	29	functions	function	NOUN
ejpam-6073	539	30	.	.	PUNCT
ejpam-6073	540	1	furthermore	furthermore	ADV
ejpam-6073	540	2	,	,	PUNCT
ejpam-6073	540	3	we	we	PRON
ejpam-6073	540	4	demonstrated	demonstrate	VERB
ejpam-6073	540	5	the	the	DET
ejpam-6073	540	6	global	global	ADJ
ejpam-6073	540	7	existence	existence	NOUN
ejpam-6073	540	8	of	of	ADP
ejpam-6073	540	9	solutions	solution	NOUN
ejpam-6073	540	10	and	and	CCONJ
ejpam-6073	540	11	identified	identify	VERB
ejpam-6073	540	12	conditions	condition	NOUN
ejpam-6073	540	13	leading	lead	VERB
ejpam-6073	540	14	to	to	ADP
ejpam-6073	540	15	finite	finite	ADJ
ejpam-6073	540	16	-	-	PUNCT
ejpam-6073	540	17	time	time	NOUN
ejpam-6073	540	18	blow	blow	NOUN
ejpam-6073	540	19	-	-	PUNCT
ejpam-6073	540	20	up	up	NOUN
ejpam-6073	540	21	.	.	PUNCT
ejpam-6073	541	1	a	a	DET
ejpam-6073	541	2	key	key	ADJ
ejpam-6073	541	3	contribution	contribution	NOUN
ejpam-6073	541	4	of	of	ADP
ejpam-6073	541	5	this	this	DET
ejpam-6073	541	6	study	study	NOUN
ejpam-6073	541	7	is	be	AUX
ejpam-6073	541	8	the	the	DET
ejpam-6073	541	9	consideration	consideration	NOUN
ejpam-6073	541	10	of	of	ADP
ejpam-6073	541	11	damping	damp	VERB
ejpam-6073	541	12	terms	term	NOUN
ejpam-6073	541	13	with	with	ADP
ejpam-6073	541	14	variable	variable	ADJ
ejpam-6073	541	15	exponents	exponent	NOUN
ejpam-6073	541	16	,	,	PUNCT
ejpam-6073	541	17	which	which	PRON
ejpam-6073	541	18	significantly	significantly	ADV
ejpam-6073	541	19	generalizes	generalize	VERB
ejpam-6073	541	20	classical	classical	ADJ
ejpam-6073	541	21	models	model	NOUN
ejpam-6073	541	22	with	with	ADP
ejpam-6073	541	23	constant	constant	ADJ
ejpam-6073	541	24	exponent	exponent	NOUN
ejpam-6073	541	25	damping	damping	NOUN
ejpam-6073	541	26	.	.	PUNCT
ejpam-6073	542	1	this	this	DET
ejpam-6073	542	2	formulation	formulation	NOUN
ejpam-6073	542	3	allows	allow	VERB
ejpam-6073	542	4	for	for	ADP
ejpam-6073	542	5	a	a	DET
ejpam-6073	542	6	more	more	ADV
ejpam-6073	542	7	flexible	flexible	ADJ
ejpam-6073	542	8	and	and	CCONJ
ejpam-6073	542	9	realistic	realistic	ADJ
ejpam-6073	542	10	representation	representation	NOUN
ejpam-6073	542	11	of	of	ADP
ejpam-6073	542	12	energy	energy	NOUN
ejpam-6073	542	13	dissipation	dissipation	NOUN
ejpam-6073	542	14	,	,	PUNCT
ejpam-6073	542	15	capturing	capture	VERB
ejpam-6073	542	16	heterogeneous	heterogeneous	ADJ
ejpam-6073	542	17	material	material	NOUN
ejpam-6073	542	18	properties	property	NOUN
ejpam-6073	542	19	and	and	CCONJ
ejpam-6073	542	20	dynamic	dynamic	ADJ
ejpam-6073	542	21	changes	change	NOUN
ejpam-6073	542	22	in	in	ADP
ejpam-6073	542	23	the	the	DET
ejpam-6073	542	24	system	system	NOUN
ejpam-6073	542	25	.	.	PUNCT
ejpam-6073	543	1	the	the	DET
ejpam-6073	543	2	presence	presence	NOUN
ejpam-6073	543	3	of	of	ADP
ejpam-6073	543	4	variable	variable	ADJ
ejpam-6073	543	5	exponent	exponent	NOUN
ejpam-6073	543	6	damping	damp	VERB
ejpam-6073	543	7	plays	play	VERB
ejpam-6073	543	8	a	a	DET
ejpam-6073	543	9	crucial	crucial	ADJ
ejpam-6073	543	10	role	role	NOUN
ejpam-6073	543	11	in	in	ADP
ejpam-6073	543	12	influencing	influence	VERB
ejpam-6073	543	13	the	the	DET
ejpam-6073	543	14	stability	stability	NOUN
ejpam-6073	543	15	and	and	CCONJ
ejpam-6073	543	16	long	long	ADJ
ejpam-6073	543	17	-	-	PUNCT
ejpam-6073	543	18	term	term	NOUN
ejpam-6073	543	19	behavior	behavior	NOUN
ejpam-6073	543	20	of	of	ADP
ejpam-6073	543	21	solutions	solution	NOUN
ejpam-6073	543	22	.	.	PUNCT
ejpam-6073	544	1	finally	finally	ADV
ejpam-6073	544	2	,	,	PUNCT
ejpam-6073	544	3	we	we	PRON
ejpam-6073	544	4	provided	provide	VERB
ejpam-6073	544	5	numerical	numerical	ADJ
ejpam-6073	544	6	simulations	simulation	NOUN
ejpam-6073	544	7	to	to	PART
ejpam-6073	544	8	illustrate	illustrate	VERB
ejpam-6073	544	9	the	the	DET
ejpam-6073	544	10	blow	blow	NOUN
ejpam-6073	544	11	-	-	PUNCT
ejpam-6073	544	12	up	up	ADP
ejpam-6073	544	13	behavior	behavior	NOUN
ejpam-6073	544	14	,	,	PUNCT
ejpam-6073	544	15	further	far	ADV
ejpam-6073	544	16	validating	validate	VERB
ejpam-6073	544	17	our	our	PRON
ejpam-6073	544	18	theoretical	theoretical	ADJ
ejpam-6073	544	19	findings	finding	NOUN
ejpam-6073	544	20	.	.	PUNCT
ejpam-6073	545	1	while	while	SCONJ
ejpam-6073	545	2	this	this	DET
ejpam-6073	545	3	study	study	NOUN
ejpam-6073	545	4	establishes	establish	VERB
ejpam-6073	545	5	significant	significant	ADJ
ejpam-6073	545	6	results	result	NOUN
ejpam-6073	545	7	on	on	ADP
ejpam-6073	545	8	the	the	DET
ejpam-6073	545	9	existence	existence	NOUN
ejpam-6073	545	10	,	,	PUNCT
ejpam-6073	545	11	uniqueness	uniqueness	NOUN
ejpam-6073	545	12	,	,	PUNCT
ejpam-6073	545	13	and	and	CCONJ
ejpam-6073	545	14	blow	blow	NOUN
ejpam-6073	545	15	-	-	PUNCT
ejpam-6073	545	16	up	up	NOUN
ejpam-6073	545	17	of	of	ADP
ejpam-6073	545	18	solutions	solution	NOUN
ejpam-6073	545	19	for	for	ADP
ejpam-6073	545	20	swelling	swell	VERB
ejpam-6073	545	21	porous	porous	ADJ
ejpam-6073	545	22	-	-	PUNCT
ejpam-6073	545	23	elastic	elastic	ADJ
ejpam-6073	545	24	systems	system	NOUN
ejpam-6073	545	25	with	with	ADP
ejpam-6073	545	26	variable	variable	ADJ
ejpam-6073	545	27	exponent	exponent	NOUN
ejpam-6073	545	28	damping	damp	VERB
ejpam-6073	545	29	and	and	CCONJ
ejpam-6073	545	30	source	source	NOUN
ejpam-6073	545	31	terms	term	NOUN
ejpam-6073	545	32	,	,	PUNCT
ejpam-6073	545	33	several	several	ADJ
ejpam-6073	545	34	questions	question	NOUN
ejpam-6073	545	35	remain	remain	VERB
ejpam-6073	545	36	open	open	ADJ
ejpam-6073	545	37	for	for	ADP
ejpam-6073	545	38	further	further	ADJ
ejpam-6073	545	39	investigation	investigation	NOUN
ejpam-6073	545	40	:	:	PUNCT
ejpam-6073	545	41	i.	i.	NOUN
ejpam-6073	545	42	extension	extension	NOUN
ejpam-6073	545	43	to	to	ADP
ejpam-6073	545	44	higher	high	ADJ
ejpam-6073	545	45	dimensions	dimension	NOUN
ejpam-6073	545	46	and	and	CCONJ
ejpam-6073	545	47	general	general	ADJ
ejpam-6073	545	48	domains	domain	NOUN
ejpam-6073	545	49	the	the	DET
ejpam-6073	545	50	current	current	ADJ
ejpam-6073	545	51	analysis	analysis	NOUN
ejpam-6073	545	52	is	be	AUX
ejpam-6073	545	53	restricted	restrict	VERB
ejpam-6073	545	54	to	to	ADP
ejpam-6073	545	55	one	one	NUM
ejpam-6073	545	56	-	-	PUNCT
ejpam-6073	545	57	dimensional	dimensional	ADJ
ejpam-6073	545	58	settings	setting	NOUN
ejpam-6073	545	59	.	.	PUNCT
ejpam-6073	546	1	extending	extend	VERB
ejpam-6073	546	2	the	the	DET
ejpam-6073	546	3	results	result	NOUN
ejpam-6073	546	4	to	to	ADP
ejpam-6073	546	5	higher	higher	ADV
ejpam-6073	546	6	-	-	PUNCT
ejpam-6073	546	7	dimensional	dimensional	ADJ
ejpam-6073	546	8	porous	porous	ADJ
ejpam-6073	546	9	-	-	PUNCT
ejpam-6073	546	10	elastic	elastic	ADJ
ejpam-6073	546	11	systems	system	NOUN
ejpam-6073	546	12	with	with	ADP
ejpam-6073	546	13	variable	variable	ADJ
ejpam-6073	546	14	exponent	exponent	NOUN
ejpam-6073	546	15	nonlinearity	nonlinearity	NOUN
ejpam-6073	546	16	is	be	AUX
ejpam-6073	546	17	a	a	DET
ejpam-6073	546	18	significant	significant	ADJ
ejpam-6073	546	19	challenge	challenge	NOUN
ejpam-6073	546	20	that	that	PRON
ejpam-6073	546	21	could	could	AUX
ejpam-6073	546	22	lead	lead	VERB
ejpam-6073	546	23	to	to	ADP
ejpam-6073	546	24	new	new	ADJ
ejpam-6073	546	25	theoretical	theoretical	ADJ
ejpam-6073	546	26	developments	development	NOUN
ejpam-6073	546	27	.	.	PUNCT
ejpam-6073	547	1	ii	ii	PROPN
ejpam-6073	547	2	.	.	PUNCT
ejpam-6073	547	3	impact	impact	NOUN
ejpam-6073	547	4	of	of	ADP
ejpam-6073	547	5	additional	additional	ADJ
ejpam-6073	547	6	nonlinear	nonlinear	ADJ
ejpam-6073	547	7	effects	effect	NOUN
ejpam-6073	547	8	the	the	DET
ejpam-6073	547	9	current	current	ADJ
ejpam-6073	547	10	model	model	NOUN
ejpam-6073	547	11	does	do	AUX
ejpam-6073	547	12	not	not	PART
ejpam-6073	547	13	include	include	VERB
ejpam-6073	547	14	nonlocal	nonlocal	ADJ
ejpam-6073	547	15	effects	effect	NOUN
ejpam-6073	547	16	,	,	PUNCT
ejpam-6073	547	17	memory	memory	NOUN
ejpam-6073	547	18	terms	term	NOUN
ejpam-6073	547	19	,	,	PUNCT
ejpam-6073	547	20	or	or	CCONJ
ejpam-6073	547	21	fractional	fractional	ADJ
ejpam-6073	547	22	diffusion	diffusion	NOUN
ejpam-6073	547	23	.	.	PUNCT
ejpam-6073	548	1	introducing	introduce	VERB
ejpam-6073	548	2	these	these	DET
ejpam-6073	548	3	effects	effect	NOUN
ejpam-6073	548	4	could	could	AUX
ejpam-6073	548	5	provide	provide	VERB
ejpam-6073	548	6	more	more	ADV
ejpam-6073	548	7	accurate	accurate	ADJ
ejpam-6073	548	8	representations	representation	NOUN
ejpam-6073	548	9	of	of	ADP
ejpam-6073	548	10	real	real	ADJ
ejpam-6073	548	11	-	-	PUNCT
ejpam-6073	548	12	world	world	NOUN
ejpam-6073	548	13	swelling	swell	VERB
ejpam-6073	548	14	porous	porous	ADJ
ejpam-6073	548	15	media	medium	NOUN
ejpam-6073	548	16	and	and	CCONJ
ejpam-6073	548	17	lead	lead	VERB
ejpam-6073	548	18	to	to	ADP
ejpam-6073	548	19	new	new	ADJ
ejpam-6073	548	20	mathematical	mathematical	ADJ
ejpam-6073	548	21	difficulties	difficulty	NOUN
ejpam-6073	548	22	in	in	ADP
ejpam-6073	548	23	existence	existence	NOUN
ejpam-6073	548	24	and	and	CCONJ
ejpam-6073	548	25	blow	blow	NOUN
ejpam-6073	548	26	-	-	PUNCT
ejpam-6073	548	27	up	up	ADP
ejpam-6073	548	28	analysis	analysis	NOUN
ejpam-6073	548	29	.	.	PUNCT
ejpam-6073	549	1	acknowledgements	acknowledgement	NOUN
ejpam-6073	549	2	the	the	DET
ejpam-6073	549	3	first	first	ADJ
ejpam-6073	549	4	two	two	NUM
ejpam-6073	549	5	authors	author	NOUN
ejpam-6073	549	6	would	would	AUX
ejpam-6073	549	7	like	like	VERB
ejpam-6073	549	8	to	to	PART
ejpam-6073	549	9	express	express	VERB
ejpam-6073	549	10	their	their	PRON
ejpam-6073	549	11	profound	profound	ADJ
ejpam-6073	549	12	gratitude	gratitude	NOUN
ejpam-6073	549	13	to	to	ADP
ejpam-6073	549	14	king	king	PROPN
ejpam-6073	549	15	fahd	fahd	PROPN
ejpam-6073	549	16	university	university	PROPN
ejpam-6073	549	17	of	of	ADP
ejpam-6073	549	18	petroleum	petroleum	NOUN
ejpam-6073	549	19	and	and	CCONJ
ejpam-6073	549	20	minerals	mineral	NOUN
ejpam-6073	549	21	(	(	PUNCT
ejpam-6073	549	22	kfupm	kfupm	NOUN
ejpam-6073	549	23	)	)	PUNCT
ejpam-6073	549	24	for	for	ADP
ejpam-6073	549	25	its	its	PRON
ejpam-6073	549	26	continuous	continuous	ADJ
ejpam-6073	549	27	support	support	NOUN
ejpam-6073	549	28	.	.	PUNCT
ejpam-6073	550	1	this	this	DET
ejpam-6073	550	2	work	work	NOUN
ejpam-6073	550	3	is	be	AUX
ejpam-6073	550	4	funded	fund	VERB
ejpam-6073	550	5	by	by	ADP
ejpam-6073	550	6	kfupm	kfupm	NOUN
ejpam-6073	550	7	,	,	PUNCT
ejpam-6073	550	8	grant	grant	VERB
ejpam-6073	550	9	no	no	NOUN
ejpam-6073	550	10	.	.	PUNCT
ejpam-6073	551	1	incb2528	incb2528	PROPN
ejpam-6073	551	2	.	.	PUNCT
ejpam-6073	552	1	data	datum	NOUN
ejpam-6073	552	2	availability	availability	NOUN
ejpam-6073	552	3	no	no	DET
ejpam-6073	552	4	data	datum	NOUN
ejpam-6073	552	5	were	be	AUX
ejpam-6073	552	6	used	use	VERB
ejpam-6073	552	7	to	to	PART
ejpam-6073	552	8	support	support	VERB
ejpam-6073	552	9	this	this	DET
ejpam-6073	552	10	study	study	NOUN
ejpam-6073	552	11	.	.	PUNCT
ejpam-6073	553	1	conflict	conflict	NOUN
ejpam-6073	553	2	of	of	ADP
ejpam-6073	553	3	interest	interest	NOUN
ejpam-6073	553	4	the	the	DET
ejpam-6073	553	5	authors	author	NOUN
ejpam-6073	553	6	declare	declare	VERB
ejpam-6073	553	7	that	that	SCONJ
ejpam-6073	553	8	there	there	PRON
ejpam-6073	553	9	is	be	VERB
ejpam-6073	553	10	no	no	DET
ejpam-6073	553	11	conflict	conflict	NOUN
ejpam-6073	553	12	of	of	ADP
ejpam-6073	553	13	interest	interest	NOUN
ejpam-6073	553	14	.	.	PUNCT
ejpam-6073	554	1	references	reference	NOUN
ejpam-6073	554	2	[	[	X
ejpam-6073	554	3	1	1	NUM
ejpam-6073	554	4	]	]	PUNCT
ejpam-6073	554	5	richard	richard	PROPN
ejpam-6073	554	6	l.	l.	PROPN
ejpam-6073	554	7	handy	handy	PROPN
ejpam-6073	554	8	.	.	PUNCT
ejpam-6073	555	1	a	a	DET
ejpam-6073	555	2	stress	stress	NOUN
ejpam-6073	555	3	path	path	NOUN
ejpam-6073	555	4	model	model	NOUN
ejpam-6073	555	5	for	for	ADP
ejpam-6073	555	6	collapsible	collapsible	ADJ
ejpam-6073	555	7	loess	loess	NOUN
ejpam-6073	555	8	.	.	PUNCT
ejpam-6073	556	1	in	in	ADP
ejpam-6073	556	2	genesis	genesis	NOUN
ejpam-6073	556	3	and	and	CCONJ
ejpam-6073	556	4	properties	property	NOUN
ejpam-6073	556	5	of	of	ADP
ejpam-6073	556	6	collapsible	collapsible	ADJ
ejpam-6073	556	7	soils	soil	NOUN
ejpam-6073	556	8	,	,	PUNCT
ejpam-6073	556	9	pages	page	NOUN
ejpam-6073	556	10	33–47	33–47	NUM
ejpam-6073	556	11	.	.	PUNCT
ejpam-6073	556	12	springer	springer	NOUN
ejpam-6073	556	13	,	,	PUNCT
ejpam-6073	556	14	1995	1995	NUM
ejpam-6073	556	15	.	.	PUNCT
ejpam-6073	557	1	[	[	X
ejpam-6073	557	2	2	2	X
ejpam-6073	557	3	]	]	X
ejpam-6073	557	4	john	john	PROPN
ejpam-6073	557	5	nelson	nelson	PROPN
ejpam-6073	557	6	and	and	CCONJ
ejpam-6073	557	7	debora	debora	PROPN
ejpam-6073	557	8	j.	j.	PROPN
ejpam-6073	557	9	miller	miller	PROPN
ejpam-6073	557	10	.	.	PUNCT
ejpam-6073	558	1	expansive	expansive	ADJ
ejpam-6073	558	2	soils	soil	NOUN
ejpam-6073	558	3	:	:	PUNCT
ejpam-6073	558	4	problems	problem	NOUN
ejpam-6073	558	5	and	and	CCONJ
ejpam-6073	558	6	practice	practice	NOUN
ejpam-6073	558	7	in	in	ADP
ejpam-6073	558	8	foundation	foundation	NOUN
ejpam-6073	558	9	and	and	CCONJ
ejpam-6073	558	10	pavement	pavement	NOUN
ejpam-6073	558	11	engineering	engineering	NOUN
ejpam-6073	558	12	.	.	PUNCT
ejpam-6073	559	1	john	john	PROPN
ejpam-6073	559	2	wiley	wiley	PROPN
ejpam-6073	559	3	&	&	CCONJ
ejpam-6073	559	4	sons	son	NOUN
ejpam-6073	559	5	,	,	PUNCT
ejpam-6073	559	6	1997	1997	NUM
ejpam-6073	559	7	.	.	PUNCT
ejpam-6073	560	1	a.	a.	PROPN
ejpam-6073	560	2	m.	m.	PROPN
ejpam-6073	560	3	al	al	PROPN
ejpam-6073	560	4	-	-	PROPN
ejpam-6073	560	5	mahdi	mahdi	PROPN
ejpam-6073	560	6	et	et	PROPN
ejpam-6073	560	7	al	al	PROPN
ejpam-6073	560	8	.	.	PUNCT
ejpam-6073	560	9	/	/	SYM
ejpam-6073	560	10	eur	eur	PROPN
ejpam-6073	560	11	.	.	PUNCT
ejpam-6073	561	1	j.	j.	PROPN
ejpam-6073	561	2	pure	pure	PROPN
ejpam-6073	561	3	appl	appl	PROPN
ejpam-6073	561	4	.	.	PROPN
ejpam-6073	561	5	math	math	PROPN
ejpam-6073	561	6	,	,	PUNCT
ejpam-6073	561	7	18	18	NUM
ejpam-6073	561	8	(	(	PUNCT
ejpam-6073	561	9	3	3	NUM
ejpam-6073	561	10	)	)	PUNCT
ejpam-6073	561	11	(	(	PUNCT
ejpam-6073	561	12	2025	2025	NUM
ejpam-6073	561	13	)	)	PUNCT
ejpam-6073	561	14	,	,	PUNCT
ejpam-6073	561	15	6073	6073	NUM
ejpam-6073	561	16	27	27	NUM
ejpam-6073	561	17	of	of	ADP
ejpam-6073	561	18	29	29	NUM
ejpam-6073	561	19	[	[	SYM
ejpam-6073	561	20	3	3	NUM
ejpam-6073	561	21	]	]	PUNCT
ejpam-6073	561	22	a.	a.	NOUN
ejpam-6073	561	23	cemal	cemal	PROPN
ejpam-6073	561	24	eringen	eringen	PROPN
ejpam-6073	561	25	.	.	PUNCT
ejpam-6073	562	1	a	a	DET
ejpam-6073	562	2	continuum	continuum	ADJ
ejpam-6073	562	3	theory	theory	NOUN
ejpam-6073	562	4	of	of	ADP
ejpam-6073	562	5	swelling	swell	VERB
ejpam-6073	562	6	porous	porous	ADJ
ejpam-6073	562	7	elastic	elastic	ADJ
ejpam-6073	562	8	soils	soil	NOUN
ejpam-6073	562	9	.	.	PUNCT
ejpam-6073	563	1	international	international	ADJ
ejpam-6073	563	2	journal	journal	PROPN
ejpam-6073	563	3	of	of	ADP
ejpam-6073	563	4	engineering	engineering	NOUN
ejpam-6073	563	5	science	science	NOUN
ejpam-6073	563	6	,	,	PUNCT
ejpam-6073	563	7	32(8):1337–1349	32(8):1337–1349	NUM
ejpam-6073	563	8	,	,	PUNCT
ejpam-6073	563	9	1994	1994	NUM
ejpam-6073	563	10	.	.	PUNCT
ejpam-6073	564	1	[	[	X
ejpam-6073	564	2	4	4	NUM
ejpam-6073	564	3	]	]	PUNCT
ejpam-6073	564	4	a.	a.	NOUN
ejpam-6073	564	5	bedford	bedford	PROPN
ejpam-6073	564	6	and	and	CCONJ
ejpam-6073	564	7	d.	d.	PROPN
ejpam-6073	564	8	s.	s.	PROPN
ejpam-6073	564	9	drumheller	drumheller	PROPN
ejpam-6073	564	10	.	.	PUNCT
ejpam-6073	565	1	theories	theory	NOUN
ejpam-6073	565	2	of	of	ADP
ejpam-6073	565	3	immiscible	immiscible	ADJ
ejpam-6073	565	4	and	and	CCONJ
ejpam-6073	565	5	structured	structured	ADJ
ejpam-6073	565	6	mixtures	mixture	NOUN
ejpam-6073	565	7	.	.	PUNCT
ejpam-6073	566	1	international	international	ADJ
ejpam-6073	566	2	journal	journal	NOUN
ejpam-6073	566	3	of	of	ADP
ejpam-6073	566	4	engineering	engineering	NOUN
ejpam-6073	566	5	science	science	NOUN
ejpam-6073	566	6	,	,	PUNCT
ejpam-6073	566	7	21(8):863–960	21(8):863–960	PROPN
ejpam-6073	566	8	,	,	PUNCT
ejpam-6073	566	9	1983	1983	NUM
ejpam-6073	566	10	.	.	PUNCT
ejpam-6073	567	1	[	[	X
ejpam-6073	567	2	5	5	NUM
ejpam-6073	567	3	]	]	PUNCT
ejpam-6073	567	4	behzad	behzad	PROPN
ejpam-6073	567	5	kalantari	kalantari	PROPN
ejpam-6073	567	6	et	et	PROPN
ejpam-6073	567	7	al	al	PROPN
ejpam-6073	567	8	.	.	PUNCT
ejpam-6073	567	9	engineering	engineering	NOUN
ejpam-6073	567	10	significance	significance	NOUN
ejpam-6073	567	11	of	of	ADP
ejpam-6073	567	12	swelling	swell	VERB
ejpam-6073	567	13	soils	soil	NOUN
ejpam-6073	567	14	.	.	PUNCT
ejpam-6073	568	1	research	research	NOUN
ejpam-6073	568	2	journal	journal	PROPN
ejpam-6073	568	3	of	of	ADP
ejpam-6073	568	4	applied	apply	VERB
ejpam-6073	568	5	sciences	science	NOUN
ejpam-6073	568	6	,	,	PUNCT
ejpam-6073	568	7	engineering	engineering	NOUN
ejpam-6073	568	8	and	and	CCONJ
ejpam-6073	568	9	technology	technology	NOUN
ejpam-6073	568	10	,	,	PUNCT
ejpam-6073	568	11	4(17):2874–2878	4(17):2874–2878	NUM
ejpam-6073	568	12	,	,	PUNCT
ejpam-6073	568	13	2012	2012	NUM
ejpam-6073	568	14	.	.	PUNCT
ejpam-6073	569	1	[	[	X
ejpam-6073	569	2	6	6	NUM
ejpam-6073	569	3	]	]	PUNCT
ejpam-6073	569	4	d.	d.	PROPN
ejpam-6073	569	5	ieşan	ieşan	PROPN
ejpam-6073	569	6	.	.	PUNCT
ejpam-6073	570	1	on	on	ADP
ejpam-6073	570	2	the	the	DET
ejpam-6073	570	3	theory	theory	NOUN
ejpam-6073	570	4	of	of	ADP
ejpam-6073	570	5	mixtures	mixture	NOUN
ejpam-6073	570	6	of	of	ADP
ejpam-6073	570	7	thermoelastic	thermoelastic	ADJ
ejpam-6073	570	8	solids	solid	NOUN
ejpam-6073	570	9	.	.	PUNCT
ejpam-6073	571	1	journal	journal	PROPN
ejpam-6073	571	2	of	of	ADP
ejpam-6073	571	3	thermal	thermal	ADJ
ejpam-6073	571	4	stresses	stress	NOUN
ejpam-6073	571	5	,	,	PUNCT
ejpam-6073	571	6	14(4):389–408	14(4):389–408	NUM
ejpam-6073	571	7	,	,	PUNCT
ejpam-6073	571	8	1991	1991	NUM
ejpam-6073	571	9	.	.	PUNCT
ejpam-6073	572	1	[	[	X
ejpam-6073	572	2	7	7	X
ejpam-6073	572	3	]	]	X
ejpam-6073	572	4	r.	r.	PROPN
ejpam-6073	572	5	quintanilla	quintanilla	PROPN
ejpam-6073	572	6	.	.	PUNCT
ejpam-6073	572	7	exponential	exponential	ADJ
ejpam-6073	572	8	stability	stability	NOUN
ejpam-6073	572	9	for	for	ADP
ejpam-6073	572	10	one	one	NUM
ejpam-6073	572	11	-	-	PUNCT
ejpam-6073	572	12	dimensional	dimensional	ADJ
ejpam-6073	572	13	problem	problem	NOUN
ejpam-6073	572	14	of	of	ADP
ejpam-6073	572	15	swelling	swell	VERB
ejpam-6073	572	16	porous	porous	ADJ
ejpam-6073	572	17	elastic	elastic	ADJ
ejpam-6073	572	18	soils	soil	NOUN
ejpam-6073	572	19	with	with	ADP
ejpam-6073	572	20	fluid	fluid	ADJ
ejpam-6073	572	21	saturation	saturation	NOUN
ejpam-6073	572	22	.	.	PUNCT
ejpam-6073	573	1	journal	journal	NOUN
ejpam-6073	573	2	of	of	ADP
ejpam-6073	573	3	computational	computational	ADJ
ejpam-6073	573	4	and	and	CCONJ
ejpam-6073	573	5	applied	applied	ADJ
ejpam-6073	573	6	mathematics	mathematic	NOUN
ejpam-6073	573	7	,	,	PUNCT
ejpam-6073	573	8	145(2):525–533	145(2):525–533	NUM
ejpam-6073	573	9	,	,	PUNCT
ejpam-6073	573	10	2002	2002	NUM
ejpam-6073	573	11	.	.	PUNCT
ejpam-6073	574	1	[	[	X
ejpam-6073	574	2	8	8	NUM
ejpam-6073	574	3	]	]	X
ejpam-6073	574	4	jun	jun	PROPN
ejpam-6073	574	5	-	-	PUNCT
ejpam-6073	574	6	min	min	PROPN
ejpam-6073	574	7	wang	wang	PROPN
ejpam-6073	574	8	and	and	CCONJ
ejpam-6073	574	9	bao	bao	PROPN
ejpam-6073	574	10	-	-	PROPN
ejpam-6073	574	11	zhu	zhu	PROPN
ejpam-6073	574	12	guo	guo	PROPN
ejpam-6073	574	13	.	.	PUNCT
ejpam-6073	575	1	on	on	ADP
ejpam-6073	575	2	the	the	DET
ejpam-6073	575	3	stability	stability	NOUN
ejpam-6073	575	4	of	of	ADP
ejpam-6073	575	5	swelling	swell	VERB
ejpam-6073	575	6	porous	porous	ADJ
ejpam-6073	575	7	elastic	elastic	ADJ
ejpam-6073	575	8	soils	soil	NOUN
ejpam-6073	575	9	with	with	ADP
ejpam-6073	575	10	fluid	fluid	ADJ
ejpam-6073	575	11	saturation	saturation	NOUN
ejpam-6073	575	12	by	by	ADP
ejpam-6073	575	13	one	one	NUM
ejpam-6073	575	14	internal	internal	ADJ
ejpam-6073	575	15	damping	damping	NOUN
ejpam-6073	575	16	.	.	PUNCT
ejpam-6073	576	1	i	i	PRON
ejpam-6073	576	2	m	m	VERB
ejpam-6073	576	3	a	a	DET
ejpam-6073	576	4	journal	journal	NOUN
ejpam-6073	576	5	of	of	ADP
ejpam-6073	576	6	applied	apply	VERB
ejpam-6073	576	7	mathematics	mathematic	NOUN
ejpam-6073	576	8	,	,	PUNCT
ejpam-6073	576	9	71(4):565–582	71(4):565–582	PROPN
ejpam-6073	576	10	,	,	PUNCT
ejpam-6073	576	11	2006	2006	NUM
ejpam-6073	576	12	.	.	PUNCT
ejpam-6073	577	1	[	[	X
ejpam-6073	577	2	9	9	NUM
ejpam-6073	577	3	]	]	PUNCT
ejpam-6073	577	4	a.	a.	NOUN
ejpam-6073	577	5	j.	j.	PROPN
ejpam-6073	577	6	a.	a.	PROPN
ejpam-6073	577	7	ramos	ramos	PROPN
ejpam-6073	577	8	,	,	PUNCT
ejpam-6073	577	9	m.	m.	NOUN
ejpam-6073	577	10	m.	m.	NOUN
ejpam-6073	577	11	freitas	freitas	PROPN
ejpam-6073	577	12	,	,	PUNCT
ejpam-6073	577	13	d.	d.	PROPN
ejpam-6073	577	14	s.	s.	PROPN
ejpam-6073	577	15	almeida	almeida	PROPN
ejpam-6073	577	16	jr	jr	PROPN
ejpam-6073	577	17	,	,	PUNCT
ejpam-6073	577	18	a.	a.	PROPN
ejpam-6073	577	19	s.	s.	PROPN
ejpam-6073	577	20	noé	noé	PROPN
ejpam-6073	577	21	,	,	PUNCT
ejpam-6073	577	22	and	and	CCONJ
ejpam-6073	577	23	m.	m.	PROPN
ejpam-6073	577	24	j.	j.	PROPN
ejpam-6073	577	25	dos	dos	PROPN
ejpam-6073	577	26	santos	santos	PROPN
ejpam-6073	577	27	.	.	PUNCT
ejpam-6073	578	1	stability	stability	NOUN
ejpam-6073	578	2	results	result	VERB
ejpam-6073	578	3	for	for	ADP
ejpam-6073	578	4	elastic	elastic	ADJ
ejpam-6073	578	5	porous	porous	ADJ
ejpam-6073	578	6	media	medium	NOUN
ejpam-6073	578	7	swelling	swell	VERB
ejpam-6073	578	8	with	with	ADP
ejpam-6073	578	9	nonlinear	nonlinear	ADJ
ejpam-6073	578	10	damping	damping	NOUN
ejpam-6073	578	11	.	.	PUNCT
ejpam-6073	579	1	journal	journal	NOUN
ejpam-6073	579	2	of	of	ADP
ejpam-6073	579	3	mathematical	mathematical	ADJ
ejpam-6073	579	4	physics	physics	NOUN
ejpam-6073	579	5	,	,	PUNCT
ejpam-6073	579	6	61(10):101505	61(10):101505	NUM
ejpam-6073	579	7	,	,	PUNCT
ejpam-6073	579	8	2020	2020	NUM
ejpam-6073	579	9	.	.	PUNCT
ejpam-6073	580	1	[	[	X
ejpam-6073	580	2	10	10	NUM
ejpam-6073	580	3	]	]	PUNCT
ejpam-6073	580	4	tijani	tijani	PROPN
ejpam-6073	580	5	a.	a.	PROPN
ejpam-6073	580	6	apalara	apalara	PROPN
ejpam-6073	580	7	.	.	PUNCT
ejpam-6073	581	1	general	general	ADJ
ejpam-6073	581	2	decay	decay	NOUN
ejpam-6073	581	3	of	of	ADP
ejpam-6073	581	4	solutions	solution	NOUN
ejpam-6073	581	5	in	in	ADP
ejpam-6073	581	6	one	one	NUM
ejpam-6073	581	7	-	-	PUNCT
ejpam-6073	581	8	dimensional	dimensional	ADJ
ejpam-6073	581	9	porous	porous	ADJ
ejpam-6073	581	10	-	-	PUNCT
ejpam-6073	581	11	elastic	elastic	ADJ
ejpam-6073	581	12	system	system	NOUN
ejpam-6073	581	13	with	with	ADP
ejpam-6073	581	14	memory	memory	NOUN
ejpam-6073	581	15	.	.	PUNCT
ejpam-6073	582	1	journal	journal	PROPN
ejpam-6073	582	2	of	of	ADP
ejpam-6073	582	3	mathematical	mathematical	ADJ
ejpam-6073	582	4	analysis	analysis	NOUN
ejpam-6073	582	5	and	and	CCONJ
ejpam-6073	582	6	applications	application	NOUN
ejpam-6073	582	7	,	,	PUNCT
ejpam-6073	582	8	469(2):457	469(2):457	NUM
ejpam-6073	582	9	–	–	PUNCT
ejpam-6073	582	10	471	471	NUM
ejpam-6073	582	11	,	,	PUNCT
ejpam-6073	582	12	2019	2019	NUM
ejpam-6073	582	13	.	.	PUNCT
ejpam-6073	583	1	[	[	X
ejpam-6073	583	2	11	11	NUM
ejpam-6073	583	3	]	]	PUNCT
ejpam-6073	583	4	abderrahmane	abderrahmane	PROPN
ejpam-6073	583	5	youkana	youkana	PROPN
ejpam-6073	583	6	,	,	PUNCT
ejpam-6073	583	7	adel	adel	PROPN
ejpam-6073	583	8	m.	m.	PROPN
ejpam-6073	583	9	al	al	PROPN
ejpam-6073	583	10	-	-	PUNCT
ejpam-6073	583	11	mahdi	mahdi	PROPN
ejpam-6073	583	12	,	,	PUNCT
ejpam-6073	583	13	and	and	CCONJ
ejpam-6073	583	14	salim	salim	PROPN
ejpam-6073	583	15	a.	a.	PROPN
ejpam-6073	583	16	messaoudi	messaoudi	PROPN
ejpam-6073	583	17	.	.	PUNCT
ejpam-6073	584	1	general	general	ADJ
ejpam-6073	584	2	energy	energy	NOUN
ejpam-6073	584	3	decay	decay	NOUN
ejpam-6073	584	4	result	result	NOUN
ejpam-6073	584	5	for	for	ADP
ejpam-6073	584	6	a	a	DET
ejpam-6073	584	7	viscoelastic	viscoelastic	ADJ
ejpam-6073	584	8	swelling	swell	VERB
ejpam-6073	584	9	porous	porous	ADJ
ejpam-6073	584	10	-	-	PUNCT
ejpam-6073	584	11	elastic	elastic	ADJ
ejpam-6073	584	12	system	system	NOUN
ejpam-6073	584	13	.	.	PUNCT
ejpam-6073	585	1	zeitschrift	zeitschrift	NOUN
ejpam-6073	585	2	für	für	PROPN
ejpam-6073	585	3	angewandte	angewandte	PROPN
ejpam-6073	585	4	mathematik	mathematik	PROPN
ejpam-6073	585	5	und	und	PROPN
ejpam-6073	585	6	physik	physik	PROPN
ejpam-6073	585	7	,	,	PUNCT
ejpam-6073	585	8	73(3):1–17	73(3):1–17	NUM
ejpam-6073	585	9	,	,	PUNCT
ejpam-6073	585	10	2022	2022	NUM
ejpam-6073	585	11	.	.	PUNCT
ejpam-6073	586	1	[	[	X
ejpam-6073	586	2	12	12	NUM
ejpam-6073	586	3	]	]	X
ejpam-6073	586	4	adel	adel	PROPN
ejpam-6073	586	5	m.	m.	PROPN
ejpam-6073	586	6	al	al	PROPN
ejpam-6073	586	7	-	-	PUNCT
ejpam-6073	586	8	mahdi	mahdi	PROPN
ejpam-6073	586	9	,	,	PUNCT
ejpam-6073	586	10	mohammad	mohammad	PROPN
ejpam-6073	586	11	m.	m.	PROPN
ejpam-6073	586	12	al	al	PROPN
ejpam-6073	586	13	-	-	PUNCT
ejpam-6073	586	14	gharabli	gharabli	PROPN
ejpam-6073	586	15	,	,	PUNCT
ejpam-6073	586	16	and	and	CCONJ
ejpam-6073	586	17	mostafa	mostafa	PROPN
ejpam-6073	586	18	zahri	zahri	PROPN
ejpam-6073	586	19	.	.	PUNCT
ejpam-6073	587	1	theoretical	theoretical	ADJ
ejpam-6073	587	2	and	and	CCONJ
ejpam-6073	587	3	computational	computational	ADJ
ejpam-6073	587	4	decay	decay	NOUN
ejpam-6073	587	5	results	result	NOUN
ejpam-6073	587	6	for	for	ADP
ejpam-6073	587	7	a	a	DET
ejpam-6073	587	8	memory	memory	NOUN
ejpam-6073	587	9	type	type	NOUN
ejpam-6073	587	10	wave	wave	NOUN
ejpam-6073	587	11	equation	equation	NOUN
ejpam-6073	587	12	with	with	ADP
ejpam-6073	587	13	variable	variable	ADJ
ejpam-6073	587	14	-	-	PUNCT
ejpam-6073	587	15	exponent	exponent	NOUN
ejpam-6073	587	16	nonlinearity	nonlinearity	NOUN
ejpam-6073	587	17	.	.	PUNCT
ejpam-6073	588	1	mathematical	mathematical	ADJ
ejpam-6073	588	2	control	control	NOUN
ejpam-6073	588	3	and	and	CCONJ
ejpam-6073	588	4	related	related	ADJ
ejpam-6073	588	5	fields	field	NOUN
ejpam-6073	588	6	,	,	PUNCT
ejpam-6073	588	7	2022	2022	NUM
ejpam-6073	588	8	.	.	PUNCT
ejpam-6073	589	1	[	[	X
ejpam-6073	589	2	13	13	NUM
ejpam-6073	589	3	]	]	X
ejpam-6073	589	4	emilio	emilio	PROPN
ejpam-6073	589	5	acerbi	acerbi	PROPN
ejpam-6073	589	6	and	and	CCONJ
ejpam-6073	589	7	giuseppe	giuseppe	PROPN
ejpam-6073	589	8	mingione	mingione	PROPN
ejpam-6073	589	9	.	.	PUNCT
ejpam-6073	590	1	regularity	regularity	NOUN
ejpam-6073	590	2	results	result	NOUN
ejpam-6073	590	3	for	for	ADP
ejpam-6073	590	4	stationary	stationary	ADJ
ejpam-6073	590	5	electrorheological	electrorheological	ADJ
ejpam-6073	590	6	fluids	fluid	NOUN
ejpam-6073	590	7	.	.	PUNCT
ejpam-6073	591	1	archive	archive	NOUN
ejpam-6073	591	2	for	for	ADP
ejpam-6073	591	3	rational	rational	ADJ
ejpam-6073	591	4	mechanics	mechanic	NOUN
ejpam-6073	591	5	and	and	CCONJ
ejpam-6073	591	6	analysis	analysis	NOUN
ejpam-6073	591	7	,	,	PUNCT
ejpam-6073	591	8	164(3):213–259	164(3):213–259	NUM
ejpam-6073	591	9	,	,	PUNCT
ejpam-6073	591	10	2002	2002	NUM
ejpam-6073	591	11	.	.	PUNCT
ejpam-6073	592	1	[	[	X
ejpam-6073	592	2	14	14	NUM
ejpam-6073	592	3	]	]	X
ejpam-6073	592	4	michael	michael	PROPN
ejpam-6073	592	5	ruzicka	ruzicka	PROPN
ejpam-6073	592	6	.	.	PUNCT
ejpam-6073	593	1	electrorheological	electrorheological	ADJ
ejpam-6073	593	2	fluids	fluid	NOUN
ejpam-6073	593	3	:	:	PUNCT
ejpam-6073	593	4	modeling	modeling	NOUN
ejpam-6073	593	5	and	and	CCONJ
ejpam-6073	593	6	mathematical	mathematical	ADJ
ejpam-6073	593	7	theory	theory	NOUN
ejpam-6073	593	8	.	.	PUNCT
ejpam-6073	594	1	springer	springer	NOUN
ejpam-6073	594	2	science	science	PROPN
ejpam-6073	594	3	&	&	CCONJ
ejpam-6073	594	4	business	business	NOUN
ejpam-6073	594	5	media	medium	NOUN
ejpam-6073	594	6	,	,	PUNCT
ejpam-6073	594	7	2000	2000	NUM
ejpam-6073	594	8	.	.	PUNCT
ejpam-6073	595	1	[	[	X
ejpam-6073	595	2	15	15	NUM
ejpam-6073	595	3	]	]	X
ejpam-6073	595	4	stanislav	stanislav	PROPN
ejpam-6073	595	5	antontsev	antontsev	PROPN
ejpam-6073	595	6	.	.	PROPN
ejpam-6073	596	1	wave	wave	PROPN
ejpam-6073	596	2	equation	equation	NOUN
ejpam-6073	596	3	with	with	ADP
ejpam-6073	596	4	p(x	p(x	PROPN
ejpam-6073	596	5	,	,	PUNCT
ejpam-6073	596	6	t)-laplacian	t)-laplacian	NOUN
ejpam-6073	596	7	and	and	CCONJ
ejpam-6073	596	8	damping	damp	VERB
ejpam-6073	596	9	term	term	NOUN
ejpam-6073	596	10	:	:	PUNCT
ejpam-6073	596	11	existence	existence	NOUN
ejpam-6073	596	12	and	and	CCONJ
ejpam-6073	596	13	blow	blow	NOUN
ejpam-6073	596	14	-	-	PUNCT
ejpam-6073	596	15	up	up	NOUN
ejpam-6073	596	16	.	.	PUNCT
ejpam-6073	597	1	differential	differential	ADJ
ejpam-6073	597	2	equations	equation	NOUN
ejpam-6073	597	3	and	and	CCONJ
ejpam-6073	597	4	applications	application	NOUN
ejpam-6073	597	5	,	,	PUNCT
ejpam-6073	597	6	3(4):503–525	3(4):503–525	NUM
ejpam-6073	597	7	,	,	PUNCT
ejpam-6073	597	8	2011	2011	NUM
ejpam-6073	597	9	.	.	PUNCT
ejpam-6073	598	1	[	[	X
ejpam-6073	598	2	16	16	NUM
ejpam-6073	598	3	]	]	X
ejpam-6073	598	4	stanislav	stanislav	PROPN
ejpam-6073	598	5	antontsev	antontsev	PROPN
ejpam-6073	598	6	.	.	PROPN
ejpam-6073	599	1	wave	wave	PROPN
ejpam-6073	599	2	equation	equation	NOUN
ejpam-6073	599	3	with	with	ADP
ejpam-6073	599	4	p(x	p(x	PROPN
ejpam-6073	599	5	,	,	PUNCT
ejpam-6073	599	6	t)-laplacian	t)-laplacian	NOUN
ejpam-6073	599	7	and	and	CCONJ
ejpam-6073	599	8	damping	damp	VERB
ejpam-6073	599	9	term	term	NOUN
ejpam-6073	599	10	:	:	PUNCT
ejpam-6073	599	11	blowup	blowup	ADJ
ejpam-6073	599	12	of	of	ADP
ejpam-6073	599	13	solutions	solution	NOUN
ejpam-6073	599	14	.	.	PUNCT
ejpam-6073	600	1	comptes	compte	VERB
ejpam-6073	600	2	rendus	rendus	PROPN
ejpam-6073	600	3	mécanique	mécanique	PROPN
ejpam-6073	600	4	,	,	PUNCT
ejpam-6073	600	5	339(12):751–755	339(12):751–755	NUM
ejpam-6073	600	6	,	,	PUNCT
ejpam-6073	600	7	2011	2011	NUM
ejpam-6073	600	8	.	.	PUNCT
ejpam-6073	601	1	[	[	X
ejpam-6073	601	2	17	17	NUM
ejpam-6073	601	3	]	]	PUNCT
ejpam-6073	601	4	salim	salim	PROPN
ejpam-6073	601	5	a.	a.	PROPN
ejpam-6073	601	6	messaoudi	messaoudi	PROPN
ejpam-6073	601	7	and	and	CCONJ
ejpam-6073	601	8	ala	ala	PROPN
ejpam-6073	601	9	a.	a.	NOUN
ejpam-6073	601	10	talahmeh	talahmeh	NOUN
ejpam-6073	601	11	.	.	PUNCT
ejpam-6073	602	1	a	a	DET
ejpam-6073	602	2	blow	blow	NOUN
ejpam-6073	602	3	-	-	PUNCT
ejpam-6073	602	4	up	up	ADP
ejpam-6073	602	5	result	result	NOUN
ejpam-6073	602	6	for	for	ADP
ejpam-6073	602	7	a	a	DET
ejpam-6073	602	8	nonlinear	nonlinear	ADJ
ejpam-6073	602	9	wave	wave	NOUN
ejpam-6073	602	10	equation	equation	NOUN
ejpam-6073	602	11	with	with	ADP
ejpam-6073	602	12	variable	variable	ADJ
ejpam-6073	602	13	-	-	PUNCT
ejpam-6073	602	14	exponent	exponent	NOUN
ejpam-6073	602	15	nonlinearities	nonlinearitie	NOUN
ejpam-6073	602	16	.	.	PUNCT
ejpam-6073	603	1	applicable	applicable	ADJ
ejpam-6073	603	2	analysis	analysis	NOUN
ejpam-6073	603	3	,	,	PUNCT
ejpam-6073	603	4	96(9):1509–1515	96(9):1509–1515	NUM
ejpam-6073	603	5	,	,	PUNCT
ejpam-6073	603	6	2017	2017	NUM
ejpam-6073	603	7	.	.	PUNCT
ejpam-6073	604	1	[	[	X
ejpam-6073	604	2	18	18	NUM
ejpam-6073	604	3	]	]	PUNCT
ejpam-6073	604	4	salim	salim	PROPN
ejpam-6073	604	5	a.	a.	PROPN
ejpam-6073	604	6	messaoudi	messaoudi	PROPN
ejpam-6073	604	7	,	,	PUNCT
ejpam-6073	604	8	ala	ala	PROPN
ejpam-6073	604	9	a.	a.	NOUN
ejpam-6073	604	10	talahmeh	talahmeh	NOUN
ejpam-6073	604	11	,	,	PUNCT
ejpam-6073	604	12	and	and	CCONJ
ejpam-6073	604	13	jamal	jamal	PROPN
ejpam-6073	604	14	h.	h.	PROPN
ejpam-6073	604	15	al	al	PROPN
ejpam-6073	604	16	-	-	PUNCT
ejpam-6073	604	17	smail	smail	NOUN
ejpam-6073	604	18	.	.	PUNCT
ejpam-6073	605	1	nonlinear	nonlinear	ADJ
ejpam-6073	605	2	damped	damp	VERB
ejpam-6073	605	3	wave	wave	NOUN
ejpam-6073	605	4	equation	equation	NOUN
ejpam-6073	605	5	:	:	PUNCT
ejpam-6073	605	6	existence	existence	NOUN
ejpam-6073	605	7	and	and	CCONJ
ejpam-6073	605	8	blow	blow	NOUN
ejpam-6073	605	9	-	-	PUNCT
ejpam-6073	605	10	up	up	NOUN
ejpam-6073	605	11	.	.	PUNCT
ejpam-6073	606	1	computers	computer	NOUN
ejpam-6073	606	2	&	&	CCONJ
ejpam-6073	606	3	mathematics	mathematics	PROPN
ejpam-6073	606	4	with	with	ADP
ejpam-6073	606	5	applications	application	NOUN
ejpam-6073	606	6	,	,	PUNCT
ejpam-6073	606	7	74(12):3024–3041	74(12):3024–3041	PROPN
ejpam-6073	606	8	,	,	PUNCT
ejpam-6073	606	9	2017	2017	NUM
ejpam-6073	606	10	.	.	PUNCT
ejpam-6073	607	1	[	[	X
ejpam-6073	607	2	19	19	NUM
ejpam-6073	607	3	]	]	X
ejpam-6073	607	4	mustafa	mustafa	PROPN
ejpam-6073	607	5	turkyilmazoglu	turkyilmazoglu	NOUN
ejpam-6073	607	6	.	.	PUNCT
ejpam-6073	608	1	buckling	buckle	VERB
ejpam-6073	608	2	phenomenon	phenomenon	NOUN
ejpam-6073	608	3	of	of	ADP
ejpam-6073	608	4	vertical	vertical	ADJ
ejpam-6073	608	5	beam	beam	NOUN
ejpam-6073	608	6	/	/	SYM
ejpam-6073	608	7	column	column	NOUN
ejpam-6073	608	8	of	of	ADP
ejpam-6073	608	9	variable	variable	ADJ
ejpam-6073	608	10	density	density	NOUN
ejpam-6073	608	11	carrying	carry	VERB
ejpam-6073	608	12	a	a	DET
ejpam-6073	608	13	top	top	ADJ
ejpam-6073	608	14	mass	mass	PROPN
ejpam-6073	608	15	.	.	PUNCT
ejpam-6073	609	1	journal	journal	PROPN
ejpam-6073	609	2	of	of	ADP
ejpam-6073	609	3	engineering	engineering	NOUN
ejpam-6073	609	4	mathematics	mathematic	NOUN
ejpam-6073	609	5	,	,	PUNCT
ejpam-6073	609	6	147(1):4	147(1):4	NOUN
ejpam-6073	609	7	,	,	PUNCT
ejpam-6073	609	8	2024	2024	NUM
ejpam-6073	609	9	.	.	PUNCT
ejpam-6073	610	1	a.	a.	PROPN
ejpam-6073	610	2	m.	m.	PROPN
ejpam-6073	610	3	al	al	PROPN
ejpam-6073	610	4	-	-	PROPN
ejpam-6073	610	5	mahdi	mahdi	PROPN
ejpam-6073	610	6	et	et	PROPN
ejpam-6073	610	7	al	al	PROPN
ejpam-6073	610	8	.	.	PUNCT
ejpam-6073	610	9	/	/	SYM
ejpam-6073	610	10	eur	eur	PROPN
ejpam-6073	610	11	.	.	PUNCT
ejpam-6073	611	1	j.	j.	PROPN
ejpam-6073	611	2	pure	pure	PROPN
ejpam-6073	611	3	appl	appl	PROPN
ejpam-6073	611	4	.	.	PROPN
ejpam-6073	611	5	math	math	PROPN
ejpam-6073	611	6	,	,	PUNCT
ejpam-6073	611	7	18	18	NUM
ejpam-6073	611	8	(	(	PUNCT
ejpam-6073	611	9	3	3	NUM
ejpam-6073	611	10	)	)	PUNCT
ejpam-6073	611	11	(	(	PUNCT
ejpam-6073	611	12	2025	2025	NUM
ejpam-6073	611	13	)	)	PUNCT
ejpam-6073	611	14	,	,	PUNCT
ejpam-6073	611	15	6073	6073	NUM
ejpam-6073	611	16	28	28	NUM
ejpam-6073	611	17	of	of	ADP
ejpam-6073	611	18	29	29	NUM
ejpam-6073	611	19	[	[	SYM
ejpam-6073	611	20	20	20	NUM
ejpam-6073	611	21	]	]	PUNCT
ejpam-6073	611	22	mustafa	mustafa	PROPN
ejpam-6073	611	23	turkyilmazoglu	turkyilmazoglu	PROPN
ejpam-6073	611	24	.	.	PUNCT
ejpam-6073	612	1	solution	solution	NOUN
ejpam-6073	612	2	of	of	ADP
ejpam-6073	612	3	initial	initial	ADJ
ejpam-6073	612	4	and	and	CCONJ
ejpam-6073	612	5	boundary	boundary	ADJ
ejpam-6073	612	6	value	value	NOUN
ejpam-6073	612	7	problems	problem	NOUN
ejpam-6073	612	8	by	by	ADP
ejpam-6073	612	9	an	an	DET
ejpam-6073	612	10	effective	effective	ADJ
ejpam-6073	612	11	accurate	accurate	ADJ
ejpam-6073	612	12	method	method	NOUN
ejpam-6073	612	13	.	.	PUNCT
ejpam-6073	613	1	international	international	ADJ
ejpam-6073	613	2	journal	journal	NOUN
ejpam-6073	613	3	of	of	ADP
ejpam-6073	613	4	computational	computational	ADJ
ejpam-6073	613	5	methods	method	NOUN
ejpam-6073	613	6	,	,	PUNCT
ejpam-6073	613	7	14(06):1750069	14(06):1750069	NUM
ejpam-6073	613	8	,	,	PUNCT
ejpam-6073	613	9	2017	2017	NUM
ejpam-6073	613	10	.	.	PUNCT
ejpam-6073	614	1	[	[	X
ejpam-6073	614	2	21	21	NUM
ejpam-6073	614	3	]	]	X
ejpam-6073	614	4	ali	ali	PROPN
ejpam-6073	614	5	kandil	kandil	PROPN
ejpam-6073	614	6	,	,	PUNCT
ejpam-6073	614	7	yasser	yasser	PROPN
ejpam-6073	614	8	salah	salah	PROPN
ejpam-6073	614	9	hamed	hamed	PROPN
ejpam-6073	614	10	,	,	PUNCT
ejpam-6073	614	11	and	and	CCONJ
ejpam-6073	614	12	abdullah	abdullah	PROPN
ejpam-6073	614	13	m.	m.	PROPN
ejpam-6073	614	14	alsharif	alsharif	PROPN
ejpam-6073	614	15	.	.	PUNCT
ejpam-6073	615	1	rotor	rotor	NOUN
ejpam-6073	615	2	active	active	ADJ
ejpam-6073	615	3	magnetic	magnetic	ADJ
ejpam-6073	615	4	bearings	bearing	NOUN
ejpam-6073	615	5	system	system	NOUN
ejpam-6073	615	6	control	control	NOUN
ejpam-6073	615	7	via	via	ADP
ejpam-6073	615	8	a	a	DET
ejpam-6073	615	9	tuned	tuned	ADJ
ejpam-6073	615	10	nonlinear	nonlinear	ADJ
ejpam-6073	615	11	saturation	saturation	NOUN
ejpam-6073	615	12	oscillator	oscillator	NOUN
ejpam-6073	615	13	.	.	PUNCT
ejpam-6073	616	1	ieee	ieee	NOUN
ejpam-6073	616	2	access	access	NOUN
ejpam-6073	616	3	,	,	PUNCT
ejpam-6073	616	4	9:133694–133709	9:133694–133709	PROPN
ejpam-6073	616	5	,	,	PUNCT
ejpam-6073	616	6	2021	2021	NUM
ejpam-6073	616	7	.	.	PUNCT
ejpam-6073	617	1	[	[	X
ejpam-6073	617	2	22	22	NUM
ejpam-6073	617	3	]	]	PUNCT
ejpam-6073	617	4	a.	a.	PROPN
ejpam-6073	617	5	al	al	PROPN
ejpam-6073	617	6	-	-	PUNCT
ejpam-6073	617	7	mahdi	mahdi	PROPN
ejpam-6073	617	8	,	,	PUNCT
ejpam-6073	617	9	m.	m.	NOUN
ejpam-6073	617	10	al	al	PROPN
ejpam-6073	617	11	-	-	PUNCT
ejpam-6073	617	12	gharabli	gharabli	PROPN
ejpam-6073	617	13	,	,	PUNCT
ejpam-6073	617	14	i.	i.	PROPN
ejpam-6073	617	15	kissami	kissami	PROPN
ejpam-6073	617	16	,	,	PUNCT
ejpam-6073	617	17	a.	a.	NOUN
ejpam-6073	617	18	soufyane	soufyane	NOUN
ejpam-6073	617	19	,	,	PUNCT
ejpam-6073	617	20	and	and	CCONJ
ejpam-6073	617	21	m.	m.	PROPN
ejpam-6073	617	22	zahri	zahri	PROPN
ejpam-6073	617	23	.	.	PUNCT
ejpam-6073	618	1	exponential	exponential	ADJ
ejpam-6073	618	2	and	and	CCONJ
ejpam-6073	618	3	polynomial	polynomial	ADJ
ejpam-6073	618	4	decay	decay	NOUN
ejpam-6073	618	5	results	result	NOUN
ejpam-6073	618	6	for	for	ADP
ejpam-6073	618	7	a	a	DET
ejpam-6073	618	8	swelling	swell	VERB
ejpam-6073	618	9	porous	porous	ADJ
ejpam-6073	618	10	elastic	elastic	ADJ
ejpam-6073	618	11	system	system	NOUN
ejpam-6073	618	12	with	with	ADP
ejpam-6073	618	13	a	a	DET
ejpam-6073	618	14	single	single	ADJ
ejpam-6073	618	15	nonlinear	nonlinear	ADJ
ejpam-6073	618	16	variable	variable	ADJ
ejpam-6073	618	17	exponent	exponent	NOUN
ejpam-6073	618	18	damping	damping	NOUN
ejpam-6073	618	19	:	:	PUNCT
ejpam-6073	618	20	theory	theory	NOUN
ejpam-6073	618	21	and	and	CCONJ
ejpam-6073	618	22	numerics	numeric	NOUN
ejpam-6073	618	23	.	.	PUNCT
ejpam-6073	619	1	zeitschrift	zeitschrift	PROPN
ejpam-6073	619	2	für	für	PROPN
ejpam-6073	619	3	angewandte	angewandte	PROPN
ejpam-6073	619	4	mathematik	mathematik	PROPN
ejpam-6073	619	5	und	und	PROPN
ejpam-6073	619	6	physik	physik	PROPN
ejpam-6073	619	7	,	,	PUNCT
ejpam-6073	619	8	74(2):72	74(2):72	PROPN
ejpam-6073	619	9	,	,	PUNCT
ejpam-6073	619	10	2023	2023	NUM
ejpam-6073	619	11	.	.	PUNCT
ejpam-6073	620	1	[	[	X
ejpam-6073	620	2	23	23	NUM
ejpam-6073	620	3	]	]	X
ejpam-6073	620	4	howard	howard	PROPN
ejpam-6073	620	5	a.	a.	PROPN
ejpam-6073	620	6	levine	levine	PROPN
ejpam-6073	620	7	.	.	PUNCT
ejpam-6073	621	1	instability	instability	NOUN
ejpam-6073	621	2	and	and	CCONJ
ejpam-6073	621	3	nonexistence	nonexistence	NOUN
ejpam-6073	621	4	of	of	ADP
ejpam-6073	621	5	global	global	ADJ
ejpam-6073	621	6	solutions	solution	NOUN
ejpam-6073	621	7	to	to	ADP
ejpam-6073	621	8	nonlinear	nonlinear	ADJ
ejpam-6073	621	9	wave	wave	NOUN
ejpam-6073	621	10	equations	equation	NOUN
ejpam-6073	621	11	of	of	ADP
ejpam-6073	621	12	the	the	DET
ejpam-6073	621	13	form	form	NOUN
ejpam-6073	621	14	putt	putt	NOUN
ejpam-6073	621	15	=	=	SYM
ejpam-6073	621	16	−au+f(u	−au+f(u	NOUN
ejpam-6073	621	17	)	)	PUNCT
ejpam-6073	621	18	.	.	PUNCT
ejpam-6073	622	1	transactions	transaction	NOUN
ejpam-6073	622	2	of	of	ADP
ejpam-6073	622	3	the	the	DET
ejpam-6073	622	4	american	american	PROPN
ejpam-6073	622	5	mathematical	mathematical	PROPN
ejpam-6073	622	6	society	society	NOUN
ejpam-6073	622	7	,	,	PUNCT
ejpam-6073	622	8	192:1–21	192:1–21	NUM
ejpam-6073	622	9	,	,	PUNCT
ejpam-6073	622	10	1974	1974	NUM
ejpam-6073	622	11	.	.	PUNCT
ejpam-6073	623	1	[	[	X
ejpam-6073	623	2	24	24	NUM
ejpam-6073	623	3	]	]	X
ejpam-6073	623	4	howard	howard	PROPN
ejpam-6073	623	5	a.	a.	PROPN
ejpam-6073	623	6	levine	levine	PROPN
ejpam-6073	623	7	.	.	PUNCT
ejpam-6073	624	1	some	some	DET
ejpam-6073	624	2	additional	additional	ADJ
ejpam-6073	624	3	remarks	remark	NOUN
ejpam-6073	624	4	on	on	ADP
ejpam-6073	624	5	the	the	DET
ejpam-6073	624	6	nonexistence	nonexistence	NOUN
ejpam-6073	624	7	of	of	ADP
ejpam-6073	624	8	global	global	ADJ
ejpam-6073	624	9	solutions	solution	NOUN
ejpam-6073	624	10	to	to	ADP
ejpam-6073	624	11	nonlinear	nonlinear	ADJ
ejpam-6073	624	12	wave	wave	NOUN
ejpam-6073	624	13	equations	equation	NOUN
ejpam-6073	624	14	.	.	PUNCT
ejpam-6073	625	1	siam	siam	PROPN
ejpam-6073	625	2	journal	journal	PROPN
ejpam-6073	625	3	on	on	ADP
ejpam-6073	625	4	mathematical	mathematical	ADJ
ejpam-6073	625	5	analysis	analysis	NOUN
ejpam-6073	625	6	,	,	PUNCT
ejpam-6073	625	7	5(1):138–146	5(1):138–146	NOUN
ejpam-6073	625	8	,	,	PUNCT
ejpam-6073	625	9	1974	1974	NUM
ejpam-6073	625	10	.	.	PUNCT
ejpam-6073	626	1	[	[	X
ejpam-6073	626	2	25	25	NUM
ejpam-6073	626	3	]	]	X
ejpam-6073	626	4	vladimir	vladimir	PROPN
ejpam-6073	626	5	georgiev	georgiev	PROPN
ejpam-6073	626	6	and	and	CCONJ
ejpam-6073	626	7	grozdena	grozdena	VERB
ejpam-6073	626	8	todorova	todorova	PROPN
ejpam-6073	626	9	.	.	PUNCT
ejpam-6073	627	1	existence	existence	NOUN
ejpam-6073	627	2	of	of	ADP
ejpam-6073	627	3	a	a	DET
ejpam-6073	627	4	solution	solution	NOUN
ejpam-6073	627	5	of	of	ADP
ejpam-6073	627	6	the	the	DET
ejpam-6073	627	7	wave	wave	NOUN
ejpam-6073	627	8	equation	equation	NOUN
ejpam-6073	627	9	with	with	ADP
ejpam-6073	627	10	nonlinear	nonlinear	ADJ
ejpam-6073	627	11	damping	damp	VERB
ejpam-6073	627	12	and	and	CCONJ
ejpam-6073	627	13	source	source	NOUN
ejpam-6073	627	14	terms	term	NOUN
ejpam-6073	627	15	.	.	PUNCT
ejpam-6073	628	1	journal	journal	PROPN
ejpam-6073	628	2	of	of	ADP
ejpam-6073	628	3	differential	differential	ADJ
ejpam-6073	628	4	equations	equation	NOUN
ejpam-6073	628	5	,	,	PUNCT
ejpam-6073	628	6	109(2):295–308	109(2):295–308	NUM
ejpam-6073	628	7	,	,	PUNCT
ejpam-6073	628	8	1994	1994	NUM
ejpam-6073	628	9	.	.	PUNCT
ejpam-6073	629	1	[	[	X
ejpam-6073	629	2	26	26	NUM
ejpam-6073	629	3	]	]	PUNCT
ejpam-6073	629	4	salim	salim	PROPN
ejpam-6073	629	5	a.	a.	PROPN
ejpam-6073	629	6	messaoudi	messaoudi	PROPN
ejpam-6073	629	7	.	.	PUNCT
ejpam-6073	630	1	blow	blow	VERB
ejpam-6073	630	2	up	up	ADP
ejpam-6073	630	3	in	in	ADP
ejpam-6073	630	4	the	the	DET
ejpam-6073	630	5	cauchy	cauchy	ADJ
ejpam-6073	630	6	problem	problem	NOUN
ejpam-6073	630	7	for	for	ADP
ejpam-6073	630	8	a	a	DET
ejpam-6073	630	9	nonlinearly	nonlinearly	ADV
ejpam-6073	630	10	damped	damp	VERB
ejpam-6073	630	11	wave	wave	NOUN
ejpam-6073	630	12	equation	equation	NOUN
ejpam-6073	630	13	.	.	PUNCT
ejpam-6073	631	1	communications	communication	NOUN
ejpam-6073	631	2	in	in	ADP
ejpam-6073	631	3	applied	apply	VERB
ejpam-6073	631	4	analysis	analysis	NOUN
ejpam-6073	631	5	,	,	PUNCT
ejpam-6073	631	6	7(2	7(2	X
ejpam-6073	631	7	-	-	PUNCT
ejpam-6073	631	8	3):379–386	3):379–386	NUM
ejpam-6073	631	9	,	,	PUNCT
ejpam-6073	631	10	2003	2003	NUM
ejpam-6073	631	11	.	.	PUNCT
ejpam-6073	632	1	[	[	X
ejpam-6073	632	2	27	27	NUM
ejpam-6073	632	3	]	]	PUNCT
ejpam-6073	632	4	salim	salim	PROPN
ejpam-6073	632	5	a.	a.	PROPN
ejpam-6073	632	6	messaoudi	messaoudi	PROPN
ejpam-6073	632	7	.	.	PUNCT
ejpam-6073	633	1	blow	blow	VERB
ejpam-6073	633	2	up	up	ADP
ejpam-6073	633	3	and	and	CCONJ
ejpam-6073	633	4	global	global	ADJ
ejpam-6073	633	5	existence	existence	NOUN
ejpam-6073	633	6	in	in	ADP
ejpam-6073	633	7	a	a	DET
ejpam-6073	633	8	nonlinear	nonlinear	ADJ
ejpam-6073	633	9	viscoelastic	viscoelastic	ADJ
ejpam-6073	633	10	wave	wave	NOUN
ejpam-6073	633	11	equation	equation	NOUN
ejpam-6073	633	12	.	.	PUNCT
ejpam-6073	634	1	mathematische	mathematische	PROPN
ejpam-6073	634	2	nachrichten	nachrichten	PROPN
ejpam-6073	634	3	,	,	PUNCT
ejpam-6073	634	4	260(1):58–66	260(1):58–66	NOUN
ejpam-6073	634	5	,	,	PUNCT
ejpam-6073	634	6	2003	2003	NUM
ejpam-6073	634	7	.	.	PUNCT
ejpam-6073	635	1	[	[	X
ejpam-6073	635	2	28	28	NUM
ejpam-6073	635	3	]	]	X
ejpam-6073	635	4	salim	salim	PROPN
ejpam-6073	635	5	a.	a.	PROPN
ejpam-6073	635	6	messaoudi	messaoudi	PROPN
ejpam-6073	635	7	and	and	CCONJ
ejpam-6073	635	8	ala	ala	PROPN
ejpam-6073	635	9	a.	a.	NOUN
ejpam-6073	635	10	talahmeh	talahmeh	NOUN
ejpam-6073	635	11	.	.	PUNCT
ejpam-6073	636	1	blow	blow	VERB
ejpam-6073	636	2	up	up	ADP
ejpam-6073	636	3	of	of	ADP
ejpam-6073	636	4	negative	negative	ADJ
ejpam-6073	636	5	initial	initial	ADJ
ejpam-6073	636	6	-	-	PUNCT
ejpam-6073	636	7	energy	energy	NOUN
ejpam-6073	636	8	solutions	solution	NOUN
ejpam-6073	636	9	of	of	ADP
ejpam-6073	636	10	a	a	DET
ejpam-6073	636	11	system	system	NOUN
ejpam-6073	636	12	of	of	ADP
ejpam-6073	636	13	nonlinear	nonlinear	ADJ
ejpam-6073	636	14	wave	wave	NOUN
ejpam-6073	636	15	equations	equation	NOUN
ejpam-6073	636	16	with	with	ADP
ejpam-6073	636	17	variable	variable	ADJ
ejpam-6073	636	18	-	-	PUNCT
ejpam-6073	636	19	exponent	exponent	NOUN
ejpam-6073	636	20	nonlinearities	nonlinearitie	NOUN
ejpam-6073	636	21	.	.	PUNCT
ejpam-6073	637	1	discrete	discrete	ADJ
ejpam-6073	637	2	and	and	CCONJ
ejpam-6073	637	3	continuous	continuous	ADJ
ejpam-6073	637	4	dynamical	dynamical	ADJ
ejpam-6073	637	5	systems	system	NOUN
ejpam-6073	637	6	-	-	PUNCT
ejpam-6073	637	7	s	s	NOUN
ejpam-6073	637	8	,	,	PUNCT
ejpam-6073	637	9	15(5):1233	15(5):1233	NUM
ejpam-6073	637	10	,	,	PUNCT
ejpam-6073	637	11	2022	2022	NUM
ejpam-6073	637	12	.	.	PUNCT
ejpam-6073	638	1	[	[	X
ejpam-6073	638	2	29	29	NUM
ejpam-6073	638	3	]	]	X
ejpam-6073	638	4	mohammad	mohammad	PROPN
ejpam-6073	638	5	kafini	kafini	PROPN
ejpam-6073	638	6	.	.	PUNCT
ejpam-6073	639	1	on	on	ADP
ejpam-6073	639	2	the	the	DET
ejpam-6073	639	3	blow	blow	NOUN
ejpam-6073	639	4	-	-	PUNCT
ejpam-6073	639	5	up	up	NOUN
ejpam-6073	639	6	of	of	ADP
ejpam-6073	639	7	the	the	DET
ejpam-6073	639	8	cauchy	cauchy	ADJ
ejpam-6073	639	9	problem	problem	NOUN
ejpam-6073	639	10	of	of	ADP
ejpam-6073	639	11	higher	high	ADJ
ejpam-6073	639	12	-	-	PUNCT
ejpam-6073	639	13	order	order	NOUN
ejpam-6073	639	14	nonlinear	nonlinear	ADJ
ejpam-6073	639	15	viscoelastic	viscoelastic	ADJ
ejpam-6073	639	16	wave	wave	NOUN
ejpam-6073	639	17	equation	equation	NOUN
ejpam-6073	639	18	.	.	PUNCT
ejpam-6073	640	1	discrete	discrete	ADJ
ejpam-6073	640	2	and	and	CCONJ
ejpam-6073	640	3	continuous	continuous	ADJ
ejpam-6073	640	4	dynamical	dynamical	ADJ
ejpam-6073	640	5	systems	system	NOUN
ejpam-6073	640	6	-	-	PUNCT
ejpam-6073	640	7	s	s	NOUN
ejpam-6073	640	8	,	,	PUNCT
ejpam-6073	640	9	15(5):1221	15(5):1221	NUM
ejpam-6073	640	10	,	,	PUNCT
ejpam-6073	640	11	2022	2022	NUM
ejpam-6073	640	12	.	.	PUNCT
ejpam-6073	641	1	[	[	X
ejpam-6073	641	2	30	30	NUM
ejpam-6073	641	3	]	]	X
ejpam-6073	641	4	y.	y.	PROPN
ejpam-6073	641	5	nguyen	nguyen	PROPN
ejpam-6073	641	6	van	van	PROPN
ejpam-6073	641	7	,	,	PUNCT
ejpam-6073	641	8	le	le	PROPN
ejpam-6073	641	9	xuan	xuan	PROPN
ejpam-6073	641	10	truong	truong	PROPN
ejpam-6073	641	11	,	,	PUNCT
ejpam-6073	641	12	et	et	PROPN
ejpam-6073	641	13	al	al	PROPN
ejpam-6073	641	14	.	.	PROPN
ejpam-6073	642	1	on	on	ADP
ejpam-6073	642	2	a	a	DET
ejpam-6073	642	3	thermo	thermo	NOUN
ejpam-6073	642	4	-	-	PUNCT
ejpam-6073	642	5	viscoelastic	viscoelastic	ADJ
ejpam-6073	642	6	system	system	NOUN
ejpam-6073	642	7	with	with	ADP
ejpam-6073	642	8	variable	variable	ADJ
ejpam-6073	642	9	exponent	exponent	NOUN
ejpam-6073	642	10	sources	source	NOUN
ejpam-6073	642	11	.	.	PUNCT
ejpam-6073	643	1	nonlinear	nonlinear	ADJ
ejpam-6073	643	2	analysis	analysis	NOUN
ejpam-6073	643	3	:	:	PUNCT
ejpam-6073	643	4	real	real	ADJ
ejpam-6073	643	5	world	world	NOUN
ejpam-6073	643	6	applications	application	NOUN
ejpam-6073	643	7	,	,	PUNCT
ejpam-6073	643	8	71:103807	71:103807	NUM
ejpam-6073	643	9	,	,	PUNCT
ejpam-6073	643	10	2023	2023	NUM
ejpam-6073	643	11	.	.	PUNCT
ejpam-6073	644	1	[	[	X
ejpam-6073	644	2	31	31	NUM
ejpam-6073	644	3	]	]	X
ejpam-6073	644	4	sen	sen	PROPN
ejpam-6073	644	5	ming	ming	PROPN
ejpam-6073	644	6	,	,	PUNCT
ejpam-6073	644	7	xiongmei	xiongmei	PROPN
ejpam-6073	644	8	fan	fan	PROPN
ejpam-6073	644	9	,	,	PUNCT
ejpam-6073	644	10	cui	cui	PROPN
ejpam-6073	644	11	ren	ren	PROPN
ejpam-6073	644	12	,	,	PUNCT
ejpam-6073	644	13	and	and	CCONJ
ejpam-6073	644	14	yeqin	yeqin	PROPN
ejpam-6073	644	15	su	su	PROPN
ejpam-6073	644	16	.	.	PUNCT
ejpam-6073	645	1	blow	blow	PROPN
ejpam-6073	645	2	-	-	PUNCT
ejpam-6073	645	3	up	up	ADP
ejpam-6073	645	4	dynamic	dynamic	NOUN
ejpam-6073	645	5	of	of	ADP
ejpam-6073	645	6	solution	solution	NOUN
ejpam-6073	645	7	to	to	ADP
ejpam-6073	645	8	the	the	DET
ejpam-6073	645	9	semilinear	semilinear	PROPN
ejpam-6073	645	10	moore	moore	PROPN
ejpam-6073	645	11	-	-	PUNCT
ejpam-6073	645	12	gibson	gibson	PROPN
ejpam-6073	645	13	-	-	PUNCT
ejpam-6073	645	14	thompson	thompson	NOUN
ejpam-6073	645	15	equation	equation	NOUN
ejpam-6073	645	16	with	with	ADP
ejpam-6073	645	17	memory	memory	NOUN
ejpam-6073	645	18	terms	term	NOUN
ejpam-6073	645	19	.	.	PUNCT
ejpam-6073	646	1	aims	aim	VERB
ejpam-6073	646	2	mathematics	mathematic	NOUN
ejpam-6073	646	3	,	,	PUNCT
ejpam-6073	646	4	8(2):4630–4644	8(2):4630–4644	NUM
ejpam-6073	646	5	,	,	PUNCT
ejpam-6073	646	6	2023	2023	NUM
ejpam-6073	646	7	.	.	PUNCT
ejpam-6073	647	1	[	[	X
ejpam-6073	647	2	32	32	NUM
ejpam-6073	647	3	]	]	X
ejpam-6073	647	4	soh	soh	PROPN
ejpam-6073	647	5	edwin	edwin	PROPN
ejpam-6073	647	6	mukiawa	mukiawa	PROPN
ejpam-6073	647	7	and	and	CCONJ
ejpam-6073	647	8	salim	salim	PROPN
ejpam-6073	647	9	a.	a.	PROPN
ejpam-6073	647	10	messaoudi	messaoudi	PROPN
ejpam-6073	647	11	.	.	PUNCT
ejpam-6073	648	1	blow	blow	VERB
ejpam-6073	648	2	up	up	ADP
ejpam-6073	648	3	result	result	NOUN
ejpam-6073	648	4	for	for	ADP
ejpam-6073	648	5	a	a	DET
ejpam-6073	648	6	viscoelastic	viscoelastic	ADJ
ejpam-6073	648	7	plate	plate	NOUN
ejpam-6073	648	8	equation	equation	NOUN
ejpam-6073	648	9	with	with	ADP
ejpam-6073	648	10	nonlinear	nonlinear	ADJ
ejpam-6073	648	11	source	source	NOUN
ejpam-6073	648	12	.	.	PUNCT
ejpam-6073	649	1	boletim	boletim	PROPN
ejpam-6073	649	2	da	da	PROPN
ejpam-6073	649	3	sociedade	sociedade	PROPN
ejpam-6073	649	4	paranaense	paranaense	PROPN
ejpam-6073	649	5	de	de	PROPN
ejpam-6073	649	6	matemática	matemática	PROPN
ejpam-6073	649	7	,	,	PUNCT
ejpam-6073	649	8	41:1–11	41:1–11	PROPN
ejpam-6073	649	9	,	,	PUNCT
ejpam-6073	649	10	2023	2023	NUM
ejpam-6073	649	11	.	.	PUNCT
ejpam-6073	650	1	[	[	X
ejpam-6073	650	2	33	33	NUM
ejpam-6073	650	3	]	]	PUNCT
ejpam-6073	650	4	salim	salim	PROPN
ejpam-6073	650	5	a.	a.	PROPN
ejpam-6073	650	6	messaoudi	messaoudi	PROPN
ejpam-6073	650	7	,	,	PUNCT
ejpam-6073	650	8	ala	ala	PROPN
ejpam-6073	650	9	a.	a.	NOUN
ejpam-6073	650	10	talahmeh	talahmeh	NOUN
ejpam-6073	650	11	,	,	PUNCT
ejpam-6073	650	12	and	and	CCONJ
ejpam-6073	650	13	jamal	jamal	PROPN
ejpam-6073	650	14	h.	h.	PROPN
ejpam-6073	650	15	al	al	PROPN
ejpam-6073	650	16	-	-	PUNCT
ejpam-6073	650	17	smail	smail	NOUN
ejpam-6073	650	18	.	.	PUNCT
ejpam-6073	651	1	nonlinear	nonlinear	ADJ
ejpam-6073	651	2	damped	damp	VERB
ejpam-6073	651	3	wave	wave	NOUN
ejpam-6073	651	4	equation	equation	NOUN
ejpam-6073	651	5	:	:	PUNCT
ejpam-6073	651	6	existence	existence	NOUN
ejpam-6073	651	7	and	and	CCONJ
ejpam-6073	651	8	blow	blow	NOUN
ejpam-6073	651	9	-	-	PUNCT
ejpam-6073	651	10	up	up	NOUN
ejpam-6073	651	11	.	.	PUNCT
ejpam-6073	652	1	computers	computer	NOUN
ejpam-6073	652	2	&	&	CCONJ
ejpam-6073	652	3	mathematics	mathematics	PROPN
ejpam-6073	652	4	with	with	ADP
ejpam-6073	652	5	applications	application	NOUN
ejpam-6073	652	6	,	,	PUNCT
ejpam-6073	652	7	74(12):3024–3041	74(12):3024–3041	PROPN
ejpam-6073	652	8	,	,	PUNCT
ejpam-6073	652	9	2017	2017	NUM
ejpam-6073	652	10	.	.	PUNCT
ejpam-6073	653	1	[	[	X
ejpam-6073	653	2	34	34	NUM
ejpam-6073	653	3	]	]	X
ejpam-6073	653	4	salim	salim	PROPN
ejpam-6073	653	5	messaoudi	messaoudi	PROPN
ejpam-6073	653	6	,	,	PUNCT
ejpam-6073	653	7	mohammad	mohammad	PROPN
ejpam-6073	653	8	al	al	PROPN
ejpam-6073	653	9	-	-	PUNCT
ejpam-6073	653	10	gharabli	gharabli	PROPN
ejpam-6073	653	11	,	,	PUNCT
ejpam-6073	653	12	and	and	CCONJ
ejpam-6073	653	13	adel	adel	PROPN
ejpam-6073	653	14	al	al	PROPN
ejpam-6073	653	15	-	-	PROPN
ejpam-6073	653	16	mahdi	mahdi	PROPN
ejpam-6073	653	17	.	.	PUNCT
ejpam-6073	654	1	on	on	ADP
ejpam-6073	654	2	the	the	DET
ejpam-6073	654	3	existence	existence	NOUN
ejpam-6073	654	4	and	and	CCONJ
ejpam-6073	654	5	decay	decay	NOUN
ejpam-6073	654	6	of	of	ADP
ejpam-6073	654	7	a	a	DET
ejpam-6073	654	8	viscoelastic	viscoelastic	ADJ
ejpam-6073	654	9	system	system	NOUN
ejpam-6073	654	10	with	with	ADP
ejpam-6073	654	11	variable	variable	ADJ
ejpam-6073	654	12	-	-	PUNCT
ejpam-6073	654	13	exponent	exponent	NOUN
ejpam-6073	654	14	nonlinearity	nonlinearity	NOUN
ejpam-6073	654	15	.	.	PUNCT
ejpam-6073	655	1	discrete	discrete	ADJ
ejpam-6073	655	2	and	and	CCONJ
ejpam-6073	655	3	continuous	continuous	ADJ
ejpam-6073	655	4	dynamical	dynamical	ADJ
ejpam-6073	655	5	systems	system	NOUN
ejpam-6073	655	6	-	-	PUNCT
ejpam-6073	655	7	s	s	NOUN
ejpam-6073	655	8	,	,	PUNCT
ejpam-6073	655	9	pages	page	NOUN
ejpam-6073	655	10	0–0	0–0	NUM
ejpam-6073	655	11	,	,	PUNCT
ejpam-6073	655	12	2022	2022	NUM
ejpam-6073	655	13	.	.	PUNCT
ejpam-6073	656	1	a.	a.	PROPN
ejpam-6073	656	2	m.	m.	PROPN
ejpam-6073	656	3	al	al	PROPN
ejpam-6073	656	4	-	-	PROPN
ejpam-6073	656	5	mahdi	mahdi	PROPN
ejpam-6073	656	6	et	et	PROPN
ejpam-6073	656	7	al	al	PROPN
ejpam-6073	656	8	.	.	PUNCT
ejpam-6073	656	9	/	/	SYM
ejpam-6073	656	10	eur	eur	PROPN
ejpam-6073	656	11	.	.	PUNCT
ejpam-6073	657	1	j.	j.	PROPN
ejpam-6073	657	2	pure	pure	PROPN
ejpam-6073	657	3	appl	appl	PROPN
ejpam-6073	657	4	.	.	PROPN
ejpam-6073	657	5	math	math	PROPN
ejpam-6073	657	6	,	,	PUNCT
ejpam-6073	657	7	18	18	NUM
ejpam-6073	657	8	(	(	PUNCT
ejpam-6073	657	9	3	3	NUM
ejpam-6073	657	10	)	)	PUNCT
ejpam-6073	657	11	(	(	PUNCT
ejpam-6073	657	12	2025	2025	NUM
ejpam-6073	657	13	)	)	PUNCT
ejpam-6073	657	14	,	,	PUNCT
ejpam-6073	657	15	6073	6073	NUM
ejpam-6073	657	16	29	29	NUM
ejpam-6073	657	17	of	of	ADP
ejpam-6073	657	18	29	29	NUM
ejpam-6073	657	19	[	[	SYM
ejpam-6073	657	20	35	35	NUM
ejpam-6073	657	21	]	]	X
ejpam-6073	657	22	abdelaziz	abdelaziz	PROPN
ejpam-6073	657	23	soufyane	soufyane	NOUN
ejpam-6073	657	24	,	,	PUNCT
ejpam-6073	657	25	adel	adel	PROPN
ejpam-6073	657	26	m.	m.	PROPN
ejpam-6073	657	27	al	al	PROPN
ejpam-6073	657	28	-	-	PUNCT
ejpam-6073	657	29	mahdi	mahdi	PROPN
ejpam-6073	657	30	,	,	PUNCT
ejpam-6073	657	31	mohammed	mohammed	PROPN
ejpam-6073	657	32	m.	m.	PROPN
ejpam-6073	657	33	al	al	PROPN
ejpam-6073	657	34	-	-	PUNCT
ejpam-6073	657	35	gharabli	gharabli	PROPN
ejpam-6073	657	36	,	,	PUNCT
ejpam-6073	657	37	imad	imad	PROPN
ejpam-6073	657	38	kissami	kissami	PROPN
ejpam-6073	657	39	,	,	PUNCT
ejpam-6073	657	40	and	and	CCONJ
ejpam-6073	657	41	mostafa	mostafa	PROPN
ejpam-6073	657	42	zahri	zahri	PROPN
ejpam-6073	657	43	.	.	PUNCT
ejpam-6073	658	1	exponential	exponential	ADJ
ejpam-6073	658	2	and	and	CCONJ
ejpam-6073	658	3	polynomial	polynomial	ADJ
ejpam-6073	658	4	decay	decay	NOUN
ejpam-6073	658	5	results	result	NOUN
ejpam-6073	658	6	for	for	ADP
ejpam-6073	658	7	a	a	DET
ejpam-6073	658	8	swelling	swell	VERB
ejpam-6073	658	9	porous	porous	ADJ
ejpam-6073	658	10	elastic	elastic	ADJ
ejpam-6073	658	11	system	system	NOUN
ejpam-6073	658	12	with	with	ADP
ejpam-6073	658	13	a	a	DET
ejpam-6073	658	14	single	single	ADJ
ejpam-6073	658	15	nonlinear	nonlinear	ADJ
ejpam-6073	658	16	variable	variable	ADJ
ejpam-6073	658	17	exponent	exponent	NOUN
ejpam-6073	658	18	damping	damping	NOUN
ejpam-6073	658	19	:	:	PUNCT
ejpam-6073	658	20	theory	theory	NOUN
ejpam-6073	658	21	and	and	CCONJ
ejpam-6073	658	22	numerics	numeric	NOUN
ejpam-6073	658	23	.	.	PUNCT
ejpam-6073	659	1	zeitschrift	zeitschrift	PROPN
ejpam-6073	659	2	für	für	PROPN
ejpam-6073	659	3	angewandte	angewandte	PROPN
ejpam-6073	659	4	mathematik	mathematik	PROPN
ejpam-6073	659	5	und	und	PROPN
ejpam-6073	659	6	physik	physik	PROPN
ejpam-6073	659	7	,	,	PUNCT
ejpam-6073	659	8	74(2):72	74(2):72	PROPN
ejpam-6073	659	9	,	,	PUNCT
ejpam-6073	659	10	2022	2022	NUM
ejpam-6073	659	11	.	.	PUNCT